Поиск информационных совокупностей при исправлении пакетов ошибок квазициклическими кодами

Abstract

This article discusses the question of assessing the probability of finding information sets in block-permutation and block-circulant matrices. Traditionally, interference-resistant coding is considered independent errors, however, in real systems they can be grouped and generate a so-called error burst. Known estimates of the probability of finding information sets are conducted for random matrices, and for correcting error bursts widespread block-permutation low density parity check codes (LDPC-codes) or block-circulant quasi cyclic codes (QC-codes) can be used. To estimate the probability of finding information sets mathematical modeling was used. Experiments have been carried out to identify parameters for specific structures that give the greatest probability of finding information sets. The article presents the results reflecting certain features in the values of the probability of finding information sets for matrices of different types, given assumptions and hypotheses about the features. Dependence of the presence of an information set from the size and location of its search interval inside the block permutation matrix was identified. The results of this research may be used to reduce the complexity of decoding by information sets, which, when considering random matrices, is exponential.