text:
Research Article | Open | Published: 03 August 2009
Secured Communication over Frequency-Selective Fading Channels: A Practical Vandermonde Precoding
Mari Kobayashi1,
Mérouane Debbah2 &
Shlomo Shamai (Shitz)3
EURASIP Journal on Wireless Communications and Networkingvolume 2009, Article number: 386547 (2009) | Download Citation
We study the frequency-selective broadcast channel with confidential messages (BCC) where the transmitter sends a confidential message to receiver 1 and a common message to receivers 1 and 2. In the case of a block transmission of symbols followed by a guard interval of symbols, the frequency-selective channel can be modeled as a Toeplitz matrix. For this special type of multiple-input multiple-output channels, we propose a practical Vandermonde precoding that projects the confidential messages in the null space of the channel seen by receiver 2 while superposing the common message. For this scheme, we provide the achievable rate region and characterize the optimal covariance for some special cases of interest. Interestingly, the proposed scheme can be applied to other multiuser scenarios such as the -user frequency-selective BCC with confidential messages and the two-user frequency-selective BCC with two confidential messages. For each scenario, we provide the secrecy degree of freedom (s.d.o.f.) region of the corresponding channel and prove the optimality of the Vandermonde precoding. One of the appealing features of the proposed scheme is that it does not require any specific secrecy encoding technique but can be applied on top of any existing powerful encoding schemes.
We consider a secured medium such that the transmitter wishes to send a confidential message to its receiver while keeping the eavesdropper, tapping the channel, ignorant of the message. Wyner [1] introduced this model named the wiretap channel to model the degraded broadcast channel where the eavesdropper observes a degraded version of the receiver's signal. In this model, the confidentiality is measured by the equivocation rate, that is, the mutual information between the confidential message and the eavesdropper's observation. For the discrete memoryless degraded wiretap channel, Wyner characterized the capacity-equivocation region and showed that a nonzero secrecy rate can be achieved [1]. The most important operating point on the capacity-equivocation region is the secrecy capacity, that is, the largest reliable communication rate such that the eavesdropper obtains no information about the confidential message (the equivocation rate is as large as the message rate). The secrecy capacity of the Gaussian wiretap channel was given in [2]. Csiszár and Körner considered a more general wiretap channel in which a common message for both receivers is sent in addition to the confidential message [3]. For this model known as the broadcast channel with confidential (BCC) messages, the rate-tuple of the common and confidential messages was characterized.
Recently, a significant effort has been made to opportunistically exploit the space/time/user dimensions for secrecy communications (see, e.g., [4–14] and references therein). In [4], the secrecy capacity of the ergodic slow fading channels was characterized and the optimal power/rate allocation was derived. The secrecy capacity of the parallel fading channels was given [6, 7] where [7] considered the BCC with a common message. Moreover, the secrecy capacity of the wiretap channel with multiple antennas has been studied in [8–13, 15] and references therein. In particular, the secrecy capacity of the multiple-input multiple-output (MIMO) wiretap channel has been fully characterized in [5, 11, 12, 14] and more recently its closed-form expressions under a matrix covariance constraint have been derived in [15]. Furthermore, a large number of recent works have considered the secrecy capacity region for more general broadcast channels. In [16], the authors studied the two-user MIMO Gaussian BCC where the capacity region for the case of one common and one confidential message was characterized. The two-user BCC with two confidential messages, each of which must be kept secret to the unintended receiver, has been studied in [17–20]. In [18], Liu and Poor characterized the secrecy capacity region for the multiple-input single-output (MISO) Gaussian BCC where the optimality of the secret dirty paper coding (S-DPC) scheme was proved. A recent contribution [19] extended the result to the MIMO Gaussian BCC. The multireceiver wiretap channels have been also studied in [21–26] (and reference therein) where the confidential messages to each receiver must be kept secret to an external eavesdropper. It has been proved that the secrecy capacity region of the MIMO Gaussian multireceiver wiretap channels is achieved by S-DPC [24, 26].
However, very few work have exploited the frequency selectivity nature of the channel for secrecy purposes [27] where the zeros of the channel provide an opportunity to "hide" information. This paper shows the opportunities provided by the broad-band channel and studies the frequency-selective BCC where the transmitter sends one confidential message to receiver 1 and one common message to both receivers 1 and 2. The channel state information (CSI) is assumed to be known to both the transmitter and the receivers. We consider the quasistatic frequency-selective fading channel with paths such that the channel remains fixed during an entire transmission of blocks for an arbitrary large . It should be remarked that in general the secrecy rate cannot scale with signal-to-noise ratio (SNR) over the channel at hand, unless the channel of receiver 2 has a null frequency band of positive Lebesgue measure (on which the transmitter can "hide'' the confidential message). In this contribution, we focus on the realistic case where receiver 2 has a full frequency band (without null subbands) but operates in a reduced dimension due to practical complexity issues. This is typical of current orthogonal frequency division multiplexing (OFDM) standards (such as IEEE802.11a/WiMax or LTE [28–30]) where a guard interval of symbols is inserted at the beginning of each block to avoid the interblock interference and both receivers discard these symbols. We assume that both users have the same standard receiver, in particular receiver 2 cannot change its hardware structure. Studying secure communications under this assumption is of interest in general and can be justified since receiver 2 is actually a legitimate receiver which can receive a confidential message in other communication periods. Of course, if receiver 2 is able to access the guard interval symbols, it can extract the confidential message and the secrecy rate falls down to zero. Although we restrict ourselves to the reduced dimension constraint in this paper, other constraints on the limited capability at the unintended receiver such as energy consumption or hardware complexity might provide a new paradigm to design physical layer secrecy systems.
In the case of a block transmission of symbols followed by a guard interval of symbols discarded at both receivers, the frequency-selective channel can be modeled as an MIMO Toeplitz matrix. In this contribution, we aim at designing a practical linear precoding scheme that fully exploits the degrees of freedom (d.o.f.) offered by this special type of MIMO channels to transmit both the common message and the confidential message. To this end, let us start with the following remarks. On one hand, the idea of using OFDM modulation to convert the frequency-selective channel represented by the Toeplitz matrix into a set of parallel fading channel turns out to be useless from a secrecy perspective. Indeed, it is known that the secrecy capacity of the parallel wiretap fading channels does not scale with SNR [7]. On the other hand, recent contributions [5, 11, 12, 14, 15] showed that the secrecy capacity of the MIMO wiretap channel grows linearly with SNR, that is, where denotes the secrecy degree of freedom (s.d.o.f.) (to be specified). In the high SNR regime, the secrecy capacity of the MISO/MIMO wiretap channel is achieved by sending the confidential message in the null space of the eavesdropper's channel [10, 11, 14, 15, 18, 19]. Therefore, OFDM modulation is highly suboptimal in terms of the s.d.o.f.
Inspired by these remarks, we propose a linear Vandermonde precoder that projects the confidential message in the null space of the channel seen by receiver 2 while superposing the common message. Thanks to the orthogonality between the precoder of the confidential message and the channel of receiver 2; receiver 2 obtains no information on the confidential message. This precoder is regarded as a single-antenna frequency beamformer that nulls the signal in certain directions seen by receiver 2. The Vandermonde structure comes from the fact that the frequency beamformer is of the type where is one of the roots of the channel seen by receiver 2. Note that Vandermonde matrices [31] have already been considered for cognitive radios [32] and CDMA systems [33] to reduce/null interference but not for secrecy applications. One of the appealing aspects of Vandermonde precoding is that it does not require a specific secrecy encoding technique but can be applied on top of any classical capacity achieving encoding scheme.
For the proposed scheme, we characterize its achievable rate region, the rate-tuple of the common message, the confidential message, respectively. Unfortunately, the optimal input covariances achieving their boundary are generally difficult to compute due to the nonconvexity of the weighted sum rate maximization problem. Nevertheless, we show that there are some special cases of interest such as the secrecy rate and the maximum sum rate point which enable an explicit characterization of the optimal input covariances. In addition, we provide the achievable d.o.f. region of the frequency-selective BCC, reflecting the behavior of the achievable rate region in the high SNR regime, and prove that the Vandermonde precoding achieves this region. More specifically, it enables to simultaneously transmit streams of the confidential message and streams of the common message for simultaneously over a block of dimensions. Interestingly, the proposed Vandermonde precoding can be applied to multiuser secure communication scenarios: (a) a -user frequency-selective BCC with confidential messages and one common message, (b) a two-user frequency-selective BCC with two confidential messages and one common message. For each scenario, we characterize the achievable s.d.o.f. region of the corresponding frequency-selective BCC and show the optimality of the Vandermonde precoding.
The paper is organized as follows. Section 2 presents the frequency-selective fading BCC. Section 3 introduces the Vandermonde precoding and characterizes its achievable rate region as well as the optimal input covariances for some special cases. Section 4 provides the application of the Vandermonde precoding to the multiuser secure communications scenarios. Section 5 shows some numerical examples of the proposed scheme in the various settings, and finally Section 6 concludes the paper.
Notation. In the following, upper (lower boldface) symbols will be used for matrices (column vectors) whereas lower symbols will represent scalar values, will denote transpose operator, conjugation, and hermitian transpose. , represent the identity matrix, zero matrix. denote a determinant, rank, trace of a matrix , respectively. denotes the sequence . , , , , , denote the realization of the random variables , , , , , . Finally, " '' denotes less or equal to in the positive semidefinite ordering between positive semidefinite matrices, that is, we have if is positive semidefinite.
2. System Model
We consider the quasistatic frequency-selective fading BCC illustrated in Figure 1. The received signal of receivers 1, 2 at block is given by
where denote an Toeplitz matrix with the -path channel vector of user 1, of user 2, respectively, denotes the transmit vector, and finally are mutually independent additive white Gaussian noise (AWGN). The input vector is subject to the power constraint given by
where we let . The structure of is given by
Frequency-selective broadcast channels with confidential messages.
We assume that the channel matrices , remain constant for the whole duration of the transmission of blocks and are known to all terminals. At each block , we transmit symbols by appending a guard interval of size larger than the delay spread, which enables to avoid the interference between neighbor blocks.
The transmitter wishes to send a common message to two receivers and a confidential message to receiver 1. A code consists of the following: (1) two message sets and with the messages uniformly distributed over the sets , , respectively; (2) a stochastic encoder that maps each message pair to a codeword ; (3) one decoder at receiver 1 that maps a received sequence to a message pair and another at receiver 2 that maps a received sequence to a message . The average error probability of a code is defined as
where denotes the error probability when the message pair is sent defined by
The secrecy level of the confidential message at receiver 2 is measured by the equivocation rate defined as
which is the normalized entropy of the confidential message conditioned on the received signal at receiver 2 and available CSI.
A rate-equivocation tuple is said to be achievable if for any there exists a sequence of codes such that we have
In this paper, we focus on the perfect secrecy case where receiver 2 obtains no information about the confidential message , which is equivalent to . In this setting, an achievable rate region of the general BCC (expressed in bit per channel use per dimension) is given by [3]
where the union is over all possible distribution , , satisfying [20, Lemma 1]
where might be a deterministic function of . Recently, the secrecy capacity region of the two-user MIMO-BCC (1) was characterized in [16] and is given by all possible rate tuples satisfying
for some with denotes the input covariance satisfying and , denotes the channel matrix of receiver 1, 2, respectively. Obviously, when only the confidential message is transmitted to receiver 1, the frequency-selective BCC (1) reduces to the MIMO flat-fading wiretap channel whose secrecy capacity has been characterized in [10–12, 14, 15]. In particular, Bustin et al. derived its closed-form expression under a power-covariance constraint [15]. Under a total power (trace) constraint, the secrecy capacity of the MIMO Gaussian wiretap channel is expressed as [19, Theorem 3]
where are the generalized eigen-values greater than one of the following pencil:
(In [15, 19] the authors consider the real matrices , . Nevertheless, it is conjectured that for complex matrices the following expression without in the prelog holds.) As explicitly characterized in [15, Theorem 2], the optimal input covariance achieving the above region is chosen such that the confidential message is sent over subchannels where receiver 1 observes stronger signals than receiver 2. Moreover, in the high SNR regime the optimal strategy converges to beamforming into the null subspace of [5, 11, 12, 14] as for the MISO case [14, 18]. In order to characterize the behavior of the secrecy capacity region in the high SNR regime, we define the d.o.f. region as
where denotes s.d.o.f. which corresponds precisely to the number of the generalized eigenvalues greater than one in the high SNR.
3. Vandermonde Precoding
For the frequency-selective BCC specified in Section 2, we wish to design a practical linear precoding scheme which fully exploits the d.o.f. offered by the frequency-selective channel. We remarked previously that for a special case when only the confidential message is sent to receiver 1 (without a common message), the optimal strategy consists of beamforming the confidential signal into the null subspace of receiver 2. By applying this intuitive result to the special Toeplitz MIMO channels , while including a common message, we propose a linear precoding strategy named Vandermonde precoding. Prior to the definition of the Vandermonde precoding, we provide some properties of a Vandermonde matrix [31].
Property 1.
Given a full-rank Toeplitz matrix , there exists a Vandermonde matrix for whose structure is given by
where are the roots of the polynomial with coefficients of the channel . Clearly satisfies the following orthogonal condition:
and if are all different.
It is well known that as the dimension of and increases, the Vandermonde matrix becomes ill-conditioned unless the roots are on the unit circle. In other words, the elements of each column either grow in energy or tend to zero [31]. Hence, instead of the brut Vandermonde matrix (14), we consider a unitary Vandermonde matrix obtained either by applying the Gram-Schmidt orthogonalization or singular value decomposition (SVD) on .
Definition 1.
We let be a unitary Vandermonde matrix obtained by orthogonalizing the columns of . We let be a unitary matrix in the null space of such that . The common message , the confidential message , is sent along , , respectively. We call Vandermonde precoder.
Further, the precoding matrix for the confidential message satisfies the following property.
Lemma 2.
Given two Toeplitz matrices , where , are linearly independent, there exists a unitary Vandermonde matrix for satisfying
Appendix A.
In order to send the confidential message intended to receiver 1 as well as the common message to both receivers over the frequency-selective channel (1), we consider the Gaussian superposition coding based on the Vandermonde precoder of Definition 1. Namely, at block , we form the transmit vector as
where the common message vector and the confidential message vector are mutually independent Gaussian vectors with zero mean and covariance , , respectively. Under this condition, the input covariances subject to
satisfy the power constraint (2). We let denote the feasible set satisfying (18).
The Vandermonde precoding achieves the following secrecy rate region:
where denotes the convex hull and we let , , .
Due to the orthogonal property (16) of the unitary Vandermonde matrix, receiver 2 only observes the common message, which yields the received signals given by
where we drop the block index. We examine the achievable rate region of the Vandermonde precoding. By letting the auxiliary variables and , we have
Plugging these expressions to (8), we obtain (19).
The boundary of the achievable rate region of the Vandermonde precoding can be characterized by solving the weighted sum rate maximization. Any point on the boundary of the convex region is obtained by solving
for nonnegative weights satisfying . When the region , obtained without convex hull, is nonconvex, the set of the optimal covariances achieving the boundary point might not be unique. Figure 2 depicts an example in which the achievable rate region is obtained by the convex hull operation on the region , that is, replacing the non-convex subregion by the line segment , . For the weight ratio corresponding to the slope of the line segment , , there exist two optimal sets of the covariances yielding the points and (which clearly dominate the point ). These points are the solution to the weighted sum rate maximization (22). In summary, an optimal covariance set achieving (22) (might not be unique) is the solution of
where we let
Following [34, Section II-C] (and also [7, Lemma 2]), we remark that the solution to the max-min problem (23) can be found by hypothesis testing of three cases, , , and . Formally, we have the following lemma.
Achievable rate region obtained by the convex hull on .
The optimal , solution of (23), is given by one of the three solutions.
Case 1.
maximizes
and satisfies .
and satisfies for some .
Before considering the weighted sum rate maximization (23), one applies SVD to ,
where , , and are unitary, contain positive singular values , , respectively. Following [7, Theorem 3], one applies Lemma 4 to solve the weighted sum rate maximization.
The set of the optimal covariances , achieving the boundary of the achievable rate region of the Vandermonde precoding, corresponds to one of the following three solutions.
, if , solution of the following KKT conditions, satisfies
where with a positive semidefinite for , is determined such that , and we let .
if the following fulfills .
We let and where , are diagonal with the th element given by
where is determined such that .
, if , solution of the following KKT conditions, satisfies for some
where with a positive semidefinite for ,  is determined such that .
Appendix B.
Remark 6.
Due to the non-concavity of the underlying weighted sum rate functions, it is generally difficult to characterize the boundary of the achievable rate region except for some special cases. The special cases include the corner points, in particular, the secrecy rate for the case of sending only the confidential message ( ), as well as the maximum sum rate point for the equal weight case ( ). It is worth noticing that under equal weight the objective functions in three cases are all concave in , since is concave if and is concave if and .
The maximum sum rate point can be found by applying the following greedy search [7].
Greedy Search to Find the Maximum Sum Rate Point
( ) Find , maximizing and check . If yes stop. Otherwise go to (2).
( ) Find , maximizing and check for some .
For the special case of , Theorem 5 yields the achievable secrecy rate with the Vandermonde precoding.
Corollary 7.
The Vandermonde precoding achieves the secrecy rate
where the last equality is obtained by applying SVD to and plugging the power allocation of (30) with , , is determined such that .
Finally, by focusing the behavior of the achievable rate region in the high SNR regime, we characterize the achievable d.o.f. region of the frequency-selective BCC (1).
The d.o.f. region of the frequency-selective BCC (1) with Toeplitz matrices is given as a union of satisfying
where , denote non-negative integers. The Vandermonde precoding achieves the above d.o.f. region.
The achievability follows rather trivially by applying Theorem 3. By considering equal power allocation over all streams such that , , we obtain the rate tuple where
We first notice that the prelog factor of as depends only on the rank of . From Lemma 2, we obtain
where (a) follows from orthogonality between and , (b) follows from the fact that is unitary satisfying . Notice that (36) yields . For the d.o.f. of the common message, (36) and (38) yield
which is dominated by the pre-log of in (37). This establishes the achievability.
The converse follows by noticing that the inequalities (33) and (34) correspond to trivial upper bounds. The first inequality (33) corresponds to the s.d.o.f. of the MIMO wiretap channel with the legitimate channel and the eavesdropper channel , which is bounded by . The second inequality (34) follows because the total number of streams for receiver 1 cannot be larger than the d.o.f. of , that is, .
Figure 3 illustrates the region of the frequency-selective BCC over dimensions. We notice that the s.d.o.f. constraint (33) yields the line segment , while the constraint (34) in terms of the total number of streams for receiver 1 yields the line segment , .
d. o.f. region of frequency-selective BCC.
4. Multiuser Secure Communications
In this section, we provide some applications of the Vandermonde precoding in the multi-user secure communication scenarios where the transmitter wishes to send confidential messages to more than one intended receivers. The scenarios that we address are: (a) a -user frequency-selective BCC with confidential messages and one common message, (b) a two-user frequency-selective BCC with two confidential messages and one common message. For each scenario, by focusing on the behavior in the high SNR regime, we characterize the achievable s.d.o.f. region and show the optimality of the Vandermonde precoding.
4.1. K + 1-User BCC with K Confidential Messages
As an extension of Section 3, we consider the -user frequency-selective BCC where the transmitter sends confidential messages to the first receivers as well as one common message to all receivers. Each of the confidential messages must be kept secret to receiver . Notice that this model, called multireceiver wiretap channel, has been studied in the literature ([20, 22–26] and reference therein). In particular, the secrecy capacity region of the Gaussian MIMO multireceiver wiretap channel has been characterized in [24, 26] for , an arbitrary , respectively, where the optimality of the S-DPC is proved.
The received signal of receiver and the received signal of receiver at any block are given by
where is the transmit vector satisfying the total power constraint and , are mutually independent AWGN with covariance . We assume that the vectors , of length are linearly independent and perfectly known to all the terminals. As an extension of the frequency-selective BCC in Section 2, we say that the rate tuple is achievable if for any there exists a sequence of codes such that
where we denote and define
An achievable secrecy rate region for the case of , when the transmitter sends two confidential messages in the presence of an external eavesdropper, is provided in [25, Theorem 1]. This theorem can be extended to an arbitrary while including the common message. Formally we state the following lemma.
An achievable rate region of the +1-user BCC, where the transmitter sends confidential messages intended to the first receivers as well as a common message to all users, is given as a union of all non-negative rate-tuple satisfying
where denotes a permutation over the subset , denotes the cardinality of , we let , and the random variables , , , , satisfy the Markov chain
Notice that the second term of the last equation in (44) can be also expressed by
It can be easily seen that without the secrecy constraint the above region reduces to the Marton's achievable region for the general -user broadcast channel [35].
In order to focus on the behavior of the region in the high SNR regime, we define the s.d.o.f. region as
where denotes the d.o.f. of the common message and denotes the s.d.o.f. of confidential message . As an extension of Theorem 8, we have the following s.d.o.f. region result.
Theorem 10.
The s.d.o.f. region of the -user frequency-selective BCC (40) is a union of satisfying
where are non-negative integers. The Vandermonde precoding achieves this region.
Appendix D.
Figure 4 illustrates the region for the case of confidential messages. It can be easily seen that the constraint (49) in terms of the total number of streams for the virtual receiver yields the subspace , , while the s.d.o.f. constraint (48) for the virtual receiver yields the subspace , , , . We remark that for the special case of one confidential message and one common message ( ), the region reduces to Figure 3.
s. d.o.f. region over dimensions of three-user frequency-selective BCC.
Remark 11.
When only the confidential messages are transmitted to the intended receivers in the presence of the eavesdropper, the s.d.o.f. region has the equivalent MIMO interpretation [36]. More specifically, the frequency-selective BCC (40) is equivalent to the MIMO-BCC where the transmitter with dimensions (antennas) sends messages to receivers with antennas each in the presence of the eavesdropper with antennas. The secrecy constraint (orthogonal constraint) consumes dimensions of the channel seen by the virtual receiver and lets the number of effective transmit antennas be . The resulting channel is the MIMO-BC without secrecy constraint with transmit antennas and receivers with antennas each, whose multiplexing gain is (we assume ). Figure 5 illustrates the example with , , .
Equivalent MIMO interpretation for three-user frequency-selective BCC with two confidential messages.
4.2. Two-User BCC with Two Confidential Messages
We consider the two-user BCC where the transmitter sends two confidential messages , as well as one common message . Each of the confidential messages must be kept secret to the unintended receiver. This model has been studied in [17–19] for the case of two confidential messages and in [20] for the case of two confidential messages and a common message. In [19], the secrecy capacity region of the MIMO Gaussian BCC was characterized. The received signal at receivers 1, 2 at any block is given, respectively, by
where is the input vector satisfying the total power constraint and , are mutually independent AWGN with covariance . We assume the channel vectors , are linearly independent.
We say that the rate tuple is achievable if for any there exists a sequence of codes such that
where we define the average error probability as
where is the output of decoders 1, 2, respectively. A secrecy achievable rate region of the two-user BCC with two confidential messages and a common message is given by [20, Theorem 1]
where the random variables satisfy the Markov chain
We extend Theorem 8 to the two-user frequency-selective BCC (50) and obtain the following s.d.o.f. result.
The s.d.o.f. region of the two-user frequency-selective BCC (50) is a union of satisfying
where are non-negative integers. The Vandermonde precoding achieves the region.
Appendix F.
Figure 6 represents the s.d.o.f. region over dimensions of the two-user frequency-selective BCC. The per-receiver s.d.o.f. constraints (55) yield the subspace , , , for user 1 and the subspace , , , for user 2. The constraints (56) in terms of the total number of streams per receiver yield the subregion , , for user 1 and the subregion , , for user 2. For the special case of one confidential message and one common message, the region reduces to Figure 3.
s. d.o.f. region over dimensions of -user frequency-selective BCC.
Comparing Theorems 10, 12 as well as Figures 4, 6 for , it clearly appears that the s.d.o.f. of -user BCC with confidential messages is dominated by the s.d.o.f. of -user BCC with confidential messages. In other words, the s.d.o.f. region critically depends on the assumption on the eavesdropper(s) to whom each confidential message must be kept secret.
When only two confidential messages are transmitted in the two-user frequency-selective BCC, the set of the s.d.o.f. has the equivalent MIMO interpretation [36]. More specifically, the frequency-selective BCC (40) is equivalent to the MIMO-BCC where the transmitter with dimensions (antennas) sends two confidential messages to two receivers with antennas. The secrecy constraint consumes dimensions for each MIMO link and lets the number of effective transmit antennas be for each user. The resulting channel is a two parallel point-to-point MIMO channel without eavesdropper. Notice that the same parallel MIMO links can be obtained by applying the block diagonalization on the MIMO-BC without secrecy constraint [36]. In other words, the secrecy constraint in the BCC with inner eavesdroppers is equivalent to the orthogonal constraint in the classical MIMO-BC. Figure 7 shows the example with , and confidential messages.
Equivalent MIMO interpretation for the two-user frequency-selective BCC with two confidential messages.
5. Numerical Examples
In order to examine the performance of the proposed Vandermonde precoding, this section provides some numerical results in different settings.
5.1. Secrecy Rate versus SNR
We evaluate the achievable secrecy rate in (32) when the transmitter sends only a confidential message to receiver 1 (without a common message) in the presence of receiver 2 (eavesdropper) over the frequency-selective BCC studied in Section 3.
5.1.1. MISO Wiretap Channel
For the sake of comparison (albeit unrealistic), we consider the special case of the frequency-selective wiretap channel when receiver 1 has a scalar observation and the eavesdropper has observations. This is equivalent to the MISO wiretap channel with the receiver 1 channel and the eavesdropper channel . Without loss of generality, we assume that the observation at receiver 1 is the first row of . We consider that all entries of , are i.i.d. and average the secrecy rate over a large number of randomly generated channels with , . In Figure 8, we compare the optimal beamforming strategy [10, 13, 14] and the Vandermonde precoding as a function of SNR . Since only one stream is sent to receiver 1, the s.d.o.f. is . In fact, the MISO secrecy capacity in the high SNR regime is given by
where is the beamforming vector. The Vandermonde precoding achieves
where denotes the th column of orthogonal to . Clearly, there exists a constant gap between (57) and (58) due to the suboptimal choice of the beamforming vector.
Achievable secrecy rate with one observation at receiver 1 and , (MISO wiretap channel).
5.1.2. MIMO Wiretap Channel
We consider the frequency-selective wiretap channel with , . Although there exists a closed-form expression under a power-covariance constraint [15], the secrecy capacity under a total power constraint in (11) is still difficult to compute (especially for a large dimension of and ) because it requires a search over all possible power covariances constraints. Therefore, in Figure 9, we compare the averaged secrecy rate achieved by the generalized SVD scheme [5] and the Vandermonde precoding. We assume that all entries of are i.i.d. . For the Vandermonde precoding, we show the achievable rate with waterfilling power allocation (32) and equal power allocation (36) by allocating to streams. As observed, these two suboptimal schemes achieve the same s.d.o.f. of although the generalized SVD incurs a substantial power loss. The result agrees well with Theorem 8. We remark also that the optimal waterfilling power allocation yields a negligible gain.
Achievable secrecy rate with , (MIMO wiretap channel).
5.2. The Maximum Sum Rate Point (R0, R1) versus SNR
We consider the frequency-selective BCC with one confidential message to receiver 1 and one common message to two receivers. In particular, we characterize the maximum sum rate-tuple corresponding to on the boundary of the achievable rate region . Figure 10 shows the averaged maximum sum rate-tuple of the Vandermonde precoding both with optimal input covariance computed by the greedy algorithm and with equal power allocation. We remark that there is essentially no loss with the equal power allocation.
Achievable secrecy/common rates in the frequency-selective BCC.
5.3. Two-User Secrecy Rate Region in the Frequency-Selective BCC
We consider the two-user frequency-selective BCC where the transmitter sends two confidential messages (no common message) of Section 4.2. For the sake of comparison (albeit unrealistic), we consider the special case of one observation at each receiver. Notice that the two-user frequency-selective BCC is equivalent to the two-user MISO BCC with whose secrecy capacity region is achieved by the S-DPC scheme [18]. The proposed Vandermonde precoding achieves the secrecy rate region given by all possible rate-tuples
satisfying where denotes the th column of orthogonal to , orthogonal to , respectively. Figure 11 compares the averaged secrecy rate region of the Vandermonde precoding, zero-forcing beamforming, and the optimal S-DPC scheme for where all entries of are i.i.d. . As observed, the Vandermonde precoding achieves the near-optimal rate region. As the number of paths increases, the gap with respect to the S-DPC becomes smaller since the Vandermonde precoding tends to choose the optimal beamformer matched to the channels.
Achievable secrecy rate region (MISO-BCC).
We considered the secured communication over the frequency-selective channel by focusing on the frequency-selective BCC. In the case of a block transmission of symbols followed by a guard interval of symbols discarded at both receivers, the frequency-selective channel can be modeled as an Toeplitz matrix. For this special type of MIMO channels, we proposed a practical yet order-optimal Vandermonde precoding which enables to send streams of the confidential messages and streams of the common messages simultaneously over a block of dimensions. The key idea here consists of exploiting the frequency dimension to "hide" confidential information in the zeros of the channel seen by the unintended receiver similarly to the spatial beamforming. We also provided some application of the Vandermonde precoding in the multiuser secured communication scenarios and proved the optimality of the proposed scheme in terms of the achievable s.d.o.f. region.
We conclude this paper by noticing that there exists a simple approach to establish secured communications. More specifically, perfect secrecy can be built in two separated blocks: (1) a precoding that cancels the channel seen by the eavesdropper to fulfill the equivocation requirement, (2) the powerful off-the-shelf encoding techniques to achieve the secrecy rate. Since the practical implementation of secrecy encoding techniques (double binning) remains a formidable challenge, such design is of great interest for the future secrecy systems.
Wyner AD: The wiretap channel. Bell System Technical Journal 1975., 54:
Leung-Yan-Cheong SK, Hellman ME: The Gaussian wire-tap channel. IEEE Transactions on Information Theory 1978, 24(4):451-456. 10.1109/TIT.1978.1055917
Csiszár I, Körner J: Broadcast channels with confidential messages. IEEE Transactions on Information Theory 1978, 24(3):339-348. 10.1109/TIT.1978.1055892
Gopala PK, Lai L, El Gamal H: On the secrecy capacity of fading channels. IEEE Transactions on Information Theory 2008, 54(10):4687-4698.
Khisti A, Wornell G: The MIMOME channel. Proceedings of the 45th Annual Allerton Conference on Communication, Control, and Computing, 2007
Liu T, Prabhakaran V, Vishwanath S: The secrecy capacity of a class of parallel Gaussian compound wiretap channels. Proceedings of the IEEE International Symposium on Information Theory (ISIT '08), 2008, Toronto, Canada 116-120.
Liang Y, Poor HV, Shamai S: Secure communication over fading channels. IEEE Transactions on Information Theory 2008, 54(6):2470-2492.
Goel S, Negi R: Secret communication in presence of colluding eavesdroppers. Proceedings of the 62nd IEEE Vehicular Technology Conference (VTC '05), 2005, Atlantic City, NJ, USA 3:
Parada P, Blahut R: Secrecy capacity of SIMO and slow fading channels. Proceedings of the IEEE International Symposium on Information Theory (ISIT '05), 2005 2152-2155.
Khisti A, Wornell G: Secure transmission with multiple antennas: the MISOME wiretap channel. submitted to IEEE Transactions on Information Theory, 2007
Liu T, Shamai S: A note on the secrecy capacity of the multi-antenna wiretap channel. submitted to IEEE Transactions on Information Theory, 2007
Oggier F, Hassibi B: The secrecy capacity of the MIMO wiretap channel. Proceedings of the IEEE International Symposium on Information Theory (ISIT '08), 2008, Toronto, Canada 524-528.
Shafiee S, Ulukus S: Achievable rates in Gaussian MISO channels with secrecy constraints. Proceedings of the IEEE International Symposium on Information Theory, 2007 2466-2470.
Khisti A, Wornell G, Wiesel A, Eldar Y: On the Gaussian MIMO wiretap channel. Proceedings of the IEEE International Symposium on Information Theory (ISIT '07), 2007, Nice, France 2471-2475.
Bustin R, Liu R, Poor HV, Shamai (Shitz) S: An MMSE approach to the secrecy capacity of the MIMO Gaussian wiretap channel. EURASIP Journal on Wireless Communications and Networking. In press
Ly HD, Liu T, Liang Y: MIMO broadcasting with common, private, and confidential messages. Proceedings of the International symposium on Information Theory and Its Applications (ISITA '08), December 2008, Auckland, New Zealand
Liu R, Maric I, Spasojevic P, Yates RD: Discrete memoryless interference and broadcast channels with confidential messages: secrecy rate regions. IEEE Transactions on Information Theory 2008, 54(6):2493-2507.
Liu R, Poor HV: Secrecy capacity region of a multi-antenna Gaussian broadcast channel with confidential messages. IEEE Transactions on Information Theory 2009, 55(3):1235-1249.
Liu R, Liu T, Poor HV, Shamai (Shitz) S: MIMO Gaussian broadcast channels with confidential messages. Proceedings of the IEEE Symposium on Information Theory (ISIT '09), June-July 2009, Seoul, Korea
Choo LC, Wong KK: The K-receiver broadcast channel with confidential messages. Proceedings of the IEEE International Symposium on Information Theory (ISIT '09), 2009, Seoul, Korea
Khisti A, Tchamkerten A, Wornell GW: Secure broadcasting over fading channels. IEEE Transactions on Information Theory 2008, 54(6):2453-2469.
Choo LC, Wong KK: The three-receiver broadcast channel with degraded message sets and confidential messages. submitted to IEEE Transactions on Information Theory
Ekrem E, Ulukus S: Secrecy capacity of a class of broadcast channels with an eavesdropper. submitted to EURASIP Journal on Wireless Communications and Networking
Ekrem E, Ulukus S: The secrecy capacity region of the Gaussian MIMO multi-receiver wiretap channel. submitted to IEEE Transactions on Information Theory
Bagherikaram G, Motahari AS, Khandani AK: The secrecy rate region of the broadcast channel. preprint, 2008, http://arxiv.org/abs/0806.4200
Bagherikaram G, Motahari AS, Khandani AK: The secrecy capacity region of the Gaussian MIMO broadcast channel. preprint, 2009, http://arxiv.org/abs/0903.3261
Koyluoglu OO, El Gamal H, Lai L, Poor HV: Interference alignment for secrecy. preprint, 2008, http://arxiv.org/abs/0810.1187
ANSI/IEEE Std 802.11, Edition (R2003), 1999, http://standards.ieee.org/getieee802/download/802.11-1999.pdf
Air Interface for Fixed and Mobile Broadband Wireless Access Systems, 2005, http://standards.ieee.org/getieee802/download/802.16e-2005.pdf
http://www.3gpp.org/Highlights/LTE/LTE.htm
Ryan Ø, Debbah M: Asymptotic behaviour of random vandermonde matrices with entries on the unit circle. IEEE Transactions on Information Theory 2009., 55(7):
Cardoso LS, Kobayashi M, Ryan Ø, Debbah M: Vandermonde frequency division multiplexing for cognitive radio. Proceedings of the 9th IEEE Workshop on Signal Processing Advances in Wireless Communications (SPAWC '08), 2008, Recife, Brazil 421-425.
Scaglione A, Giannakis GB, Barbarossa S: Lagrange/Vandermonde MUI eliminating user codes forquasi-synchronous CDMA in unknown multipath. IEEE Transactions on Signal Processing 2000, 48(7):2057-2073. 10.1109/78.847790
Poor HV: An Introduction to Signal Detection and Estimation. Springer, New York, NY, USA; 1994.
Viswanath P, Tse DNC: Sum capacity of the vector Gaussian broadcast channel and uplink-downlink duality. IEEE Transactions on Information Theory 2003, 49(8):1912-1921. 10.1109/TIT.2003.814483
Lee J, Jindal N: High SNR analysis for MIMO broadcast channels: dirty paper coding versus linear precoding. IEEE Transactions on Information Theory 2007, 53(12):4787-4792.
Viswanathan H, Venkatesan S, Huang H: Downlink capacity evaluation of cellular networks with known-interference cancellation. IEEE Journal on Selected Areas in Communications 2003, 21(5):802-811. 10.1109/JSAC.2003.810346
Zhang X, Chen J, Wicker SB, Berger T: Successive coding in multiuser information theory. IEEE Transactions on Information Theory 2007, 53(6):2246-2254.
Cover T, Thomas J: Elements of Information Theory. John Wiley & Sons, New York, NY, USA; 1991.
The work is supported by the European Commission in the framework of the FP7 Network of Excellence in Wireless COMmunications NEWCOM++. The work of M. Debbah is supported by Alcatel-Lucent within the Alcatel-Lucent Chair on Flexible Radio at Supelec. The authors wish to thank Yingbin Liang for helpful discussions, and the anonymous reviewers for constructive comments. The material in this paper was partially presented at IEEE 19th International Symposium on Personal, Indoor and Mobile Radio Communications (PIMRC), Cannes, France, September 2008.
Department of Telecommunications, SUPELEC, 3 Rue Joliot-Curie, Gif-sur-Yvette, 91192, France
Mari Kobayashi
Alcatel-Lucent Chair on Flexible Radio, SUPELEC, 3 Rue Joliot-Curie, Gif-sur-Yvette, 91192, France
Mérouane Debbah
Department of Electrical Engineering, Technion-Israel Institute of Technology, Haifa, 32000, Israel
Shlomo Shamai (Shitz)
Search for Mari Kobayashi in:
Search for Mérouane Debbah in:
Search for Shlomo Shamai (Shitz) in:
Correspondence to Mari Kobayashi.
A. Proof of Lemma 2
In this appendix, we consider the rank of where satisfies the orthogonality . By letting denote the th column of we have for the case of . We define the matrix orthogonal to by appending rows to
Notice that all rows are linearly independent. By definition of , it is not difficult to see that and form a complete set of basis for an -dimensional linear space. Indeed for the matrix reduces to , while , a subset of a projection matrix onto the null space of is appended to . Hence can be expressed as
where is the projection of onto the row vectors of with an coefficient matrix , is the projection of onto the row vectors of with an coefficient matrix
where (a) follows from the orthogonality and , (b) follows from . The equality (c) is obtained as follows. We notice
where in (d) adding does not change the rank, (e) follows because any set of rows taken from is linearly independent (from the assumption that , are linearly independent). Since is orthogonal to , (A.4) yields
which establishes (c).
B. Proof of Theorem 5
We consider the following three cases given in Lemma 4.
Supposing , we consider the objective function in (25). The objective is concave only when . Nevertheless, we consider the KKT conditions which are necessary for the optimality. It can be easily shown that the KKT conditions are given by (29) where is the Lagrangian dual matrix associated to the positive semidefiniteness constraint of for and is the Lagrangian dual variable associated to the total power constraint. It clearly appears that for the objective is concave in , and the problem at hand is convex. In this case, any convex optimization algorithm, the gradient-based algorithm [37] for example, can be applied to find the optimal solution while the algorithm converges to a local optimal solution for .
Supposing , we consider the objective function in (26). Since the problem is convex ( is concave and the constraint is linear in ), the KKT conditions are necessary and sufficient for optimality. We form the Lagrangian and obtain the following KKT conditions:
where is the Lagrangian dual matrix associated to the positive semidefiniteness constraint of for and is the Lagrangian dual variable associated to the total power constraint. By creating parallel channels via SVD on , in (28), we readily obtain the solution (30).
For , we consider the objective function in (27). In the following we focus on . Notice that if we have which yields the corner point where denotes the secrecy rate characterized in (32). The KKT conditions, necessary for the optimality, are given by (31) where is the Lagrangian dual matrix associated to the positive semidefiniteness constraints for and is the Lagrangian dual variable associated to the total power constraint. The gradient-based algorithm [37] can be applied to find the solution satisfying these KKT conditions. Although this algorithm yields the optimal and unique solution for , the algorithm converges to a local optimal solution for .
C. Proof of Lemma 9
In the following, we provide the encoding/decoding scheme to achieve a vertex point within corresponding to a specific encoding order . Our proof builds on the successive Gel'fand-Pinsker coding [38] and random binning for ensuring the perfect secrecy. The overall region is obtained by taking the union over all possible encoding orders followed by the convex hull operation. We extensively use the notation to denote a set of jointly typical sequences of length with respect to the distribution . We let arbitrary small for a large .
(a) Codebook Generation
Fix and . We define for
and we let . the joint distribution factors as The stochastic encoder randomly generates
i.i.d. codewords according where .
For user , i.i.d. codewords with , where the indices are given by
(b) Encoding
To send the messages , we first choose randomly the index and the corresponding codeword . Given the common message , we choose randomly the codeword within the bin , that is, the index , such that . Then successively choose the codeword , that is, the indices , such that
If there are more than one such sequence, it randomly selects one. Finally the encoder selects according to .
(c) Decoding
The received signals at the legitimate receivers are , the outputs of the channels for any . Receiver chooses so that
if such pair exists and unique. Otherwise it declares an error.
(d) Error Probability Analysis
Without loss of generality, we assume that the message set is . We remark that an error is declared if one or more of the following events occur.
Encoding fails
From the construction of the codebook above, we have .
Decoding step 1 fails; there does not exist a jointly typical sequence for some , that is,
From joint typicality [39] we have for any .
Decoding step 2 fails; there exits other sequences satisfying the joint typicality for some
It can be shown that we have if
for any . Hence, the error probability if the rate-tuple satisfies (44).
(e) Equivocation Calculation
To prove the equivocation requirement
(C10)
where we denote , we remark that it is sufficient to verify the above inequality for due to [24, Lemma 1]. Hence, we check whether the the sum rate secrecy constraint is satisfied by the proposed encoding strategy.
where (a) follows because the conditioning decrease the entropy, (b) follows from Fano's inequality [39] stating that for a sufficiently large we have
where denotes the eavesdropper's error probability when decoding with the knowledge on the message indices . We have that as if . (c) follows from the Markov chain , (d) follows by ignoring a nonnegative term , (e) follows because for any permutation over the set , (f) follows because for any , finally (g) follows because the successive encoder yields the sum rate given by
This establishes the achievability.
D. Proof of Theorem 10
The achievability follows by extending Theorem 8 to the case of confidential messages. First we remark that as a straightforward extension of Lemma 2 the following lemma holds.
Lemma D.15.
For , there exists a matrix with orthonormal columns with size satisfying
where denotes the number of columns of
A sketch of proof is given in Appendix E.
We let be unitary matrix with orthonormal columns in the null space of such that . In other words, the Vandermonde precoder is a squared unitary matrix satisfying . Based on the Vandermonde precoder , we construct the transmit vector as
where are mutually independent Gaussian vectors with zero mean and covariance satisfying . From the orthogonality properties (D.1), the received signals become
where receiver observes the common message, the intended confidential message, and the interference from other users, while receiver observes only the common message. By letting , for , and considering the equal power allocation to all streams, we readily obtain
and we also have from the independency between conditioned on . Plugging this together with (D.7) and (D.8) into (44), we have
In order to find the d.o.f. region, we notice
where (a) follows from orthogonality between and for , (b) follows from the fact that is unitary satisfying , and (c) follows from Lemma D.15. From (D.11) and (D.12), we readily obtain , which is dominated by (D.10). Combining (D.12) and (D.13), we obtain for . This completes the achievability.
The converse follows by a natural extension of Theorem 8 to the -user BCC. To obtain the constraint (48), we consider that the first receivers perfectly cooperate to decode the confidential messages and one common message. By treating these receivers as a virtual receiver with antennas, we immediately obtain the bound (48) corresponding to the s.d.o.f. of the MIMO wiretap channel with the virtual receiver channel and the eavesdropper channel . The bound (49) is obtained by noticing that the total number of streams that receiver can decode is limited by the d.o.f. of , that is, . Namely, we have the following inequalities:
which yields . Further by letting for any and and for any , we obtain . Adding the last inequality and (48), we obtain (49). This establishes the converse.
E. Proof of Lemma D.15
We consider for a subset . First we let denote orthonormal columns that form a unitary Vandermonde matrix orthogonal to . For any subset , we let be the unitary matrix formed by columns corresponding to the subset taken from . Since a unitary matrix formed by for any can be expressed equivalently as , we consider . For a given , we let denote a unitary matrix composed by columns corresponding to the complementary set such that . In order to derive the rank, we follow the same approach as Appendix A. We define the matrix orthogonal to by appending to
(E1)
where the rows are linearly independent. Since and form a complete set of an -dimensional linear space, can be expressed as
where is a coefficient matrix with dimension , respectively. By recalling that any set of rows taken from is linearly independent for (from the assumption that are linearly independent), we can repeat the same argument as Appendix A and obtain
which yields the result.
F. Proof of Theorem 12
The achievability follows by generalizing Theorem 8 for the case of two confidential messages. We remark that by symmetry Lemma 2 for one beamforming matrix can be trivially extended to two beamforming matrices and . Namely, we have
Lemma F.16.
For and , there exists with orthnormal columns for satisfying
(F1)
Further, we let be a unitary matrix with orthonormal columns in the null space of such that . We construct by Gaussian superposition coding based on the Vandermonde precoder , , and . From (F.1), each user observes the vector of its confidential message and that of the common message, that is,
By letting , for , and considering equal power allocation to all streams with , we readily obtain
We remark
where (a) follows from orthogonality between and for , (b) follows because or spans a complete -dimensional space. These equations yield for . This establishes the achievability.
The converse follows by noticing that the constraints (55) and (56) correspond to trivial upper bounds. To obtain (55), we consider the special case when the transmitter sends only one confidential message to one of two receivers in the presence of the eavesdropper. When sending one confidential message to receiver 1, the two-user frequency-selective BCC reduces to the MIMO wiretap channel with the legitimate channel and the eavesdropper channel , whose s.d.o.f. is upper bounded by . The same bound holds for receiver 2 when transmitting one confidential message to receiver 2 in the presence the eavesdropper (receiver 1). The upper bounds (56) follow because the total number of streams per receiver is limited by the individual MIMO link. This establishes the converse.
Toeplitz Matrix
Broadcast Channel
Secrecy Rate
Secrecy Capacity
Equal Power Allocation
Wireless Physical Layer Security


text:
Artist recycling toys into grand sculptures
Community, Featured
By Dana Delgado
Accomplished and self-proclaimed "Pixilated Artist" Terry Parks (aka Terry Tunes) is onto something wildly new at his rural home studio in Liberty Hill.
That something, which has been two years in the making, amounts to a collection of amazing sculptures bordering bizarre but impressively creative.
"It's the 'Keep Austin Weird' in me," said Parks who was born and raised in Austin and lived the Austin lifestyle for much of his life.
The eccentric, bohemian and very up-beat artist has been toying with a multitude of off-the-wall creative projects including some small wooden "TV Box" sculptures that incorporate intriguing objects and natural materials. While the materials are uniquely arranged and reflect Terry's creative genius, it's the underlying message or theme of each box, which is both provocative and powerful, that draws you in.
Although seemingly inexplicable and simply weird, it is Parks' way of challenging one's senses and reaching into the recesses of one's mind and personal experience. Not only is he a talented and an imaginative artist, he is a wordsmith master that intertwines words with music and culture to produce a life revelation and provides for serious introspection. Most of his ideas, he says, come from listening to music.
"I just do what inspires me with art," Tunes said, but his wife had a different take.
"I never know what I'm going to find when I get home," says Sue Lacy, Terry's wife. "It's crazy."
Parks is also a furniture craftsman and for a while had a store in Georgetown. He also has grown interested in carving objects with Native American themes and has made a few caskets for family members who wanted a green burial.
"I love working with wood," said Terry, who also relishes peeling and using the bark off tree branches and collecting armadillo tails to incorporate into his small creations.
Knotholes are also a favorite thing to use because of their character.
He is eager to share and show his intricate wooden creations, but the larger-than-life, oversized sculptures are what have him motivated these days because they are out on his property for everyone to see as they drive by.
"I love that people get to see my work instead of sitting on a shelf or sitting in a closet," he said. "It also slows down the cars, too, but I really appreciate that people are interested in my art and that it makes them happy."
To come across these sculptures on San Gabriel Road while driving by is a surreal feeling. The synergy between the sun and the trees add to the drama with an array of ever-changing light rays filtering through that glisten off the artistic pieces.
On much closer inspection of the sculptures, your jaw drops.
You are awestruck because unexpectedly, you find hundreds upon hundreds upon hundreds of tiny plastic toys of all kinds from superheroes to toy trucks to animal figures to Barbie dolls fastidiously fastened to cover every inch of the frames of each of the sculptures.
"I thought about covering the sculptures with light bulbs to light up at night but then I thought what a hassle that would be changing them out," Parks said. "Besides, plastic lasts a long time, is waterproof and cheap and I'm recycling the toys."
Two years ago while rummaging through his storeroom, he came across a ready supply of toys to get him started.
"I had some toys that I would take with me to play with the kids at family reunions and had been keeping some doll body parts I got from my mother's house when she passed away. She had been a doll maker," he said.
Surprising to the artist, people who closely exam his sculptures are often equally moved by the sculpture design as well as by the toys themselves that cover the frame.
"You have to remember that we were all kids at one time and we all played with toys," Parks said. "Sometimes, people see a toy on my sculptures that brings back fond memories. If I do that I'm happy. It's about making people happy."
Parks likes to use a twist of the macabre in some sculptures, but most revolve around music or cultural themes. All of his off-the-wall art pieces, however, are always clever and outrageously witty, and yes, at times deep.
To really understand the objects is to understand the artist. The 60-something Parks has a larger than life grasp of life with an abundance of energy, is big-hearted and sincerely generous and very much connected with nature and people.
Terry's art influences came from his mother who had been an artist during her lifetime, as well as his middle school woodshop teacher who inspired him to be creative.
"When I was young, I loved to paint and draw," he said. "I would save a lot of my money from my paper route to buy art supplies."
In 1974, he began a property search to build a home. Liberty Hill was his first stop and his last.
"When I saw this tree (large oak tree) on the property, it was like I was struck by lightning," he said. "I knew I wanted this lot and didn't go anywhere else."
Terry with the help of his younger brother Scott built his Liberty Hill home from the ground up by harvesting many of the raw materials from the area. The brothers added bohemian touches and blended in artistic accents like stain glass windows. Where he could, Terry reused trees or branches removed to construct the house. It's an interesting piece of art in its own right.
In 1984, Terry married Sue McKown Lacy. They had met a year earlier when they were both cooks at the old Threadgill's Restaurant in Austin. Sue says they really got to know each other when they were literally locked into the kitchen at the restaurant to prepare Thanksgiving dinner for customers.
Throughout his life, Terry has been heavily vested in the music scene in Austin. He would do artistic work for various bands and lived and loved the vibes of the music scene until a health issue put the skids on his lifestyle and life's work.
Parks was diagnosed with Hepatitis and given six months to live. With the help of family and a dog he didn't want but his wife got for him anyway, Terry "Tunes" Parks realized he needed to make some life adjustments. Returning to his previous work pace was not an option. He became bored and restless.
Terry and his brother Scott brainstormed some ideas and soon after, the music vibes and artistic juices that once resonated strongly in him, returned and he began to create again. That was 10 years ago.
After a series of projects, his wildly imaginative sculptures might well be his major breakthrough. Among them is freakish-looking sculpture of a mass of doll heads and body parts mounted on sticks titled "Leave Your Body Behind." This was one of his first sculptures that from afar resembles a flock of flamingos.
The sculptures that followed, however, have been more in the vein of music and culture; after all, that's been Terry's lifeblood. Among them are a nearly eight-foot tall guitar sculpture titled "Woodstock 45" and a nine-foot tall Peace Sign Sculpture titled "For What it's Worth."
Another is a nine-foot tall banana sculpture designed as a play on an old Andy Warhol album cover. This one is titled "Exploding Plastic Inevitable."
Others on exhibit on his property are the Hat Sculpture titled "My Heroes Have Always Been Cowgirls," the High Heel Slipper Sculpture titled "The Low Sparks of High-Heeled Toys," and the Easter Island Sculpture titled "Easter Island Everywhere."
There is also a massive 20-foot Cow's Skull Longhorn Sculpture that captivates with Barbie dolls covering the horns.
The newest project and in-progress in a back work area is a 10-foot Pistol Sculpture inspired by an Austin band Black Angels and one of their songs, "Don't Play with Guns." Yet another project, a 15-foot Tepee Sculpture sits idle with frame only in the far back of the property waiting to be outfitted.
In the center of all the sculptures is a small rock mound with a staked sign. The sign names the site of his collection of works and peculiarly identifies himself. The sign proclaims: "Itchycoo Park -Pixilated Artist."
This weekend, the Pixilated Artist will exhibit his sculptures and demonstrate his work at Legacy Antiques and Estate Auctions, 2023 Loop 332. The exhibit is scheduled for Friday through Sunday, September 27-29, from 10 a.m to 6 p.m.
"I'm really excited to have him show his sculptures and demonstrate his work," said Legacy owner Melissa Fiero. Ms. Fiero was one of those curious people who happened to drive by the Parks' property and stopped to explore.
"He is such a wonderful person and talented artist. To help him out we encourage people to drop off toys which he recycles in his sculptures," she said, adding that other arts and crafts supplies will also be available.
"It's all been great therapy," said Parks who says he is happier than ever, very much at peace and ready to let go of some of the sculptures. They are for sale and he will take special orders. He can be reached at suelacy@sbcglobal.net or you can visit him at his home studio at 208 San Gabriel Road off County Road 214 in Liberty Hill.
Liberty Hill downs Wimberley in second half ...
Hostilities escalate as Mayor argues no money ...
Softball forced to adjust due to preseason injuries
Featured, Throwback Thursday
THROWBACK THURSDAY: Mather's fearless reputation included confrontation with bear during expedition
LHHS back on winning track after beating Badgers 27-16 behind Wright's huge night
Community, Featured, News
Backyard chicken flocks ruffling some town feathers
Panthers lose in penalty kicks after two delays
Lady Panthers' full-court press causing problems for opponents
Council keeps Bojorquez law firm, but rejects attorney's advice on police camera equipment purchase

redpajama_set_name: RedPajamaCommonCrawl


AUD 141,120 ? OMR 38,083Program fees are indicative only. Speak to your IDP study counsellor to get up-to-date course prices.
AUD 144,450 ? OMR 38,981Program fees are indicative only. Speak to your IDP study counsellor to get up-to-date course prices.
AUD 128,400 ? OMR 34,650Program fees are indicative only. Speak to your IDP study counsellor to get up-to-date course prices.
AUD 200,200 ? OMR 54,026Program fees are indicative only. Speak to your IDP study counsellor to get up-to-date course prices.
AUD 145,800 ? OMR 39,346Program fees are indicative only. Speak to your IDP study counsellor to get up-to-date course prices.
AUD 163,500 ? OMR 44,122Program fees are indicative only. Speak to your IDP study counsellor to get up-to-date course prices.
AUD 146,400 ? OMR 39,508Program fees are indicative only. Speak to your IDP study counsellor to get up-to-date course prices.


Location: The apartment Casa con Angel is located near Plaza España and the Abastos cultural centre. It is on the third floor of a 1922 stately property renovated in a modernist style.
Layout: The apartment consists of three bedrooms, two with twin beds and one with double bed and en suite bathroom, a spacious living/dining room, an independent kitchen and another bathroom for the rest of the apartment.
Equipment: The apartment is equipped with air conditioning cool/heat, bed linen and towels, ironing facilities, flat-screen TV and DVD player, fridge, oven, washing machine, dish washer, microwave, coffee maker, toaster, kettle and complete kitchenware.
Connection: The historical centre is just a few minutes? walk. It is also very well connected with the City of Arts and Sciences and the beach with several bus lines and a metro station in a 200m radius.
1 Double bed, 2 Single beds, 2 Bunk beds.
1 TV, Stereo, DVD, 3rd floor, lift, iron, internet (Wi-Fi), balcony, 90 m² property, air conditioning (hot/cold), air conditioning in the living room and in some bedrooms.


There is a little bit of sadness around me tonight. No, it's nothing horrible or anything. It's just the stark realization that my ability to run in the mornings is coming to a very abrupt end. I haven't run in the early morning (5:30 ish) since last Tuesday. Thursday I was out of town and I ran Sunday around 8:00 am. And now - this week - the sun doesn't come up until 5:51 am tomorrow, and by the end of the week it will be nearly 6:00 am. This leaves me with issues I don't have the time or the desire to deal with right now. See... I work at 7:00 am. My run takes about 35 minutes. I have to pretty much leave by 5:30 in order to get back in time to shower and make it to work by 7:00.
Sure, I could run in the evenings, but here's the thing... I can't. As I found out during a couple of previous disaster runs, and was again terribly reminded of on Sunday morning - my body has no heat tolerance. Even at 8:00 at 70 some degrees it was too hot for me on Sunday and caused a spell with dizziness and nausea I'd rather not think about, let alone discuss. Oh yeah, and if you haven't heard enough excuses, I don't belong to a gym, so the dreadmill is not an option. I belong to Curves right now, and it's just circuit training.
Sigh. I swear I am not trying to sound all whiny, but yet as I reread those last 2 paragraphs that's exactly how I sound. I'm just trying to process the demise of summer and figure this thing out, without it sending me in a tailspin. It is not an option to quit, and while wearing a hat with a light on the head is an interesting idea, I'm thinking maybe not the safest.
I will figure this out... I will. But no reason for me to figure it out alone. So tell me, what would you do?
Should I quit Curves and join a gym? I'm looking for some advice here, because it is not an option to quit what I've now started - even though some days... I really really want to.
I totally hear you! Are you 100% opposed to running in the early-dark? If not, reflective gear and a safe running route (maybe requiring you to drive somewhere) are a must.
Otherwise, I would suggest you quit Curves and join a gym. Your fitness level and running require more than they offer there. And, as a bonus, you'll then be able to work out in the morning OR the evening, because overheating won't be an issue!
My immediate thought was to buy/rent/borrow a treadmill from somewhere, to see you through the darker months. I'm sure you could pick up a reasonably priced treadmill on eBay that would fit the bill.
Since you'll be getting years of use out of it, it may work out cheaper than joining a gym just so that you can use theirs. You can get up and go running whenever you want, no matter how dark it is. Also, it'll be great for whenever the weather is really bad but you need to get the run done. Just use it when you need to and run outside when the conditions are good.
It would probably be cheaper to just get the hat light and reflectors and go at night or really early before the sun is up. However, I would feel unsafe at night at least. Could you do morning runs on the weekends and other workouts during the week? Of course, you could always just quit Curves and go to the gym. Sounds like you need a treadmill option anyway with inclement weather. Do any of your friends have a treadmill you could go over and use? Just trying to think of options.


text:
This Time, Time Got It Right: Tarana Burke Covers the 100 Most Influential People Issue
Filed to:Tarana Burke
Photo: Time Inc.
We will never not stan for Tarana Burke because of the way she so unapologetically and steadfastly stands for us. Watching her profile rise in recent months is like watching the sun rise on a precious and fertile piece of earth that has been ignored far too long.
And since Time magazine was deeply egregious in naming the movement Burke founded its 2017 Person of the Year but not placing the founder herself upon its accompanying cover, we take some cold comfort in seeing her portrait finally land on one of the six covers of its 100 Most Influential People issue.
The Cover That Time Forgot: Why We're Placing #MeToo's Tarana Burke Front and CenterThe Cover That Time Forgot: Why We're Placing #MeToo's Tarana Burke Front and CenterThe Cover That Time Forgot: Why We're Placing…
News that the #MeToo movement had been named Time magazine's coveted 2017 Person of the Year…
Labeled an "Icon" and joining a list that includes Kehinde Wiley, Maxine Waters, Jesmyn Ward, Trevor Noah, Issa Rae, Ryan Coogler, Lena Waithe, Oprah Winfrey, Kevin Durant, Chadwick Boseman, Janet Mock, Cardi B, Virgil Abloh, Sterling K. Brown, Rihanna and fellow cover star Tiffany Haddish, Burke's penetrating gaze reminds us that not all icons and influencers are celebrity byproducts. While Hollywood may have brought much-needed attention to the #MeToo movement, Burke's advocacy has a long history and reach and promises to remain more than a trending topic.
In Burke's profile, actress and fellow activist Gabrielle Union zeros in on exactly what makes Burke so special. While she has never sought the spotlight, she continues to use it to fight for all of us. Union writes:
You want a leader who truly believes in inclusivity. For Tarana, it's not about personal gain or attention but doing the work in a way that makes people feel like they can join in.
When you've been sidelined for so long, it's exhilarating to know that such a powerful voice is finally breaking through. Tarana will continue to do this work, but the stage will be bigger and the microphone turned all the way up. She will inspire legislation and new crops of voters. She will sway old voters. She will open eyes. She's not even going to bring more seats to the table—she's going to turn the table over and build a new one.


You've almost succeeded in destroying the 4th estate and you should be ashamed of yourselves.
This is why 94% of the American people don't trust you.
When are you going to get that through your thick skulls?
You lie, you smear, you ingratiate yourselves with wanton abandon.
Dear mainstream media: You've betrayed your profession, sacrificed its once sacred principles, and stabbed the American people in the back.


text:
accessibility | a-z site map | graphics version | text version
Salford Priors Parish Council and Community Website
Previous Updates
Previous updates to this website, made since its relaunch in September 2013:
25/05/19: Council Meetings - meeting dates for 2019/20.
25/05/19: Councillors - new and amended Councillor contact information and working groups.
25/05/19: Annual Reports - 2018/19 report from the Chair of Salford Parish Council.
25/05/19: Finance - Accounting Statements and Inspection Notice for 2018/19.
25/05/19: Minutes - draft minutes from May's Parish Council meeting.
25/05/19: Minutes - draft minutes from May's Annual Parish Council meeting.
25/05/19: Contact Us - contact information for the Chair of the Council.
25/05/19: Documents - updated Standing Orders.
12/05/19: Agenda - for the Annual Parish Council Meeting on 15 May 2019.
12/05/19: Agenda - for the Parish Council Meeting on 15 May 2019.
13/04/19: Agenda - for the Annual Parish Meeting on 17 April 2019.
13/04/19: Agenda - for the Parish Council Meeting on 17 April 2019.
03/04/19: Minutes - draft minutes from March's Parish Council meeting.
03/04/19: Agenda - for the Parish Council Meeting on 20 March 2019.
06/03/19: Minutes - minutes from February's Parish Council meeting.
14/02/19: Agenda - for the Parish Council Meeting on 20 February 2019.
14/02/19: Minutes - minutes from January's Parish Council meeting.
14/02/19: Local Groups - contact name and email address for the Scout group.
19/01/19: Events - Hearts and Homes (Syrian Refugee Charity) open meeting.
19/01/19: Minutes - minutes from December's Parish Council meeting.
19/01/19: Agenda - for the Parish Council Meetings on 19 December and 16 January.
11/01/19: Working Groups - updated names of Council appointees to various groups.
28/12/18: Documents - some new and updated Policy documents.
28/12/18: Local Businesses - new website for The Bell.
07/12/18: Minutes - minutes from November's Parish Council meeting.
16/11/18: Agenda - for the Parish Council Meeting on 21 November 2018.
01/11/18: Agenda - for the Extraordinary Parish Council Meeting on 7 November 2018.
01/11/18: Minutes - approved minutes from October's Parish Council meeting.
27/10/18: Minutes - draft minutes from October's Parish Council meeting.
27/10/18: Events - Bidford Community Choir Winter Concert.
17/10/18: Agenda - for the Parish Council Meeting on 17 October 2018.
09/10/18: Documents - some new and updated Procedure/Policy documents.
04/10/18: Events - WW1 Centenary Remembrance Day: A Nation's Tribute.
19/09/18: Minutes - from September's Parish Council meeting.
18/09/18: A link to a petition on the home page.
18/09/18: Notice - Salford Priors resident is raising money for the Royal British Legion.
14/09/18: Agenda - for the Parish Council Meeting on 19 September 2018.
14/09/18: Notice - details about the Battle's Over Scarecrow Competition.
12/09/18: Newsletters - September's newsletter from CSW Broadband.
04/09/18: Finance - updated Account Reports and Statements for 2017/18.
29/08/18: Notice - an update on the Warwickshire Minerals Plan.
10/08/18: Documents - updated Financial Regulations.
03/08/18: Documents - updated Terms of Reference for Parish Council Working Groups.
29/07/18: Minutes - draft minutes from July's Parish Council meeting.
18/07/18: Finance - Accounts Report, Statements and Inspection Notice for 2017/18.
18/07/18: Agenda - for the Parish Council Meeting on 18 July 2018.
18/07/18: Newsletters - July's newsletter from CSW Broadband.
18/07/18: Minutes - from June's Parish Council meeting.
16/06/18: Agenda - for the Parish Council Meeting on 20 June 2018.
11/06/18: Documents - updated Privacy Notice.
02/06/18: Newsletters - May's newsletter from CSW Broadband.
25/05/18: Notice - Perkins' Educational Foundation Awards.
25/05/18: Minutes - from May's Annual and Ordinary Parish Council meetings.
25/05/18: Documents - updated Code of Conduct.
22/05/18: E-News - latest E-News Bulletin from the Parish Council Clerk.
22/05/18: Documents - updated Standing Orders and some Council policies.
22/05/18: Working Groups - names of Council appointees to various groups.
15/05/18: Documents - two Privacy Notices.
04/05/18: Events - Bidford Community Choir Summer of Love concert.
25/04/18: Minutes - from April's Parish Council and Annual Parish meetings.
25/04/18: Newsletters - April's newsletter from CSW Broadband.
28/03/18: Minutes - from March's Parish Council meeting.
28/03/18: Councillors - details of new Councillor Paula Gordon.
18/03/18: Newsletters - March's newsletter from CSW Broadband.
27/02/18: Minutes - from February's Parish Council meeting.
22/02/18: Newsletters - February's newsletter from CSW Broadband.
25/01/18: Minutes - from January's Parish Council meeting.
19/01/18: Notice - Co-option for Parish Councillor vacancy.
19/01/18: Documents - some new and updated Council Procedures.
13/01/18: Agenda - for the Parish Council Meeting on 17 January 2018.
03/01/18: Minutes - from December's Parish Council meeting.
23/12/17: Notice - Parish Councillor vacancy for the parish of Salford Priors.
23/12/17: Events - Salford Priors Ladies Group meetings for Spring 2018.
23/12/17: Agenda - for the Parish Council Meeting on 20 December 2017.
27/11/17: Notice - thanks to sponsors and donators to our Christmas Lights Switch-On.
27/11/17: Minutes - from November's Parish Council meeting.
27/11/17: Events - Bidford Choir Winter Concert.
17/11/17: Events - Christmas Fayre at Salford Priors Primary School.
10/11/17: Events - Christmas Tree Lights Switch-On.
10/11/17: Newsletters - October's Parish Council Newsletter.
28/10/17: Minutes - from October's Parish Council meeting.
25/08/17: Notice - a questionnaire on play equipment in Salford Priors.
15/08/17: Events - Ragley Hall events in August and September.
24/07/17: Finance - Conclusion of Audit and Auditor Certificate for 2016/17.
24/07/17: Minutes - from July's Parish Council meeting.
18/07/17: Events - Salford Priors Ladies Group meeting on 13 September 2017.
15/06/17: Minutes - from May's Annual Parish meeting.
15/06/17: Events - Bidford History Society meetings for 2017/18.
03/06/17: Events - Salford Priors Memorial Hall AGM.
03/06/17: Minutes - from May's Annual Parish Council meeting.
29/05/17: Notice - presentation relating to the development of the land off School Road.
23/05/17: Churches - new service times for Dunnington Baptist Church.
24/05/17: Finance - Accounts Statements, Declaration and Inspection Notice for 2016/17.
20/05/17: Notice - parliamentary elections for Stratford-on-Avon Constituency.
20/05/17: Minutes - from April's Annual Parish meeting.
13/05/17: Agenda - for the Parish Council Meetings on 17 May 2017.
02/05/17: Minutes - from April's Parish Council meeting.
02/05/17: Councillors - amended email addresses for certain Parish Councillors.
05/04/17: Neighbourhood Plan - a link to the current Plan on the SDC website.
04/04/17: Newsletters - April's Parish Council Newsletter.
04/04/17: Local Groups - information and contact details for Bidford Area Community Choir.
02/04/17: Events - Salford Priors Ladies Group events for spring/summer 2017.
28/03/17: Notice - election of County Councillor for Bidford and Welford Division.
28/03/17: Notice - referendum on the Salford Priors Neighbourhood Plan.
28/03/17: Events - Cinema Club films for April 2017.
28/03/15: Memorial Hall - new website for Salford Priors Memorial Hall.
21/03/17: Documents - Terms of Reference for Parish Council Working Groups.
08/03/17: Notice - interactive property-level Broadband Checker now available.
24/02/17: Notice - the Parish Council's response to the Minerals Plan Consultation.
19/02/17: Welcome Booklet - pdf version of booklet added to our home page.
11/02/17: Minutes - from February's Extraordinary Parish Council meeting.
11/02/17: Notice - details of Salford Priors Cinema Club.
29/01/17: Agenda - for the Parish Council Meeting on 1 February 2017.
19/01/17: Notice - Salford Priors Primary School seeking two gardening club volunteers.
12/01/17: Agenda - for the Parish Council Meeting in January 2017.
03/01/17: Councillors - additional contact information for recent new Parish Councillors.
17/12/16: Agenda - for the Parish Council Meeting in December 2016.
17/12/16: Notice - consultation on Worcestershire Minerals local plan.
07/12/16: Councillors - updated list of Parish Councillors.
26/11/16: Documents - Code of Members's Conduct for the Parish Council.
22/11/16: Schools - confirmed website for Salford Priors CE Primary School.
16/11/16: Agenda - for the Parish Council Meeting in November 2016.
14/10/16: Agenda - for the Parish Council Meeting in October 2016.
14/10/16: Finance - a certificate and opinion from the external auditor on 2015/16 accounts.
22/09/16: Finance - conclusion of audit of Parish Council accounts for 2015/16.
22/09/16: Agenda - for the Parish Council Meeting in September 2016.
03/09/16: Minutes - from August's Parish Council meeting.
30/08/16: Neighbourhood Plan - core documents and links relating to the NDP examination.
16/07/16: Agenda - for the Parish Council Meeting in July 2016.
14/07/16: Parish Office - revised Parish Council Office opening hours.
02/07/16: Contact Us - contact information for the new Clerk to the Council.
02/07/16: Notice - the appointment of a new Clerk for Salford Priors Parish Council.
02/07/16: Neighbourhood Plan - Basic Conditions Statement and Consultaton Statement.
02/07/16: Minutes - from May's Parish Council meetings.
24/06/16: Documents - an extract from the Local Audit and Accountability Act 2014.
03/06/16: Newsletters - June's Parish Council Newsletter.
24/05/16: Notice - Neighbourhood Development Plan six week consultation.
14/05/16: Agenda - for the Parish Council Meetings in May 2016.
22/04/16: Events - Annual Parish Meeting.
18/04/16: Agenda - for the Parish Council Meeting in April 2016.
30/03/16: Notice - upcoming vacancy for Parish Clerk/Responsible Financial Officer.
30/03/16: Notice - election of Police and Crime Commissioner for Warwickshire area.
30/03/16: Documents - application forms for employment within the Parish Council.
30/03/16: Newsletters - March's Parish Council Newsletter.
30/03/16: Agenda - for the Parish Council Meeting in March 2016.
02/03/16: Local Groups - updated contact details for Salford Priors Royal British Legion.
02/03/16: Minutes - updated minutes from January's Parish Council meetings.
02/03/16: Events - Photos and Memories of Days Past in Salford Priors.
19/02/16: Events - Party in the Park to celebrate The Queen's 90th Birthday.
13/02/16: Agenda - for the Parish Council Meeting in February 2016.
13/02/16: Minutes - from January's Parish Council meetings.
22/01/16: Agenda - for the Extraordinary Parish Council Meeting on 27 January 2016.
18/12/15: Notice - consultation on the Warwickshire Minerals Plan extended to 4 January 2016.
15/12/15: Neighbourhood Plan - Questionnaire Results on Orchard Farm Development.
15/12/15: Neighbourhood Plan - Feedback from Exhibition on Orchard Close Development.
28/11/15: Minutes - and Agenda from November's Extraordinary Parish Council meeting.
13/11/15: Minutes - from October's Parish Council meetings.
13/11/15: Events - Parish Christmas Tree Illumination event.
13/11/15: Events - public exhibition re: housing development site on Evesham Road.
11/11/15: Notice - Bidford Bridge is now open again.
21/10/15: Neighbourhood Plan - questionnaire for non-residents of Salford Priors.
17/10/15: Minutes - from September's Parish Council meetings.
02/10/15: Documents - Community Grant Scheme Application Form and Terms.
10/09/15: Minutes - from July and August's Parish Council meetings.
06/08/15: Councillors - updated list of Council members and working groups.
06/08/15: Newsletters - July's Parish Council Newsletter.
06/08/15: Parish Council Office - opening times.
06/08/15: Web Links - additional websites of interest.
28/07/15: Events - Bidford and District History Society events for 2015/16.
03/07/15: Notice - Bidford Bridge closed to all traffic.
03/07/15: Events - invite to visit Salford Priors Primary School.
03/07/15: Events - Salford Priors Youth Club Open Evening.
03/07/15: Agenda - for the Parish Council Meeting in June 2015.
25/06/15: Notice - consultation on the draft Neighbourhood Development Plan.
25/06/15: Neighbourhood Plan - draft NDP, comment forms and associated documents.
08/06/15: Minutes - from May's Annual Parish Council and ordinary Council meetings.
16/05/15: Minutes - from 2015's Annual Parish Meeting.
16/05/15: Agenda - for the Parish Council Meeting in May 2015.
30/04/15: Neighbourhood Plan - presentation made at the Annual Parish Meeting.
30/04/15: Events - Parish Council Annual Meeting.
28/04/15: Notice - opinions sought on the provision of a Salford Priors Parish War Memorial.
22/03/15: Minutes - from March's Extraordinary Parish Council meeting.
05/03/15: Agenda - for the Extraordinary Meeting on 10 March 2015.
05/03/15: Memorial Hall - grant received for improving the energy efficiency of the building.
26/02/15: Newsletters - February's Parish Council Newsletter.
17/12/14: Neighbourhood Plan - consultation posters for presentations in November 2014.
10/11/14: Events - Neighbourhood Development Plan Consultation Exhibition.
12/10/14: Minutes - from August's ordinary and extraordinay Parish Council meetings.
08/10/14: Memorial Hall - new contact for bookings or hire information.
08/10/14: TOPS - updated Booking Secretary name and contact information.
08/10/14: Notice - appointment of Mr Paul Mills as Clerk to Salford Priors Parish Council.
08/10/14: Notice - the final curtain for Salford Priors Amateur Theatre Society.
08/10/14: Events - Royal British Legion Coffee Morning and Table Top Sale.
27/09/14: TOPS - additional information and photos of The Other Place.
17/09/14: Events - Jumble Sale in aid of Salford Priors Youth Club.
17/09/14: Events - get-together and reunion of the 'Photos and Memories of Salford Priors' group.
17/09/14: Local Groups - 'Photos and Memories of Days Past in Salford Priors' Facebook group.
14/09/14: Events - Parish Council Meeting including latest plans for Orchard Close.
14/09/14: Events - World's Biggest Coffee Morning in aid of Macmillan Cancer Support.
02/09/14: Notice - resignation of the Clerk to Salford Priors Parish Council.
26/08/14: Notice - first parish Christmas Tree has been chosen.
26/08/14: Neighbourhood Plan - the vision for the parish by 2031.
23/08/14: Newsletters - August's Parish Council Newsletter.
23/08/14: Notice - two private firework displays at Ragley Hall during August.
23/08/14: Agenda - for the Extraordinary Parish Council Meeting on 28 August 2014.
21/08/14: Events - planning presentation on the proposed development of Orchard Farm.
16/08/14: Notice - proposed planning proposal for solar panels at Salford Loge Farm.
15/08/14: Agenda - for the Parish Council Meeting on 20 August 2014.
15/08/14: Minutes - from June and July's Parish Council meetings.
14/08/14: Notice - details on how individuals need to register to vote.
14/08/14: Notice - temporary closure of C103 Bidford Road, Broom.
09/08/14: Notice - Neighbourhood Development Group 'Call for Sites'.
06/08/14: Neighbourhood Plan - latest newsletter.
26/07/14: Events - The Other Place (TOPS) Annual General Meeting.
18/07/14: Police News - Warwickshire Police newsletter for July 14.
18/07/14: Planning - Council response to application 14/01126/OUT.
18/07/14: Planning - Council response to application A/01206/FUL.
18/07/14: Agenda - for past meetings in June/July 2014.
01/07/14: Annual Reports - 2013/14 report from the Warwickshire Police and Crime Panel.
01/07/14: Contact Us - communication streams for locality and partnerships in the county.
02/06/14: Agenda - for the Extraordinary Parish Council Meeting on 4 June 2014.
31/05/14: Notice - cheque presentation to the new Health Centre in Bidford.
31/05/14: Events - Broom Open Gardens.
25/05/14: Councillors - updated list of Parish Council members.
25/05/14: Notice - public question time introduced at Police and Crime Panel.
25/05/14: Annual Reports - 2013/14 report from our Stratford on Avon District Councillor.
17/05/14: Agenda - for the Annual Meeting and Parish Council Meeting on 21 May 2014.
17/05/14: Notice - Perkins' Educational Foundation Awards for 2014/15.
10/05/14: Events - Memorial Hall recruitment and open day.
24/04/14: Annual Reports - 2013/14 report from our Warwickshire County Councillor.
24/04/14: Neighbourhood Plan - questionnaire results and latest news update.
10/04/14: Minutes - from an Extraordinary Parish Council meeting in March.
10/04/14: Notice - District and European Elections on 22 May 2014.
04/04/14: Notice - WCC Library Service Rural Housebound Scheme.
04/04/14: Notice - part-time job vacancy with The Rowan Organisation.
04/04/14: Events - Police and Crime Commissioner public meeting in Stratford.
04/04/14: Notice - allotment gardens available to rent.
04/04/14: Notice - filled sandbags no longer available from the Parish Council.
01/04/14: Contact Us - new telephone number for the Acting Clerk to the Council.
01/04/14: Events - Coffee Morning at Dunnington Baptist Church.
30/03/14: Notice - fundraising appeal for Susie Pick's volunteer work in the Philippines.
30/03/14: Notice - the 2011 Census Profile for Salford Priors parish.
21/03/14: Events - Theatre Workshop sessions.
21/03/14: Events - Public Consultation Meeting re: Alamo Residential Development Site.
21/03/14: Events - Neighbourhood Development Plan Information Exhibition and Surgery.
21/03/14: Notice - proceeds from the Salford Priors Memorial Hall Race Night.
12/03/14: Events - Evesham and District Lions Club Open Evening.
25/02/14: Agenda - for an Extraordinary Parish Council Meeting on 10 March 2014.
25/02/14: Notice - job vacancies for support workers in Bidford area.
22/02/14: Events - Race Meeting in aid of Bidford Health Centre.
04/02/14: Agenda - for an Extraordinary Parish Council Meeting on 5 February 2014.
16/01/14: Neighbourhood Plan - a map of the proposed Neighbourhood Plan designation area.
12/01/14: Minutes - from October, November and December's Parish Council meetings.
12/01/14: Neighbourhood Plan - a new email address for further information.
12/01/14: Events - amended date/time for the Salford Priors Readers' Group.
08/01/14: Neighbourhood Plan - a new page for details of the Neighbourhood Development Plan.
16/11/13: Councillors - updated contact informtion for Parish and District Councillors.
16/11/13: Events - Neighbourhood Planning Meeting.
16/11/13: Events - SPATS production of 'Third Week in August'.
10/11/13: Notice - urging people to check their heating oil tanks before winter sets in.
08/11/13: Events - Web Wise launch and volunteer appeal at Bidford Library.
08/11/13: Notice - information about Small Business Saturday UK.
04/11/13: Local Groups - change of contact details for St John Ambulance.
31/10/13: Notice - details of the Warwickshire Community Oil/LPG Syndicate.
30/10/13: Local Groups - details of the Perkins Educational Foundation.
26/10/13: Agenda - for the Extraordinary Parish Council Meeting on 30 October 2013.
20/10/13: Events - Parish Council Extraordinary Meeting re: Tothall Lane Planning Application.
19/10/13: Notice - details of the Warm Home Discount Scheme (help with fuel bills).
12/10/13: Local Businesses - details of Ultimate Fireworks Ltd.
26/09/13: Newsletters - September's 'Parish and Partners Briefing' from Stratford District Council.
20/09/13: Notice - grants available for small rural businesses.
20/09/13: Events - Public Meeting re: Salford Priors Memorial Hall.
10/09/13: Local Businesses - details of Limebridge Rural Services Ltd.
05/09/13: Events - Neighbourhood Planning Event.
05/09/13: Our new-look website is launched.
HOME NEWS AND NOTICES NEWSLETTERS EVENTS OUR PARISH
Gallery: Yesteryear
The Other Place (TOPS)
Procedures and Documents
NEIGHBOURHOOD PLAN LOCAL GROUPS LOCAL BUSINESSES WEB LINKS CONTACT US
Home | News and Notices | Newsletters | Events
Our Parish > History | Gallery: Yesteryear | Memorial Hall | The Other Place (TOPS) | Churches | Schools
Parish Council > Introduction | Council Meetings | Planning Applications | Councillors | Annual Reports | Procedures/Documents
Neighbourhood Plan | Local Groups | Local Businesses | Web Links | Contact Us
Unauthorised copying of any images,
or content by any means is not permitted.
Content © 2008 to , Salford Priors Parish Council
This website designed August 2013
Website designed and maintained by Arrowscape
Disclaimer: This website is provided by Salford Priors Parish Council for the benefit of the whole community of the parish. All information contained under the heading 'Parish Council' is provided on behalf of the Parish Council. All other information is provided by organisations, companies and individuals with no particular links to the Parish Council and as such the Parish Council cannot be held responsible for the content or the content of any links to other sites.
Contact the Clerk to the Council - Telephone: 01386 421028


Available in pellets and flakes, Calcium Chloride has versatile applications including de-icing, dust control and concrete acceleration.
Dust Control Calcium Chloride draws moisture from the air and resists evaporation and stays in solution. It's ability to regulate moisture on road surfaces is the key to building roads that last.
De-Icer Calcium chloride is the most powerful of all the common deicers used for melting ice and snow on sidewalks, driveways, parking lots, and streets. The exothermic (heat releasing) reaction when calcium chloride goes into solution makes it the de-icer of choice. No other product melts more ice, and melts ice faster than 94% calcium chloride pellets.