{"paper":{"title":"LP decoding of expander codes: a simpler proof","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Michael Viderman","submitted_at":"2012-06-12T15:41:27Z","abstract_excerpt":"A code $C \\subseteq \\F_2^n$ is a $(c,\\epsilon,\\delta)$-expander code if it has a Tanner graph, where every variable node has degree $c$, and every subset of variable nodes $L_0$ such that $|L_0|\\leq \\delta n$ has at least $\\epsilon c |L_0|$ neighbors. Feldman et al. (IEEE IT, 2007) proved that LP decoding corrects $\\frac{3\\epsilon-2}{2\\epsilon-1} \\cdot (\\delta n-1)$ errors of $(c,\\epsilon,\\delta)$-expander code, where $\\epsilon > 2/3+\\frac{1}{3c}$. In this paper, we provide a simpler proof of their result and show that this result holds for every expansion parameter $\\epsilon > 2/3$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1206.2568","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}