Limited search trellis decoding of convolutional codes

Abstract

The least storage and node computation required by a breadth-first tree or trellis decoder that corrects t errors over the binary symmetric channels is calculated. Breadth-first decoders work with code paths of the same length, without backtracking. The Viterbi algorithm is an exhaustive trellis decoder of this type; other schemes look at a subset of the tree or trellis paths. For random tree codes, theorems about the asymptotic number of paths required and their depth are proved. For concrete convolutional codes, the worst case storage for t error sequences is measured. In both cases the optimal decoder storage has the same simple dependence on t. The M algorithm and algorithms proposed by G.J. Foschini (ibid., vol.IT-23, p.605-9, Sept. 1977) and by S.J. Simmons (PhD. diss., Queens Univ., Kingston, Ont., Canada) are optimal, or nearly so; they are all far more efficient than the Viterbi algorithm.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>