Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

IEICE Transactions on Fundamentals of Electronics Communications and Computer Sciences

Early Termination Criterion of ADMM-LP Decoder for LDPC Codes

Ruirui XUE, Biao Wang, Zhongfei Wang

Published Oct 23, 2025• 0 citations
Publisher

Abstract

In order to terminate iterations earlier of the linear programming (LP) decoder based on the alternating direction method of multipliers (ADMM) (ADMM-LP), this letter proposes an early termination (ET) criterion based on the number of parity-check constraints of iterative solution vector. The criterion can be used to detect erroneous codewords in advance and thereby avoid unnecessary iterations, without increasing the additional computational complexity. Compared with existing termination criteria of ADMM-LP decoding algorithm, the proposed ET criterion can significantly reduce the average number of iterations at low signal-to-noise ratio (SNR) regions with little effect on the decoding performance.

DOI
10.1587/transfun.2025eal2070

Related papers

Efficient Early Termination Criterion for ADMM Penalized LDPC Decoder

Biao Wang, Xiaopeng Jiao, Jianjun Mu +1 more

By tracking the changing rate of hard decisions during every two consecutive iterations of the alternating direction method of multipliers (ADMM) penalized decoding, an efficient early termination (ET) criterion is proposed to improve the convergence rate of ADMM penalized decoder for low-density parity-check (LDPC) codes. Compared to the existing ET criterion for ADMM penalized decoding, the proposed method can reduce the average number of iterations significantly at low signal-to-noise ratios with negligible performance degradation.

IEICE Transactions on Fundamentals of Electronics Communications and Computer Sciences•Jan 1, 2018•2 citations

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

Haoyuan Wei, Xiaopeng Jiao, Jianjun Mu

The Euclidean projection onto check polytopes is the most time-consuming operation in the linear programming (LP) decoding based on alternating direction method of multipliers (ADMM) for low-density parity-check (LDPC) codes. In this letter, instead of reducing the complexity of Euclidean projection itself, we propose a new method to reduce the decoding complexity of ADMM-based LP decoder by decreasing the number of Euclidean projections. In particular, if all absolute values of the element-wise differences between the input vector of Euclidean projection in the current iteration and that in the previous iteration are less than a predefined value, then the Euclidean projection at the current iteration will be no longer performed. Simulation results show that the proposed decoder can still save roughly 20% decoding time even if both the over-relaxation and early termination techniques are used.

IEEE Communications Letters•Apr 1, 2015•51 citations

Novel Early Termination Method of an ADMM-Penalized Decoder for LDPC Codes in the IoT

Biao Wang

As a critical communication technology, low-density parity-check (LDPC) codes are widely concerned with the Internet of things (IoT). To increase the convergence rate of the alternating direction method of multiplier (ADMM)-penalized decoder for LDPC codes, a novel early termination (ET) method is presented by computing the average sum of the hard decision (ASHD) during each ADMM iteration. In terms of the flooding scheduling and layered scheduling ADMM-penalized decoders, the simulation results show that the proposed ET method can significantly reduce the average number of iterations at low signal-to-noise ratios (SNRs) with negligible decoding performance loss.

Security and Communication Networks•Oct 14, 2022•0 citations

Low-Density Parity-Check Decoding Algorithm Based on Symmetric Alternating Direction Method of Multipliers

Ji Zhang, Anmin Chen, Ying Zhang +3 more

The Alternating Direction Method of Multipliers (ADMM) has proven to be an efficient approach for implementing linear programming (LP) decoding of low-density parity-check (LDPC) codes. By introducing penalty terms into the LP decoding model's objective function, ADMM-based variable node penalized decoding effectively mitigates non-integral solutions, thereby improving frame error rate (FER) performance, especially in the low signal-to-noise ratio (SNR) region. In this paper, we leverage the ADMM framework to derive explicit iterative steps for solving the LP decoding problem for LDPC codes with penalty functions. To further enhance decoding efficiency and accuracy, We propose an LDPC code decoding algorithm based on the symmetric ADMM (S-ADMM). We also establish some contraction properties satisfied by the iterative sequence of the algorithm. Through simulation experiments, we evaluate the proposed S-ADMM decoder using three standard LDPC codes and three representative fifth-generation (5G) codes. The results show that the S-ADMM decoder consistently outperforms conventional ADMM penalized decoders, offering significant improvements in decoding performance.

Entropy•Apr 9, 2025•1 citation

ADMM Check Node Penalized Decoders for LDPC Codes

Haoyuan Wei, Amir H. Banihashemi

Alternating direction method of multipliers (ADMM) is an efficient implementation of linear programming (LP) decoding for low-density parity-check (LDPC) codes. By adding penalty terms to the objective function of the LP decoding model, ADMM variable node (VN) penalized decoding can suppress the non-integral solutions and improve the frame error rate (FER) performance in the low signal-to-noise ratio (SNR) region. In this paper, we propose a novel ADMM check node (CN) penalized decoding algorithm. Codeword solutions which satisfy all parity-check equations will have smaller penalty values than non-codeword solutions, including the non-integral solutions. We discuss the required properties of CN-penalty functions, propose a few functions that satisfy those properties, and study their performance/complexity trade-offs. We also investigate the convergence properties of the proposed algorithm and prove that its performance is independent of the transmitted codeword. Using Monte Carlo simulations and instanton analysis, we then demonstrate that the proposed CN-penalized decoder outperforms ADMM VN penalized decoders in both waterfall and error floor regions. This comes at the expense of some increase in the decoding complexity.

IEEE Transactions on Communications•Mar 15, 2021•14 citations

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

Haoyuan Wei, Amir H. Banihashemi

Alternating direction method of multipliers (ADMM) is a popular technique for linear-programming decoding of low-density parity-check codes. The computational complexity of ADMM is dominated by the Euclidean projection of a real-valued vector onto a parity-check polytope. Existing algorithms for such a projection all require sorting operations, which happen to be the most complex part of the projection. In this letter, we propose an iterative algorithm, without sorting operation, for projection onto the parity-check polytope. The proposed algorithm has a worst case complexity linear in the input dimension compared with the super-linear complexity of existing algorithms.

IEEE Communications Letters•Oct 25, 2017•50 citations
In order to terminate iterations earlier of the linear programming (LP) decoder based on the alternating direction method of multipliers (ADMM) (ADMM-LP), this letter proposes an early termination (ET) criterion based on the number of parity-check constraints of iterative solution vector. The criterion can be used to detect erroneous codewords in advance and thereby avoid unnecessary iterations, without increasing the additional computational complexity. Compared with existing termination criteria of ADMM-LP decoding algorithm, the proposed ET criterion can significantly reduce the average number of iterations at low signal-to-noise ratio (SNR) regions with little effect on the decoding performance.
By tracking the changing rate of hard decisions during every two consecutive iterations of the alternating direction method of multipliers (ADMM) penalized decoding, an efficient early termination (ET) criterion is proposed to improve the convergence rate of ADMM penalized decoder for low-density parity-check (LDPC) codes. Compared to the existing ET criterion for ADMM penalized decoding, the proposed method can reduce the average number of iterations significantly at low signal-to-noise ratios with negligible performance degradation.
The Euclidean projection onto check polytopes is the most time-consuming operation in the linear programming (LP) decoding based on alternating direction method of multipliers (ADMM) for low-density parity-check (LDPC) codes. In this letter, instead of reducing the complexity of Euclidean projection itself, we propose a new method to reduce the decoding complexity of ADMM-based LP decoder by decreasing the number of Euclidean projections. In particular, if all absolute values of the element-wise differences between the input vector of Euclidean projection in the current iteration and that in the previous iteration are less than a predefined value, then the Euclidean projection at the current iteration will be no longer performed. Simulation results show that the proposed decoder can still save roughly 20% decoding time even if both the over-relaxation and early termination techniques are used.
As a critical communication technology, low-density parity-check (LDPC) codes are widely concerned with the Internet of things (IoT). To increase the convergence rate of the alternating direction method of multiplier (ADMM)-penalized decoder for LDPC codes, a novel early termination (ET) method is presented by computing the average sum of the hard decision (ASHD) during each ADMM iteration. In terms of the flooding scheduling and layered scheduling ADMM-penalized decoders, the simulation results show that the proposed ET method can significantly reduce the average number of iterations at low signal-to-noise ratios (SNRs) with negligible decoding performance loss.
The Alternating Direction Method of Multipliers (ADMM) has proven to be an efficient approach for implementing linear programming (LP) decoding of low-density parity-check (LDPC) codes. By introducing penalty terms into the LP decoding model's objective function, ADMM-based variable node penalized decoding effectively mitigates non-integral solutions, thereby improving frame error rate (FER) performance, especially in the low signal-to-noise ratio (SNR) region. In this paper, we leverage the ADMM framework to derive explicit iterative steps for solving the LP decoding problem for LDPC codes with penalty functions. To further enhance decoding efficiency and accuracy, We propose an LDPC code decoding algorithm based on the symmetric ADMM (S-ADMM). We also establish some contraction properties satisfied by the iterative sequence of the algorithm. Through simulation experiments, we evaluate the proposed S-ADMM decoder using three standard LDPC codes and three representative fifth-generation (5G) codes. The results show that the S-ADMM decoder consistently outperforms conventional ADMM penalized decoders, offering significant improvements in decoding performance.
Alternating direction method of multipliers (ADMM) is an efficient implementation of linear programming (LP) decoding for low-density parity-check (LDPC) codes. By adding penalty terms to the objective function of the LP decoding model, ADMM variable node (VN) penalized decoding can suppress the non-integral solutions and improve the frame error rate (FER) performance in the low signal-to-noise ratio (SNR) region. In this paper, we propose a novel ADMM check node (CN) penalized decoding algorithm. Codeword solutions which satisfy all parity-check equations will have smaller penalty values than non-codeword solutions, including the non-integral solutions. We discuss the required properties of CN-penalty functions, propose a few functions that satisfy those properties, and study their performance/complexity trade-offs. We also investigate the convergence properties of the proposed algorithm and prove that its performance is independent of the transmitted codeword. Using Monte Carlo simulations and instanton analysis, we then demonstrate that the proposed CN-penalized decoder outperforms ADMM VN penalized decoders in both waterfall and error floor regions. This comes at the expense of some increase in the decoding complexity.
Alternating direction method of multipliers (ADMM) is a popular technique for linear-programming decoding of low-density parity-check codes. The computational complexity of ADMM is dominated by the Euclidean projection of a real-valued vector onto a parity-check polytope. Existing algorithms for such a projection all require sorting operations, which happen to be the most complex part of the projection. In this letter, we propose an iterative algorithm, without sorting operation, for projection onto the parity-check polytope. The proposed algorithm has a worst case complexity linear in the input dimension compared with the super-linear complexity of existing algorithms.