{"paper":{"title":"Statistical Physics of Irregular Low-Density Parity-Check Codes","license":"","headline":"","cross_cats":[],"primary_cat":"cond-mat.dis-nn","authors_text":"David Saad, Renato Vicente, Yoshiyuki Kabashima","submitted_at":"1999-08-25T14:23:28Z","abstract_excerpt":"Low-density parity-check codes with irregular constructions have been recently shown to outperform the most advanced error-correcting codes to date. In this paper we apply methods of statistical physics to study the typical properties of simple irregular codes.\n We use the replica method to find a phase transition which coincides with Shannon's coding bound when appropriate parameters are chosen.\n The decoding by belief propagation is also studied using statistical physics arguments; the theoretical solutions obtained are in good agreement with simulations. We compare the performance of irregu"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"cond-mat/9908358","kind":"arxiv","version":2},"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"}