Efficient decoding algorithms for noncoherent trellis coded phase modulation

Noncoherent decoding of trellis codes using multiple-symbol overlapped observations was shown to achieve close to the coherent performance. Optimal decoding by the Viterbi algorithm (VA) for L-symbol observations requires a number of states which grows exponentially with L. In the paper a novel suboptimal algorithm is presented, called estimated future decision feedback algorithm which is based on the VA. The number of states used is the same as in the original code, yielding complexity which depends weakly on L. A basic building block to this algorithm is the basic decision feedback algorithm (BDFA) or its modification the modified decision feedback algorithm (MDFA). The new algorithm uses 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 VA (used with coherent decoding).