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IEEE Wireless Communications and Networking Conference

Locally-optimized reweighted belief propagation for decoding finite-length LDPC codes

Jingjing Liu, Rodrigo C. de Lamare, Henk Wymeersch

Published Apr 1, 2013• 2 citations
Publisher

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
10.1109/wcnc.2013.6555271

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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 . . . . . . . .
The design of optimal linear block codes capable of being efficiently decoded is of major concern, especially for short block lengths. As near capacity-approaching codes, Low-Density Parity-Check (LDPC) codes possess several advantages over other families of codes, the most notable being its efficient decoding via Belief Propagation. While many LDPC code design methods exist, the development of efficient sparse codes that meet the constraints of modern short code lengths and accommodate new channel models remains a challenge. In this work, we propose for the first time a gradient-based data-driven approach for the design of sparse codes. We develop locally optimal codes with respect to Belief Propagation decoding via the learning of the Factor graph under channel noise simulations. This is performed via a novel complete graph tensor representation of the Belief Propagation algorithm, optimized over finite fields via backpropagation and coupled with an efficient line-search method. The proposed approach is shown to outperform the decoding performance of existing popular codes by orders of magnitude and demonstrates the power of data-driven approaches for code design.