{"title":"ML decoding via mixed-integer adaptive linear programming","authors":"S. Draper, J. Yedidia, Yige Wang","doi":"10.1109/ISIT.2007.4557459","DOIUrl":null,"url":null,"abstract":"Linear programming (LP) decoding was introduced by Feldman et al. (IEEE Trans. Inform. Theory Mar. 2005) as a novel way to decode binary low-density parity-check codes. Taghavi and Siegel (Proc. ISIT 2006) describe a computationally simplified decoding approach they term \"adaptive\" LP decoding. Adaptive LP decoding starts with a sub-set of the LP constraints, and iteratively adds violated constraints until an optimum of the original LP is found. Usually only a tiny fraction of the original constraints need to be reinstated, leading to huge efficiency gains compared to ordinary LP decoding. Here we describe a modification of the adaptive LP decoder that results in a maximum likelihood (ML) decoder. Whenever the adaptive LP decoder returns a pseudo-codeword rather than a codeword, we add an integer constraint on the least certain symbol of the pseudo-codeword. For certain codes, and especially in the high-SNR (error floor) regime, only a few integer constraints are required to force the resultant mixed-integer LP to the ML solution. We demonstrate that our approach can efficiently achieve the optimal ML decoding performance on a (155,64) LDPC code introduced by Tanner et al.","PeriodicalId":193467,"journal":{"name":"2007 IEEE International Symposium on Information Theory","volume":"58 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2007-06-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"43","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"2007 IEEE International Symposium on Information Theory","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1109/ISIT.2007.4557459","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 43
Abstract
Linear programming (LP) decoding was introduced by Feldman et al. (IEEE Trans. Inform. Theory Mar. 2005) as a novel way to decode binary low-density parity-check codes. Taghavi and Siegel (Proc. ISIT 2006) describe a computationally simplified decoding approach they term "adaptive" LP decoding. Adaptive LP decoding starts with a sub-set of the LP constraints, and iteratively adds violated constraints until an optimum of the original LP is found. Usually only a tiny fraction of the original constraints need to be reinstated, leading to huge efficiency gains compared to ordinary LP decoding. Here we describe a modification of the adaptive LP decoder that results in a maximum likelihood (ML) decoder. Whenever the adaptive LP decoder returns a pseudo-codeword rather than a codeword, we add an integer constraint on the least certain symbol of the pseudo-codeword. For certain codes, and especially in the high-SNR (error floor) regime, only a few integer constraints are required to force the resultant mixed-integer LP to the ML solution. We demonstrate that our approach can efficiently achieve the optimal ML decoding performance on a (155,64) LDPC code introduced by Tanner et al.