Supercode heuristics for tree search decoding

Viterbi decoding and sequential decoding are the standard approaches to decoding convolutional codes (and linear codes with trellis representations in general). However, when reliable communication at low signal-to-noise ratios (SNR) is desired, both techniques are impractical: the Viterbi algorithm requires large amounts of memory and numbers of computations to decode powerful codes, while sequential decoding at low SNR requires exploring large portions of the code tree. In this paper we present a novel two-pass decoder which incorporates features of both these techniques but can achieve decoding complexities lower than either of them. The decoder initially performs a backward pass that resembles the add-compare-select stage of the Viterbi decoder or the backward stage of the BCJR decoder. However, it is performed not on the trellis representing the actual code used for transmission, but on a higher rate supercode (a linear code containing all codewords of the original code) with a simpler trellis representation. The supercode state metrics obtained in the backward pass are preserved and subsequently used in the forward pass. The forward pass involves the actual tree search for the most likely transmitted codeword (of the original code), and the supercode state metrics serve as heuristics, speeding up the search process. We demonstrate that such a decoder, with a proper choice of parameters, can be made equivalent to a sequential decoder with the Fano metric, a sequential decoder with an ML metric, or a Viterbi decoder (run backwards). However, the decoder operates most effectively in between these modes, when the computational load is distributed evenly between the backward and forward stages.