Trellis coding on a channel having precoding, continuous-phase modulation, and differential detection

The author considers trellis-coded M-ary, continuous-phase modulated (CPM) signaling, with demodulation by differential detection and optimal decoding. Additive white Gaussian noise (AWGN) and optional phase jumps are present. It was shown previously (Thesken and Biglieri, 1989) that the channel´s cutoff rate R₀ can be optimized in terms of only M and one other parameter, denoted A, in other words not directly in terms of pulse type, duration, or modulation index. The author finds the performance of the channel with actual trellis codes: a suboptimal code selection criterion is found, the same as the one for the AM channel with AWGN; then error probability with good codes is obtained via simulation. The sensitivity of R₀ to A is nearly duplicated by the sensitivity of the error probability, on both a coded channel and an uncoded channel. Nearly the same coding gains are found as were found by Ungerboeck for AM signaling in AWGN