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The maximum likelihood block decoder for trellis coded noncoherent M-DPSK signals on the AWGN channel is outlined, first assuming that the decoder has no knowledge of the state of the encoder at the beginning of the block, and then assuming that it knows the state. Because these exhaustive decoders suffer from an exponential growth in complexity with blocklength. two simplified decoders are proposed that approach the performance of the exhaustive decoders with a much more manageable complexity. Through a union bound analysis and computer simulations, it is shown that it is possible to achieve large gains over uncoded systems with a very reasonable decoder complexity.

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