th coherent BPSK and QPSK modulations with one-bit (hard decision), two-bit, and three-bit quantized channel outputs. For binary convolutional codes LSI Viterbi decoders chips and sequential coder chips have been developed. It seems reasonable to exploit these developments and use binary convolu- 'These are convolutional codes using the Galois Field GF(2*). Other Coding Metrics M = = M=16,L= 2 M=16,L = 4 M = 16, M=16,L= = 16 E/N / Figure 2.131. List metric cutoff rates for broadband noise jammer. tional codes with the FH/MFSK signals. Here we examine how the M-ary input channel with outputs of M energy detector samples can be converted into a binary input channel with one-bit, two-bit, and three-bit outputs that will be suitable for binary codes with corresponding decoders. For M = 2K there are K bits associated with each M-ary channel input sym- bol. For example, with K = 3 (M = 8), we have a channel with eight input symbols and the output samples as seen in Table 2.23. Between the M-ary input and the M energy detector outputs there exists MFSK modulation, frequency hopping, the real channel, dehopping and M energy detectors. To create a binary input channel with one-bit output, we merely make a hard decision as to which M-ary symbol was sent. For exam- ple, for M = 8 above if e4 is the largest energy detector output then the chan- nel output hard decision bits would be 011. Here the probability of a bit error is denoted Sq if the signal hopped into the q-th sub-band. If the bits are inter- leaved before converting them into M-ary symbols and then deinterleaved, the hard decision bits obtained are the outputs of the usual binary symmetric Non-Coherent Frequency-Hopped Systems M = 2, L = 2 M = 4. L = 2 M = 8, L = 2 M = 16, L = 2 M = 32, L = 2 Figure 2.132. List metric cutoff rates for worst case tone jammer. channel (BSC) with crossover probability Sq, which is the uncoded bit error probability for the FH/MFSK system. For the above BSC a binary code can be used with a decoder that uses jammer state information (J