{"paper":{"title":"Improved linear programming decoding of LDPC codes and bounds on the minimum and fractional distance","arxiv_id":"1012.1425","primary_cat":"cs.IT","submitted_at":"2010-12-07T07:59:47+00:00","version_compiled":"v1"},"notice":"Every quoted sentence is the authors' text from the arXiv listing abstract. Labels and probabilities are the outputs of classifier-1.13-20260917 on the question bank abstract-p1-20260923, exactly as returned. 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presented.","hedge":{"p":1.0,"label":"asserted"},"own_p":0.9,"main_claim_p":0.08,"quantitative":true,"quantitative_p":0.87,"role_probabilities":{"gap":0.0,"method":0.0,"result":0.0,"background":0.0,"limitation":0.0,"future_work":0.0,"contribution":1.0,"interpretation":0.0}},{"i":2,"p":1.0,"id":"s2","own":true,"role":"contribution","text":"First, a new method of tightening the LP relaxation, and thus improving the LP decoder, is proposed.","hedge":{"p":0.96,"label":"asserted"},"own_p":0.93,"main_claim_p":0.21,"quantitative":false,"quantitative_p":0.13,"role_probabilities":{"gap":0.0,"method":0.0,"result":0.0,"background":0.0,"limitation":0.0,"future_work":0.0,"contribution":1.0,"interpretation":0.0}},{"i":3,"p":0.99,"id":"s3","own":true,"role":"contribution","text":"Second, we present an algorithm which calculates a lower bound on the minimum distance of a specific code.","hedge":{"p":1.0,"label":"asserted"},"own_p":0.93,"main_claim_p":0.08,"quantitative":true,"quantitative_p":0.73,"role_probabilities":{"gap":0.0,"method":0.01,"result":0.0,"background":0.0,"limitation":0.0,"future_work":0.0,"contribution":0.99,"interpretation":0.0}},{"i":4,"p":0.8,"id":"s4","own":true,"role":"result","text":"This algorithm exhibits complexity which scales quadratically with the block length.","hedge":{"p":1.0,"label":"asserted"},"own_p":0.88,"main_claim_p":0.04,"quantitative":true,"quantitative_p":0.68,"role_probabilities":{"gap":0.0,"method":0.11,"result":0.8,"background":0.0,"limitation":0.0,"future_work":0.0,"contribution":0.08,"interpretation":0.01}},{"i":5,"p":0.99,"id":"s5","own":true,"role":"contribution","text":"Third, we propose a method to obtain a tight lower bound on the fractional distance, also with quadratic complexity, and thus less than previously-existing methods.","hedge":{"p":0.99,"label":"asserted"},"own_p":0.94,"main_claim_p":0.15,"quantitative":true,"quantitative_p":0.96,"role_probabilities":{"gap":0.0,"method":0.01,"result":0.0,"background":0.0,"limitation":0.0,"future_work":0.0,"contribution":0.99,"interpretation":0.0}},{"i":6,"p":1.0,"id":"s6","own":true,"role":"contribution","text":"Finally, we show how the fundamental LP polytope for generalized LDPC codes and nonbinary LDPC codes can be obtained.","hedge":{"p":1.0,"label":"asserted"},"own_p":0.93,"main_claim_p":0.12,"quantitative":false,"quantitative_p":0.05,"role_probabilities":{"gap":0.0,"method":0.0,"result":0.0,"background":0.0,"limitation":0.0,"future_work":0.0,"contribution":1.0,"interpretation":0.0}}]},"compiled":{"main_claim":{"p":0.55,"text":"Four contributions to the LP framework are presented.","location":"abstract 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