Анализ и оптимизация схем кодирования для каналов с рэлеевскими замираниями

Abstract

Conventional approach to perform error-correcting decoding in channels with memory is an adoption of interleaving, which increases the receiver complexity and delay. In order to avoid these limitations, approaches for adapting an error-correcting scheme for memory channels may be used. One approach is to use error-correcting codes with modified design and decoding procedure, taking into account the presence of error bursts in the channel. Another approach to adapting the coding scheme for burst error correction is to use product codes with iterative decoding algorithms. Component codes of product codes themselves may not be able to correct error bursts, but a two-dimensional structure of product codes operating as an artificial interleaver and iterative decoding allow for correction of grouping errors. Purpose: The purpose of the study is to analyze the methods of error-correcting code adaptation to burst error correction in channels with memory in order to reduce the probability of error. Results: The study considered methods of error-correcting code scheme adaptation for low-density parity-check codes, polar codes, and product codes for burst error correction in Gilbert-Elliott channel (GE) and correlated Rayleigh fading channel with different correlation coefficients. Degree distribution of low-density parity-check code was optimized for GE channel. The influence of selected parameters of product code component codes on burst error correction in the GE channel was analyzed. The structure of the polar code has been optimized using a genetic algorithm for the correlated Rayleigh channel, which outperforms the 5G polar code design in terms of error probability. Discussion: Existing error-correcting code schemes do not provide theoretically possible limits, so the question remains of developing coding and decoding schemes capable of reaching theoretical limits.