Adaptive single-trial error/erasure decoding of binary codes

Abstract

We investigate adaptive single-trial error/erasure decoding of binary codes whose decoder is able to correct ε errors and τ erasures if λε + ≤ <; d <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">min</sub> -1. Thereby, d <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">min</sub> is the minimum Hamming distance and λ ϵ R, 1 <; λ <; 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 that must be erased in order to obtain the smallest possible residual codeword error probability can be determined. This was answered before for the case of fixed erasing, where only the channel state and not the individual symbol reliabilities of each received vector are taken into consideration. In this paper, we address the adaptive case, where the optimal erasing strategy is determined for every given received vector.