Figure 4 HCM encoder (left) and decoder (right) As shown in Figure 4, HCM, multiples a vector of N data symbols (where is a power of two) with a Hadamard matrix, denoted as fast Walsh-Hadamard transform (FWHT). As described in [8], the HCM signal is generated from the data sequence as , where is the Hadamard matrix of order [9], and is the complement of . The complement of is H a binary matrix in which each element of the matrix is replaced by 1-h. The components of are h assumed to be modulated using M-PAM. DC is removed by setting PAM level/ spectral FEC Line Optical Clock HCM Data Rate/Mbps efficiency RS(n,k) code Rates/MHz [bit/s/Hz] use Table 1 for (256, 248) HCM(1,1) and take into for 2 / 1 8B10B (1,1) account payload i) spectral efficiency for M-PAM 200/2n with n=0, 1, 5 …, ii) the appropriate code 2 / 1 rate of the FEC (36,24) for 4 / 2 ii) overhead for HCM header 1B1B (1-15,16) instead of 8B10B, see 8 / 3 Table 6 in Annex 3) 16 / 4 Table 5 Transmission modes using combinations of M-PAM and Line Coding or HCM Table 7 lists possible transmission modes by combining line coding, FEC, HCM and OCR. In combination with Table 1, it is possible to obtain the data rate for each transmission mode. For instance, using RS(256,248) with 2-PAM, 8B10B and n=4 (6.25 MHz) yields 4.8 Mbit/s while using RS(256,248) with 16-PAM, m=15 for HCM and n=0 (100 MHz) yields 363 Mbit/s.
Figure 4 HCM encoder (left) and decoder (right) As shown in Figure 4, HCM, multiples a vector of N data symbols (where is a power of two) with a Hadamard matrix, denoted as fast Walsh-Hadamard transform (FWHT). As described in [8], the HCM signal is generated from the data sequence as , where is the Hadamard matrix of order [9], and is the complement of . The complement of H is a binary matrix in which each element h of the matrix is replaced by 1-h. The components of are assumed to be modulated using M-PAM. DC is removed by setting PAM level/ spectral efficiency [bit/s/Hz] FEC RS(n,k) Line code HCM Optical Clock Rates/MHz Data Rate/Mbps 2 / 1 (256, 248) for payload 8B10B (1,1) 200/2n with n=0, 1, …, 5 use Table 1 for HCM(1,1) and take into account i) spectral efficiency for M-PAM ii) the appropriate code rate of the FEC ii) overhead for HCM instead of 8B10B, see Table 6 in Annex 3) (36,24) for header 2 / 1 1B1B (1-15,16) 4 / 2 8 / 3 16 / 4 Table 5 Transmission modes using combinations of M-PAM and Line Coding or HCM Table 7 lists possible transmission modes by combining line coding, FEC, HCM and OCR. In combination with Table 1, it is possible to obtain the data rate for each transmission mode. For instance, using RS(256,248) with 2-PAM, 8B10B and n=4 (6.25 MHz) yields 4.8 Mbit/s while using RS(256,248) with 16-PAM, m=15 for HCM and n=0 (100 MHz) yields 363 Mbit/s.