Adaptive Single-Trial Error/Erasure Decoding for Binary Codes

TL;DR

This paper proposes an adaptive single-trial error/erasure decoding method for binary codes that optimally erases unreliable symbols based on received data, improving decoding performance by exploiting soft information.

Contribution

It introduces an adaptive erasing strategy that determines the optimal symbols to erase for each received vector, enhancing decoding effectiveness over fixed erasing methods.

Findings

Optimal erasing strategy reduces residual error probability.

Adaptive decoding outperforms fixed erasing approaches.

Method effectively exploits soft information for improved decoding.

Abstract

We investigate adaptive single-trial error/erasure decoding of binary codes whose decoder is able to correct e errors and t erasures if le+t<=d-1. Thereby, d is the minimum Hamming distance of the code and 1<l<=2 is the tradeoff parameter between errors and erasures. The error/erasure decoder allows to exploit soft information by treating a set of most unreliable received symbols as erasures. The obvious question here is, how this erasing should be performed, i.e. how the unreliable symbols which must be erased to obtain the smallest possible residual codeword error probability are determined. In a previous paper, we answer this question for the case of fixed erasing, where only the channel state and not the individual symbol reliabilities are taken into consideration. In this paper, we address the adaptive case, where the optimal erasing strategy is determined for every given received vector.