Optimal Trellis Decoding at Given Complexity

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Abstract
A class of algorithms performing Maximum Likelihood Sequence Detection under various structural and complexity constraints is derived (BSC or AWGN). Complexity is measured by the number of paths used. By partitioning the S states into C classes and selecting B paths into each class, the signals closest to the received one shall be selected and hence NP=BC paths are used. This class of algorithms has the name SA(B,C) (SA=Search Algorithm) and the Viterbi Algorithm (VA) is the unconstrained solution denoted SA(1,S). An analysis method concerning the probability of the first error event at large SNR is developed for the whole SA(B,C) family and results in an analysis tool named the Vector Euclidean Distance (VED) of which the traditional Euclidean Distance (ED) is a scalar special case. The smallest number of paths resulting in the same asymptotic detection performance as the VA is calculated for several classes of trellis codes.

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