{"title":"List-based Optimization of Proximal Decoding for LDPC Codes","authors":"Andreas Tsouchlos, Holger Jäkel, Laurent Schmalen","doi":"arxiv-2409.07278","DOIUrl":null,"url":null,"abstract":"In this paper, the proximal decoding algorithm is considered within the\ncontext of additive white Gaussian noise (AWGN) channels. An analysis of the\nconvergence behavior of the algorithm shows that proximal decoding inherently\nenters an oscillating behavior of the estimate after a certain number of\niterations. Due to this oscillation, frame errors arising during decoding can\noften be attributed to only a few remaining wrongly decoded bit positions. In\nthis letter, an improvement of the proximal decoding algorithm is proposed by\nestablishing an additional step, in which these erroneous positions are\nattempted to be corrected. We suggest an empirical rule with which the\ncomponents most likely needing correction can be determined. Using this insight\nand performing a subsequent ``ML-in-the-list'' decoding, a gain of up to 1 dB\nis achieved compared to conventional proximal decoding, depending on the\ndecoder parameters and the code.","PeriodicalId":501082,"journal":{"name":"arXiv - MATH - Information Theory","volume":"20 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-09-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv - MATH - Information Theory","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2409.07278","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
Abstract
In this paper, the proximal decoding algorithm is considered within the
context of additive white Gaussian noise (AWGN) channels. An analysis of the
convergence behavior of the algorithm shows that proximal decoding inherently
enters an oscillating behavior of the estimate after a certain number of
iterations. Due to this oscillation, frame errors arising during decoding can
often be attributed to only a few remaining wrongly decoded bit positions. In
this letter, an improvement of the proximal decoding algorithm is proposed by
establishing an additional step, in which these erroneous positions are
attempted to be corrected. We suggest an empirical rule with which the
components most likely needing correction can be determined. Using this insight
and performing a subsequent ``ML-in-the-list'' decoding, a gain of up to 1 dB
is achieved compared to conventional proximal decoding, depending on the
decoder parameters and the code.