{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,13]],"date-time":"2026-05-13T08:53:30Z","timestamp":1778662410914,"version":"3.51.4"},"reference-count":65,"publisher":"Institute of Electrical and Electronics Engineers (IEEE)","issue":"7","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["IEEE Trans. Inform. Theory"],"published-print":{"date-parts":[[2012,7]]},"DOI":"10.1109\/tit.2012.2191697","type":"journal-article","created":{"date-parts":[[2012,4,20]],"date-time":"2012-04-20T16:02:12Z","timestamp":1334937732000},"page":"4753-4769","source":"Crossref","is-referenced-by-count":26,"title":["Mathematical Programming Decoding of Binary Linear Codes: Theory and Algorithms"],"prefix":"10.1109","volume":"58","author":[{"given":"Michael","family":"Helmling","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Stefan","family":"Ruzika","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ak\u0131n","family":"Tanatmis","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"263","reference":[{"key":"ref39","author":"ahuja","year":"1993","journal-title":"Network Flows"},{"key":"ref38","doi-asserted-by":"publisher","DOI":"10.1109\/TCOMM.2009.09.070521"},{"key":"ref33","doi-asserted-by":"publisher","DOI":"10.1016\/0022-0000(91)90024-Y"},{"key":"ref32","first-page":"460","article-title":"LP decoding achieves capacity","author":"feldman","year":"2005","journal-title":"Proc 16th Annu ACM-SIAM Symp Discrete Algorithms"},{"key":"ref31","doi-asserted-by":"publisher","DOI":"10.1109\/18.910573"},{"key":"ref30","doi-asserted-by":"publisher","DOI":"10.1109\/TIT.1962.1057683"},{"key":"ref37","doi-asserted-by":"publisher","DOI":"10.1109\/26.539767"},{"key":"ref36","doi-asserted-by":"publisher","DOI":"10.1109\/JSAC.2006.879405"},{"key":"ref35","first-page":"1546","article-title":"Pseudo-codeword landscape","author":"chertkov","year":"2007","journal-title":"Proc IEEE Int Symp Inf Theory"},{"key":"ref34","doi-asserted-by":"publisher","DOI":"10.1109\/TIT.2007.915712"},{"key":"ref60","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevE.73.065102"},{"key":"ref62","doi-asserted-by":"publisher","DOI":"10.1109\/ITW.2007.4313079"},{"key":"ref61","doi-asserted-by":"publisher","DOI":"10.1088\/1742-5468\/2006\/06\/P06009"},{"key":"ref63","first-page":"991","article-title":"On the relationship between linear programming decoding and min-sum algorithm decoding","author":"vontobel","year":"2004","journal-title":"Proc Int Symp Inf Theory"},{"key":"ref28","doi-asserted-by":"publisher","DOI":"10.1109\/TIT.2009.2023735"},{"key":"ref64","doi-asserted-by":"publisher","DOI":"10.1109\/TIT.2005.850085"},{"key":"ref27","author":"schrijver","year":"1986","journal-title":"Theory of Linear and Integer Programming"},{"key":"ref65","doi-asserted-by":"publisher","DOI":"10.1109\/TIT.2007.915695"},{"key":"ref29","doi-asserted-by":"publisher","DOI":"10.1137\/1.9780898718805.ch8"},{"key":"ref2","doi-asserted-by":"publisher","DOI":"10.1109\/TIT.2004.842696"},{"key":"ref1","author":"feldman","year":"2003","journal-title":"Decoding error-correcting codes via linear programming"},{"key":"ref20","doi-asserted-by":"publisher","DOI":"10.1016\/0095-8956(80)90075-1"},{"key":"ref22","doi-asserted-by":"publisher","DOI":"10.1109\/LCOMM.2008.080713"},{"key":"ref21","doi-asserted-by":"publisher","DOI":"10.1109\/TIT.2009.2025571"},{"key":"ref24","author":"vontobel","year":"2005","journal-title":"Graph-Cover Decoding and Finite-Length Analysis of Message-Passing Iterative Decoding of LDPC Codes"},{"key":"ref23","author":"lin","year":"2004","journal-title":"Error Control Coding"},{"key":"ref26","doi-asserted-by":"publisher","DOI":"10.1109\/ISIT.2011.6033824"},{"key":"ref25","doi-asserted-by":"crossref","first-page":"101","DOI":"10.1007\/978-1-4613-0165-3_5","volume":"123","author":"forney jr","year":"2001","journal-title":"Codes Systems and Graphical Models"},{"key":"ref50","doi-asserted-by":"publisher","DOI":"10.1109\/ISIT.2009.5205741"},{"key":"ref51","doi-asserted-by":"publisher","DOI":"10.1007\/BF02579150"},{"key":"ref59","article-title":"Loop calculus helps to improve belief propagation and linear programming decodings of low-density-parity-check codes","author":"chertkov","year":"2006","journal-title":"presented at the 44th Allerton Conf Commun Control Comput"},{"key":"ref58","doi-asserted-by":"publisher","DOI":"10.1109\/ISIT.2007.4557459"},{"key":"ref57","doi-asserted-by":"publisher","DOI":"10.1109\/TCOMM.2011.122110.090729"},{"key":"ref56","doi-asserted-by":"publisher","DOI":"10.1109\/TIT.2004.838370"},{"key":"ref55","doi-asserted-by":"publisher","DOI":"10.1109\/TIT.2010.2048489"},{"key":"ref54","doi-asserted-by":"publisher","DOI":"10.1109\/JSAC.2009.090818"},{"key":"ref53","doi-asserted-by":"publisher","DOI":"10.1016\/0024-3795(89)90478-3"},{"key":"ref52","doi-asserted-by":"publisher","DOI":"10.1137\/0801013"},{"key":"ref10","doi-asserted-by":"publisher","DOI":"10.1109\/TIT.1978.1055873"},{"key":"ref11","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4684-2001-2_9"},{"key":"ref40","doi-asserted-by":"publisher","DOI":"10.1016\/j.jcss.2003.11.005"},{"key":"ref12","doi-asserted-by":"publisher","DOI":"10.1109\/18.641542"},{"key":"ref13","first-page":"291","author":"welsh","year":"1971","journal-title":"Combinatorial Mathematics and its Applications"},{"key":"ref14","author":"oxley","year":"1992","journal-title":"Matroid Theory"},{"key":"ref15","author":"welsh","year":"1976","journal-title":"Matroid Theory"},{"key":"ref16","doi-asserted-by":"publisher","DOI":"10.1109\/TIT.2008.924700"},{"key":"ref17","doi-asserted-by":"publisher","DOI":"10.1016\/0095-8956(86)90063-8"},{"key":"ref18","article-title":"On the convex geometry of binary linear codes","author":"kashyap","year":"2006","journal-title":"presented at the Inaugural UC San Diego Workshop Inf Theory Appl"},{"key":"ref19","doi-asserted-by":"publisher","DOI":"10.1016\/0095-8956(89)90052-X"},{"key":"ref4","doi-asserted-by":"publisher","DOI":"10.1109\/18.825794"},{"key":"ref3","doi-asserted-by":"publisher","DOI":"10.1109\/18.910572"},{"key":"ref6","doi-asserted-by":"publisher","DOI":"10.1109\/MSP.2004.1267047"},{"key":"ref5","author":"wiberg","year":"1996","journal-title":"Codes and decoding on general graphs"},{"key":"ref8","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-642-97881-4","author":"grtschel","year":"1988","journal-title":"Geometric Algorithms and Combinatorial Optimization"},{"key":"ref7","doi-asserted-by":"publisher","DOI":"10.1002\/9781118627372"},{"key":"ref49","doi-asserted-by":"publisher","DOI":"10.1109\/ITA.2008.4601085"},{"key":"ref9","doi-asserted-by":"publisher","DOI":"10.1002\/ett.4460090308"},{"key":"ref46","doi-asserted-by":"publisher","DOI":"10.1002\/ett.1184"},{"key":"ref45","doi-asserted-by":"publisher","DOI":"10.1109\/TIT.2011.2161920"},{"key":"ref48","author":"bertsimas","year":"1997","journal-title":"Parallel and Distributed Computation Numerical Methods"},{"key":"ref47","doi-asserted-by":"publisher","DOI":"10.1109\/TIT.2009.2030477"},{"key":"ref42","doi-asserted-by":"publisher","DOI":"10.1109\/ISTC.2010.5613869"},{"key":"ref41","doi-asserted-by":"publisher","DOI":"10.1109\/TIT.2004.839509"},{"key":"ref44","doi-asserted-by":"publisher","DOI":"10.1109\/TIT.2008.2006384"},{"key":"ref43","first-page":"369","article-title":"A Lagrangian relaxation based decoding algorithm for LTE turbo codes","author":"tanatmis","year":"2010","journal-title":"Proc 6th Int Symp Turbo Codes Iter Inf Proc"}],"container-title":["IEEE Transactions on Information Theory"],"original-title":[],"link":[{"URL":"http:\/\/xplorestaging.ieee.org\/ielx5\/18\/6216490\/06187728.pdf?arnumber=6187728","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2017,11,14]],"date-time":"2017-11-14T02:18:44Z","timestamp":1510625924000},"score":1,"resource":{"primary":{"URL":"http:\/\/ieeexplore.ieee.org\/document\/6187728\/"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2012,7]]},"references-count":65,"journal-issue":{"issue":"7"},"URL":"https:\/\/doi.org\/10.1109\/tit.2012.2191697","relation":{},"ISSN":["0018-9448","1557-9654"],"issn-type":[{"value":"0018-9448","type":"print"},{"value":"1557-9654","type":"electronic"}],"subject":[],"published":{"date-parts":[[2012,7]]}}}