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arXiv:1403.0836

Locally-Optimized Reweighted Belief Propagation for Decoding LDPC Codes with Finite-Length

Jingjing Li, Rodrigo C. de Lamare, Henk Wymeersch

Published Mar 4, 2014• 0 citations
arXivHTMLPDF

Abstract

In practice, LDPC codes are decoded using message passing methods. These methods offer good performance but tend to converge slowly and sometimes fail to converge and to decode the desired codewords correctly. Recently, tree-reweighted message passing methods have been modified to improve the convergence speed at little or no additional complexity cost. This paper extends this line of work and proposes a new class of locally optimized reweighting strategies, which are suitable for both regular and irregular LDPC codes. The proposed decoding algorithm first splits the factor graph into subgraphs and subsequently performs a local optimization of reweighting parameters. Simulations show that the proposed decoding algorithm significantly outperforms the standard message passing and existing reweighting techniques.

DOI
10.48550/arxiv.1403.0836

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In practice, LDPC codes are decoded using message passing methods. These methods offer good performance but tend to converge slowly and sometimes fail to converge and to decode the desired codewords correctly. Recently, tree-reweighted message passing methods have been modified to improve the convergence speed at little or no additional complexity cost. This paper extends this line of work and proposes a new class of locally optimized reweighting strategies, which are suitable for both regular and irregular LDPC codes. The proposed decoding algorithm first splits the factor graph into subgraphs and subsequently performs a local optimization of reweighting parameters. Simulations show that the proposed decoding algorithm significantly outperforms the standard message passing and existing reweighting techniques.
In practice, LDPC codes are decoded using message passing methods. These methods offer good performance but tend to converge slowly and sometimes fail to converge and to decode the desired codewords correctly. Recently, tree-reweighted message passing methods have been modified to improve the convergence speed at little or no additional complexity cost. This paper extends this line of work and proposes a new class of locally optimized reweighting strategies, which are suitable for both regular and irregular LDPC codes. The proposed decoding algorithm first splits the factor graph into subgraphs and subsequently performs a local optimization of reweighting parameters. Simulations show that the proposed decoding algorithm significantly outperforms the standard message passing and existing reweighting techniques.
In this paper a new message passing algorithm, which takes advantage of both tree-based re-parameterization and the knowledge of short cycles, is introduced for the purpose of decoding LDPC codes with short block lengths. The proposed algorithm is called variable factor appearance probability belief propagation (VFAP-BP) algorithm and is suitable for wireless communications applications, where both good decoding performance and low-latency are expected. Our simulation results show that the VFAP-BP algorithm outperforms the standard BP algorithm and requires a significantly smaller number of iterations than existing algorithms when decoding both regular and irregular LDPC codes.
In this paper a new message passing algorithm, which takes advantage of both tree-based re-parameterization and the knowledge of short cycles, is introduced for the purpose of decoding LDPC codes with short block lengths. The proposed algorithm is called variable factor appearance probability belief propagation (VFAP-BP) algorithm and is suitable for wireless communications applications, where both good decoding performance and low-latency are expected. Our simulation results show that the VFAP-BP algorithm outperforms the standard BP algorithm and requires a significantly smaller number of iterations than existing algorithms when decoding both regular and irregular LDPC codes.
In this paper we propose a novel message passing algorithm which exploits the existence of short cycles to obtain performance gains by reweighting the factor graph. The proposed decoding algorithm is called variable factor appearance probability belief propagation (VFAP-BP) algorithm and is suitable for wireless communications applications with low-latency and short blocks. Simulation results show that the VFAP-BP algorithm outperforms the standard BP algorithm, and requires a significantly smaller number of iterations when decoding either general or commercial LDPC codes.
Low density parity check (LDPC) codes are one of the most popular channel codes.Based on traditional sum-product and max-product algorithms, various modified algorithms are tried to improve the performance of LDPC codes in terms of error rate, complexity and latency.Uniformly rweighted belief propagation (URW-BP) algorithm can offer better performance than traditional algorithm especially for regular LDPC codes.linear programming (LP) decoder is also competitive to traditional message passing algorithm.We describe two traditional message passing decoders, four reweighted message passing decoders based on URW-BP and LP decoder in this paper.Reweighted decoders can outperform traditional decoders especially when iteration number is limited.Considering complexity and latency, reweighted max product decoder of version 2 (R-MPD-II) is the most promising decoder.CONTENTS 4.3 Short regular LDPC codes . . . . . . . .
Error control coding is an essential part of modern communications systems. LDPC codes have been demonstrated to offer performance near the fundamental limits of channels corrupted by random noise. Optimal maximum likelihood decoding of LDPC codes is too complex to be practically useful even at short block lengths and so a graph-based message passing decoder known as the belief propagation algorithm is used instead. In fact, on graphs without closed paths known as cycles the iterative message passing decoding is known to be optimal and may converge in a single iteration, although identifying the message update schedule which allows single-iteration convergence is not trivial. At finite block lengths graphs without cycles have poor minimum distance properties and perform poorly even under optimal decoding. LDPC codes with large block length have been demonstrated to offer performance close to that predicted for codes of infinite length, as the cycles present in the graph are quite long. In this thesis, LDPC codes of shorter length are considered as they offer advantages in terms of latency and complexity, at the cost of performance degradation from the increased number of short cycles in the graph. For these shorter LDPC codes, the problems considered are: \n \nFirst, improved construction of structured and unstructured LDPC code graphs of short length with a view to reducing the harmful effects of the cycles on error rate performance, based on knowledge of the decoding process. Structured code graphs are particularly interesting as they allow benefits in encoding and decoding complexity and speed. Secondly, the design and construction of LDPC codes for the block fading channel, a particularly challenging scenario from the point of view of error control code design. Both established and novel classes of codes for the channel are considered. Finally the decoding of LDPC codes by the belief propagation algorithm is considered, in particular the scheduling of messages passed in the iterative decoder. A knowledge-aided approach is developed based on message reliabilities and residuals to allow fast convergence and significant improvements in error rate performance.