Rate-compatible pruned convolutional codes and Viterbi decoding with the Levenshtein distance metric applied to channels with insertion, deletion, and substitution errors

Abstract

Viterbi decoding is a path maximum-likehood decoding algorithm widely used in modems and error correction devices. The Levenshtein distance has been postulated to be a suitable branch comparison metric for the Viterbi algorithm on channels not only with substitution errors, but also with insertion/deletion errors. However, to a large extent, this hypothesis has still to be investigated. Pruned convolutional codes are constructed by periodically deleting branches in a high rate convolutional code trellis diagram to create a time varying code. The application of rate compatible pruned codes to hybrid ARQ/FEC schemes is proposed here for channels with insertion, deletion and substitution errors. A new type of Viterbi algorithm based on the Levenshtein distance metric is used as the decoding algorithm. Our experiments give evidence that the Viterbi algorithm with the Levenshtein distance metric is suitable as a decoder on channels with both substitution errors and insertion/deletion errors, and furthermore that rate-compatible pruned codes can improve the performance of the decoding