{"paper":{"title":"Asymptotic Average Multiplicity of Structures within Different Categories of Trapping Sets, Absorbing Sets and Stopping Sets in Random Regular and Irregular LDPC Code Ensembles","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Ali Dehghan, Amir H. Banihashemi","submitted_at":"2017-05-18T20:53:36Z","abstract_excerpt":"The performance of low-density parity-check (LDPC) codes in the error floor region is closely related to some combinatorial structures of the code's Tanner graph, collectively referred to as {\\it trapping sets (TSs)}. In this paper, we study the asymptotic average number of different types of trapping sets such as {\\em elementary TSs (ETS)}, {\\em leafless ETSs (LETS)}, {\\em absorbing sets (ABS)}, {\\em elementary ABSs (EABS)}, and {\\em stopping sets (SS)}, in random variable-regular and irregular LDPC code ensembles. We demonstrate that, regardless of the type of the TS, as the code's length te"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.06798","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"}