Correct Undetected Errors with List Decoding in ARQ Error-control Systems

TL;DR

This paper explores using list decoding to correct undetected errors in ARQ systems, significantly improving error correction rates especially for Hamming and Reed-Muller codes by leveraging constraints among codewords.

Contribution

It introduces a list decoding approach combined with a selection algorithm based on Markov context models to enhance undetected error correction in ARQ systems.

Findings

List decoding improves correction of undetected errors by up to 40%.

Selection algorithms based on context constraints are effective.

A lower bound for correct selection probability is derived.

Abstract

Undetected errors are important for linear codes, which are the only type of errors after hard decision and automatic-repeat-request (ARQ), but do not receive much attention on their correction. In concatenated channel coding, suboptimal source coding and joint source-channel coding, constrains among successive codewords may be utilized to improve decoding performance. In this paper, list decoding is used to correct the undetected errors. The benefit proportion of the correction is obviously improved especially on Hamming codes and Reed-Muller codes, which achieves about 40% in some cases. But this improvement is significant only after the selection of final codewords from the lists based on the constrains among the successive transmitted codewords. The selection algorithm is investigated here to complete the list decoding program in the application of Markov context model. The performance of the algorithm is analysed and a lower bound of the correctly selected probability is derived to determine the proper context length.