An Iterative Check Polytope Projection Algorithm for ADMM-Based LP Decoding of LDPC Codes

Wei, Haoyuan; Banihashemi, Amir H.

doi:10.1109/lcomm.2017.2766223

Cited by 47 publications

(57 citation statements)

References 13 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%

“…In the end, as for the conventional sum-product BP decoder, it costs d(2d − 2) multiplications and d(d − 1) hyperbolic tangent operations for updating each check node and hence its per-iteration complexity is about O(md 2 ). From the above analysis, it is clear that computational complexity per iteration of the proposed ADMM-QP decoder is cheaper than state-of-the-art MP decoders [32] [33] [35] [41] [44] and is comparable to the conventional sum-product BP decoder in [5].…”

Section: Decoding Algorithmmentioning

confidence: 99%

“…In [34], authors designed a hardware compatible projection onto the check polytope by combing the methods in [32] and [33]. In [35], an iterative check projection algorithm to reduce the complexity of the projection operation was proposed. Authors in [36] simplified the check projection operation by jointly using uniform quantization and look-up tables.…”

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: Decoding Algorithmmentioning

confidence: 99%

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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“…(5c) III. LEARNED ADMM DECODER In this section, we first review the ADMM-penalized decoder to address problem (5), and then we present a detailed description of the proposed LADN and its improved versions. Finally, we provide the loss function of the proposed networks, which is essential to achieve better decoding performance.…”

Section: B Cascaded Formulation Of Pc Constraintsmentioning

confidence: 99%

“…The essence of the ADMM-penalized decoder is the introduction of a penalty term to the linear objective of the LP decoding problem, with the intent of suppressing the pseudocodewords. In order to put problem (5) in the standard ADMM framework, an auxiliary variable z is first added to constraint (5b), and consequently, problem (5) can be equivalently formulated as the following optimization problem:…”

Section: A Admm-penalized Decodermentioning

confidence: 99%

ADMM-Based Decoder for Binary Linear Codes Aided by Deep Learning

2020

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Inspired by the recent advances in deep learning (DL), this work presents a deep neural network aided decoding algorithm for binary linear codes. Based on the concept of deep unfolding, we design a decoding network by unfolding the alternating direction method of multipliers (ADMM)-penalized decoder. In addition, we propose two improved versions of the proposed network. The first one transforms the penalty parameter into a set of iteration-dependent ones, and the second one adopts a specially designed penalty function, which is based on a piecewise linear function with adjustable slopes. Numerical results show that the resulting DL-aided decoders outperform the original ADMM-penalized decoder for various low density parity check (LDPC) codes with similar computational complexity.

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