Comparison of the Probability of Reed – Solomon and LDPC Codes Decoding Error in the Gilbert – Elliott Channel

Veresova, A. M.; Ovchinnikov, A. A.

doi:10.1109/weconf55058.2022.9803501

Cited by 3 publications

(1 citation statement)

References 10 publications

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“…At the same time, it is known from information theory, that if an interleaving is applied to channel, and the property of noise correlation is not taken into account during decoding, we get an equivalent (in terms of average number of erroneous bits in channel) memoryless channel with less capacity [9]. Burst correction has low attention in classical coding theory, and is considered mainly for cyclic codes КОДИРОВАНИЕ И ПЕРЕДАЧА ИНФОРМАЦИИ [10][11][12]. In the recent publication [13] the burst erasure correction is considered, but only for the family of block-permutation LDPC codes and under consumption of fixed burst positions (phased burst).…”

Section: Introductionmentioning

confidence: 99%

Decoding of linear codes for single error bursts correction based on the determination of certain events

Ovchinnikov

Veresova

Fominykh

2022

ICS

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Introduction: In modern systems for communication, data storage and processing the error-correction capability of codes are estimated for memoryless channels. In real channels the noise is correlated, which leads to grouping error in bursts. A traditional method to fight this phenomenon is channel decorrelation, which does not allow developing of coding schemes, mostly utilizing the channel capacity. Thus the development of bursts decoding algorithms for arbitrary linear codes is the actual task. Purpose: To develop a single error burst decoding algorithm for linear codes, to estimate the decoding error probability and computational complexity. Results: Two approaches are proposed to burst error correction. The first one is based on combining the window sliding modification of well-known bit-flipping algorithm with preliminary analysis of the structure of parity check matrix. The second one is based on the recursive procedure of constructing the sequence of certain events which, in the worst case, performs the exhaustive search of error bursts, but in many cases the search may be significantly decreased by using the proposed heuristics. The proposed recursive decoding algorithm allows a guaranteed correction of any single error bursts within burst-correction capability of the code, and in many cases beyond the burst-correction capability. The complexity of this algorithm is significantly lower than that of a bit flipping algorithm if the parity-check matrix of the code is sparse enough. An alternative hybrid decoding algorithm is proposed utilizing the bit-flipping approach and showing the error probability and completion time comparable to the recursive algorithm, however, in this case the possibility of a guaranteed burst correction hardly can be proved. Practical relevance: The proposed decoding methods may be used in modern and perspective communication systems, allowing energy saving and increasing reliability of data transmission by better error performance and computational complexity.

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Section: Introductionmentioning

confidence: 99%

Decoding of linear codes for single error bursts correction based on the determination of certain events

Ovchinnikov

Veresova

Fominykh

2022

ICS

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About the Joint Correcting of Error Bursts and Independent Errors Using LDPC Codes

Veresova,

Ovchinnikov

2023

2023 XVIII International Symposium Problems of Redundancy in Information and Control Systems (REDUNDANCY)

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Usage of LDPC Codes in a Gilbert Channel

Ovchinnikov

Veresova

Fominykh

2023

jour

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Although low-density parity-check (LDPC) codes in modern communication standards have been extensively studied over a memoryless channel, their burst error correction capacity in channels with memory has yet to be thoroughly analyzed. The conventional approach to transmission in channels with memory uses interleaving within a buffer of several codewords. However, such an approach reduces the efficiency of the redundancy embedded by the error-correcting code. It is known from information theory that considering channel memory during decoding allows the transmission rate to be increased. An evaluation of the decoding error probability of different types of low-density parity-check codes in channels with memory is presented along with estimates of minimum distance and burst error correction capability for the considered codes. The decoding error probability is estimated for conventional decoding with deinterleaving and decoding taking channel memory into account. The decoding error probability is estimated for several parameters of a channel with memory and different buffer lengths. The obtained results reveal the absence of the unique decoding approach for all parameters of the channel with memory. The best decoding error probability is determined by the degree of channel memory correlation.

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Comparison of the Probability of Reed – Solomon and LDPC Codes Decoding Error in the Gilbert – Elliott Channel

Cited by 3 publications

References 10 publications

Decoding of linear codes for single error bursts correction based on the determination of certain events

Decoding of linear codes for single error bursts correction based on the determination of certain events

About the Joint Correcting of Error Bursts and Independent Errors Using LDPC Codes

Usage of LDPC Codes in a Gilbert Channel

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