基于Nesterov动量加速的ADMM译码算法
ADMM Decoding Algorithm Based on Nesterov Momentum Acceleration
摘要
Abstract
The alternating direction method of multipliers(ADMM)algorithm has emerged as an innovative decoding solution for 5G low-density parity-check(LDPC)codes,leveraging two key features:geometrically-aware processing of linear programming(LP)decoding constraints and efficient implementation of message passing mechanisms.By incorporating a penalty term into the objective function of the LP decoding model,ADMM-based variable node penalty decoding effectively mitigates non-integral decomposition,thereby enhancing frame error rate(FER)performance.De-spite the strong performance of ADMM in various practical applications,its relatively slow convergence speed and sensi-tivity to initial conditions and parameter tuning hinder its effectiveness in high-dimensional and real-time demanding sce-narios.In particular,during the LDPC linear programming decoding process,the alternating update mechanism of ADMM can result in oscillation along the optimization path and exhibit suboptimal performance when handling impre-cise constraints.To address the issue of slow convergence of the ADMM algorithm,we proposed a new optimization al-gorithm that integrates Nesterov momentum acceleration with ADMM.This approach aims to mitigate the impact of the ADMM algorithm on the error correction performance and convergence speed of LDPC decoders.By introducing a mo-mentum term,the algorithm reduces the number of iterations and extends Nesterov's accelerated scheme from uncon-strained composite optimization problems to the ADMM penalty function model.First,the ADMM algorithm was em-ployed to effectively reformulate the constraints of the original problem as a component of the objective function,thereby transforming it into an unconstrained optimization subproblem.Building on this foundation,Nesterov accelera-tion technology was further used to enhance the gradient descent iteration process to improve both convergence speed and solution accuracy.Simulation experiments were conducted using three different rates of 5G LDPC short codes.Com-pared to existing ADMM-based penalty decoding algorithms,the proposed momentum-accelerated ADMM decoding al-gorithm achieved a signal-to-noise rate gain of approximately 0.2 dB and reduced the average number of iterations by ap-proximately 20%,thereby accelerating the convergence speed.关键词
线性规划译码/交替方向乘子法译码/动量加速/梯度下降Key words
linear programming decoding/alternating direction multiplier decoder/momentum acceleration/gradient descent分类
信息技术与安全科学引用本文复制引用
张冀,陈安民,冀保峰..基于Nesterov动量加速的ADMM译码算法[J].信号处理,2025,41(7):1255-1263,9.基金项目
国家重点研发计划(2024YFB2907700) （2024YFB2907700）
国家自然科学基金(62271192,62172142) （62271192,62172142）
河南省重大科技专项(231100220400,231100220300) （231100220400,231100220300）
中原科技创新领军人才项目(244200510048) （244200510048）
教育部智能群体系统工程研究中心开放基金(ZZU-CISS-2024003)National Key Research and Development Program(2024YFB2907700) （ZZU-CISS-2024003）
The National Natural Science Foundation of China(62271192,62172142) （62271192,62172142）
Major Science and Technology Projects in Henan Province(231100220400,231100220300) （231100220400,231100220300）
Central Plains Leading Talent in Scientific and Technological Innovation Program(244200510048) （244200510048）
Open Fund of the Intelligent Group System Engineering Research Center of the Ministry of Education(ZZU-CISS-2024003) （ZZU-CISS-2024003）
