Decoding Algorithms for Noncoherent Trellis Coded Modulation

Noncoherent decoding of trellis codes using multiplesymbol overlapped observations was shown previously to achieve close to the coherent performance. Optimal decoding by the Viterbi algorithm for L-symboI observations requires a number of states which grows exponentially with L. In this paper, two novel suboptimal algorithms are presented, for which the number of states is the same as the Original code, yielding complexity depending weakly on L. For practical values of L, both algorithms are substantially less complex than the optimal algorithm. The first algorithm, the basic decision feedback algorithm (BDFA), is a low complexity feedback decoding scheme, based on the Viterbi algorithm. This algorithm is shown to suffer from increased error probability and from error propagation. A slight modification to this algorithm can, in most cases, reduce these effects significantly. The second algorithm uses the BDFA as a basic building block. This algorithm is based on a novel concept called estimated future and its performance is very close to optimum for most practical cases with some additional complexity and memory requirements as compared to the first algorithm. Performance analysis and simulation results are also given.