Fast Converging ADMM-Penalized Algorithm for LDPC Decoding

Debbabi, Imen; Gal, Bertrand Le; Khouja, Nadia; Tlili, Fethi; Jégo, Christophe

doi:10.1109/lcomm.2016.2531040

Cited by 34 publications

(15 citation statements)

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“…from auxiliary variables introduced to the three-variables parity-equations. • Compared with the state-of-the-art works [31]- [33], [35], [37]- [39] and [41]- [44], the proposed ADMM algorithm is free of the complex Euclidean projection on each check polytope. From (17), it is easy to see that updating the variables in z only requires a simple Euclidean projection onto the positive quadrant.…”

Section: B Admm Algorithm Frameworkmentioning

confidence: 99%

“…Authors in [36] simplified the check projection operation by jointly using uniform quantization and look-up tables. Moreover, a projection reduction method [37] and two different approaches based on node-wise scheduling and horizontal-layered scheduling in [38] and [39] respectively were proposed to reduce the decoding complexity by decreasing the number of projections. Furthermore, authors in [40] introduced an efficient ADMM-based LP decoding algorithm, which can eliminate the expensive projection operation onto the check polytope.…”

Section: Introductionmentioning

confidence: 99%

“…By combining ideas of relaxation of the three-variables parity-check equation in [21], quadratic penalty in [41] and LP decoder in [40] respectively, we obtain a new decoder, called QP-ADMM, for LDPC codes, which has favorable error correction performance meanwhile providing cheap linear complexity in terms of LDPC code length. The main technical contributions of this paper are twofold: 1) Efficient implementation: compared with the state-ofthe-art ADMM-based MP decoders [32]- [39] and [41]- [45], the main novelty of the proposed QP-ADMM decoder is the reduction of the Euclidean projections onto check polytopes to simple Euclidean projections onto positive quadrant. Moreover, all the variables are solved analytically and updated in parallel in each ADMM step.…”

Section: Introductionmentioning

confidence: 99%

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Efficient QP-ADMM Decoder for Binary LDPC Codes and Its Performance Analysis

Bai

Wang

Shi

2020

IEEE Trans. Signal Process.

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This paper presents an efficient quadratic programming (QP) decoder via the alternating direction method of multipliers (ADMM) technique, called QP-ADMM, for binary low-density parity-check (LDPC) codes. Its main contents are as follows: first, we relax maximum likelihood (ML) decoding problem to a non-convex quadratic program. Then, we develop an ADMM solving algorithm for the formulated non-convex QP decoding model. In the proposed QP-ADMM decoder, complex Euclidean projections onto the check polytope are eliminated and variables in each updated step can be solved analytically in parallel. Moreover, it is proved that the proposed ADMM algorithm converges to a stationary point of the non-convex QP problem under the assumption of sequence convergence. We also verify that the proposed decoder satisfies the favorable property of the all-zeros assumption. Furthermore, by exploiting the inside structures of the QP model, the complexity of the proposed algorithm in each iteration is shown to be linear in terms of LDPC code length. Simulation results demonstrate the effectiveness of the proposed QP-ADMM decoder.

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Section: B Admm Algorithm Frameworkmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Efficient QP-ADMM Decoder for Binary LDPC Codes and Its Performance Analysis

Bai

Wang

Shi

2020

IEEE Trans. Signal Process.

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“…Several implementation papers have also considered ADMM-LP decoding in other contexts. Debbabi et al investigated how to schedule messages more efficiently and developed a multicore implementation [22], [23]. Jiao et al modified penalization to improve error-rate performance of irregular LDPC codes [24].…”

Section: Introductionmentioning

confidence: 99%

Hardware-Based Linear Program Decoding With the Alternating Direction Method of Multipliers

Wasson

Milicevic

Draper

et al. 2019

IEEE Trans. Signal Process.

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We present a hardware-based implementation of Linear Program (LP) decoding for binary linear codes. LP decoding frames error-correction as an optimization problem. In contrast, variants of Belief Propagation (BP) decoding frame error-correction as a problem of graphical inference. LP decoding has several advantages over BP-based methods, including convergence guarantees and better error-rate performance in high-reliability channels. The latter makes LP decoding attractive for optical transport and storage applications. However, LP decoding, when implemented with general solvers, does not scale to large blocklengths and is not suitable for a parallelized implementation in hardware. It has been recently shown that the Alternating Direction Method of Multipliers (ADMM) can be applied to decompose the LP decoding problem. The result is a message-passing algorithm with a structure very similar to BP. We present new intuition for this decoding algorithm as well as for its major computational primitive: projection onto the parity polytope. Furthermore, we present results for a fixed-point Verilog implementation of ADMM-LP decoding. This implementation targets a Field-Programmable Gate Array (FPGA) platform to evaluate error-rate performance and estimate resource usage. We show that Frame Error Rate (FER) performance well within 0.5dB of double-precision implementations is possible with 10-bit messages. Finally, we outline a number of research opportunities that should be explored en-route to the realization of an Application Specific Integrated Circuit (ASIC) implementation capable of gigabit per second throughput.

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“…There are also works simplifying ADMM decoding from other aspects. For example, layered scheduling was successfully applied to ADMM decoding [51], and it achieved a faster convergence speed than the flooding scheme in [33]. We note that it is also possible to apply other scheduling schemes [52][53][54][55][56][57][58][59][60][61] proposed for BP decoders on ADMM decoding.…”

Section: Complexity Reduction Of Admm Decodingmentioning

confidence: 97%

ADMM Decoding of LDPC Codes: Simplification and Improvement

Wei¹

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In this dissertation, we study linear programming (LP) decoding of low-density parity-check (LDPC) codes based on the alternating direction method of multipliers (ADMM) technique, or ADMM decoding for short. The decoding of LDPC codes is formulated as an LP model and solved efficiently by the ADMM technique. However, compared with traditional belief-propagation decoding, ADMM decoding suffers from higher complexity and worse error correction performance, which prevents the employment of ADMM decoding in reality.To reduce the complexity of ADMM decoding, we first focus on the simplification of the check polytope projection, the most complex operation in ADMM decoding. We propose an iterative check polytope projection algorithm without the sorting operation. The proposed algorithm converges with the increase of iterations. Moreover, for a fixed number of iterations, its average complexity and the worst-case complexity are linear in the input dimension.Another direction we propose to simplify ADMM decoding is to devise a better scheduling scheme than the standard flooding scheme. We start from the node-wise scheduling scheme which only updates the check node messages with the maximum message residual. Then we simplify the calculation of the message residual and propose a reduced-complexity node-wise scheduling scheme.To improve the error correction performance of ADMM decoding, we propose a novel ADMM penalized decoding algorithm whose penalty term is based on check nodes (CN). We investigate the properties of the CN penalty functions and show several examples. We make conclusions on its convergence properties and prove its failure probability is independent of the transmitted codewords for symmetric channels. Monte-Carlo simulation and the instanton analysis show its better error correction performance in the low and high SNR regions.Finally, we propose a post-processing technique to lower the error floor of LDPC codes. The output of the first stage decoder can be revised if the syndrome is found This is a journey with joys and tears. I encountered many amazing people. They instructed me, helped me, and accompanied me.First of all, I would like to thank Prof. Amir H. Banihashemi for his guidance. His attitudes towards the research and devotion to one specific area are impressive. All these will have a life-long influence on me. It is also a great time working with people in his coding research group. I have a great memory of learning from their presentations.Next, I should thank Prof. Xiaopeng Jiao and Prof. Jianjun Mu from Xidian University. They offered me suggestions both in work and life even if we cannot meet with each other as before. More importantly, their encouragement always made me full of confidence in the future.I would like to thank my committee members. Especially, Prof. Ian Marsland kindly reviewed my draft more than once and helped improve the quality of the dissertation significantly. It is a wonderful experience to discuss with him. Prof. Yongyi Mao spared time from his busy schedule for my defen...

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Fast Converging ADMM-Penalized Algorithm for LDPC Decoding

Cited by 34 publications

References 8 publications

Efficient QP-ADMM Decoder for Binary LDPC Codes and Its Performance Analysis

Efficient QP-ADMM Decoder for Binary LDPC Codes and Its Performance Analysis

Hardware-Based Linear Program Decoding With the Alternating Direction Method of Multipliers

ADMM Decoding of LDPC Codes: Simplification and Improvement

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