Performance Bound and Trellis-Code Design Criterion for Discrete Memoryless Channels and Finite-Delay Symbol-by-Symbol Decoding

A new tight analytical upper bound is presented for the performance of finite-delay symbol-by-symbol (SBS) Abend–Fritchman-like decoding of trellis-encoded data crossing arbitrary (eventually time-varying) discrete memoryless channels (DMC’s). On the basis of this bound, a related criterion for the optimal design of trellis codes with SBS decoding is then proposed. It gives rise to an effective procedure for the construction of good trellis codes (generally time varying and nonlinear) with assigned decoding complexity.