Random-coding-exponent-based design of coded modulation for multiple-symbol differential detection

Coded modulation (CM) matched to M-ary differential phase-shift keying (MDPSK) modulation over Rayleigh block fading channels with multiple-symbol differential detection (MSDD) is discussed. Different coding techniques are assessed by evaluating the associated random coding exponent (RCE), i.e., taking the decoding delay into account. Let the channel coherence time be N samples. At the transmitter, N-1 uniform i.i.d. (differential) PSK data symbols (phase increments, i.e., prior to differential encoding) are combined into a vector a. At the receiver, a vector y comprises the N corresponding received signal samples. Between a and y a vector channel is established, which is assumed to be memoryless, even when imposing delay constraints. Channel coding and decoding is done with respect to vectors a and y, respectively, containing l=(N-1)log₂(M) coded binary digits