matrices is proportional to the area of the particular matrix thus fig8 represents the minimum power condition for transmitting a six bit word two orthogonal three bit words this optimized bit transmission density can be achieved by inserting a read only digital memory between the data readout and the digital to analogue converters as shown in fig9 and 10 it will be seen that fig9 and 10 are simplified and generalized versions of the transmitter 16 and receiver 36 diagrammatically illustrated in fig2 and 4 with read only memory look up table 142 replacing 12 bit shift register 42 in transmitter 16 and read only memory lookup table replacing 194 replacing 12 bit shift register 94 in receiver 36 referring to fig9 transmitter 136 includes a read only memory having an m u00d7 m lookup table 142 which receives a stream of n bit digital data where m is the number of bits required to encode half of the n bits in the digital data stream so that one of the alternate amplitude phase vector matrices discussed above may be obtained it will be noted that m will generally be greater than n 2 the read only memory 142 outputs.