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Wave Electronics and its Application in Information and Telecommunication Systems (WECONF)

About One Algorithm for Correcting Bursts Using Block-Permutation LDPC-Codes

Вересова Алина Максимовна, Andrei A. Ovchinnikov

Published Jun 1, 2019• 19 citations
Publisher

Abstract

The approaches to decoding block-permutation low-density parity-check codes in channels with memory are considered. The modification of windowed bit-flipping algorithm for bursty channels is proposed, which is guaranteed to correct bursts within the correcting capabilities of the code. The method of determining the position of bursts is proposed. The simulation results in a memory channel with a limit on the burst length are presented.

DOI
10.1109/weconf.2019.8840580

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The approaches to decoding block-permutation low-density parity-check codes in channels with memory are considered. The modification of windowed bit-flipping algorithm for bursty channels is proposed, which is guaranteed to correct bursts within the correcting capabilities of the code. The method of determining the position of bursts is proposed. The simulation results in a memory channel with a limit on the burst length are presented.
The article discusses the issue of determining the location of an error burst based on the structure of a block-permutation low-density parity-check code. Quasi-cyclic low-density parity-check codes with a small number of blocks are considered, making it possible to correct the longest possible bursts within this construction. Through experimentation, the maximum, minimum, and average number of attempts was estimated when determining the start position of the error burst. The features of determining the location of a packet in block-permutation low-density parity-check codes are revealed. The proposed method is based on using majority decoding techniques and allows reducing the average number of attempts to locate a burst from hundreds to units for the codes under consideration. Using the packet detection method, which is based on the analysis of the structure of the parity-check matrix, algorithms for decoding Gilbert and extended Gilbert codes have been proposed, ensuring the correction of bursts within their error-correction capabilities. The process of decoding extended Gilbert codes utilizes list decoding in a supercode, with a criterion for selecting the error vector based on the syndrome.
We derive burst error correctable length of the lowdensity parity-check (LDPC) codes by the iterative decoding algorithms. By results of simulation, we show that the decoding performance of iterative decoding algorithms for the LDPC codes over the Markovmodulated binary symmetric channels (MM-BSC) are aected by the distance between elements (DBE). We also show that some column permuted LDPC codes that have larger DBE, have robustness in error performance over the MM-BSC, compared to the original LDPC codes.
The performance of iterative decoding of low density parity check (LDPC) codes over binary erasure channels can be completely characterized by the study of stopping sets. Therefore, the burst erasure correction capability of a given LDPC code can be readily quantified by searching for stopping sets within consecutive bit nodes. In this work we study the optimal permutation of the bit nodes that will result in the maximum possible burst erasure correction capability for a given LDPC code. Noting that this is essentially a combinatorial optimization problem that is highly likely to be NP-hard, we adopt a simulated annealing based approach for finding the optimal permutation. We present bounds based on stopping sets that limit the burst erasure correction capability. As part of our results, we provide interleavers that greatly improve the burst erasure correction capability of protograph quasi-cyclic LDPC codes used in the WiMax standard.
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.