Reduced-Complexity Linear Programming Decoding Based on ADMM for LDPC Codes

Wei, Haoyuan; Jiao, Xiaopeng; Mu, Jianjun

doi:10.1109/lcomm.2015.2418261

Cited by 51 publications

(21 citation statements)

References 8 publications

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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%

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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%

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

Bai

Wang

Shi

2020

IEEE Trans. Signal Process.

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“…Jiao et al modified penalization to improve error-rate performance of irregular LDPC codes [24]. Finally, Wei et al implemented ADMM-LP avoiding projections when possible [25].…”

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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“…In fact, the projection on parity check polytope is the most computationally intensive part of the whole decoding process. To deal with the problem of high computational complexity of projection, Wei et al proposed the reduction of useless projection in [2]. Besides, Jiao et al suggested increasing the projection efficiency using the look-up table to reduce the projection operation [3].…”

Section: Introductionmentioning

confidence: 99%

A Fast Iterative Check Polytope Projection Algorithm for ADMM Decoding of LDPC Codes by Bisection Method

Lin

Xia

et al. 2019

IEICE Trans. Fundamentals

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Using linear programming (LP) decoding based on alternating direction method of multipliers (ADMM) for low-density paritycheck (LDPC) codes shows lower complexity than the original LP decoding. However, the development of the ADMM-LP decoding algorithm could still be limited by the computational complexity of Euclidean projections onto parity check polytope. In this paper, we proposed a bisection method iterative algorithm (BMIA) for projection onto parity check polytope avoiding sorting operation and the complexity is linear. In addition, the convergence of the proposed algorithm is more than three times as fast as the existing algorithm, which can even be 10 times in the case of high input dimension.

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Reduced-Complexity Linear Programming Decoding Based on ADMM for LDPC Codes

Cited by 51 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

A Fast Iterative Check Polytope Projection Algorithm for ADMM Decoding of LDPC Codes by Bisection Method

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