{"paper":{"title":"Stopping Redundancy Hierarchy Beyond the Minimum Distance","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Boris D. Kudryashov, Irina E. Bocharova, Vitaly Skachek, Yauhen Yakimenka","submitted_at":"2018-04-18T14:52:08Z","abstract_excerpt":"Stopping sets play a crucial role in failure events of iterative decoders over a binary erasure channel (BEC). The $\\ell$-th stopping redundancy is the minimum number of rows in the parity-check matrix of a code, which contains no stopping sets of size up to $\\ell$. In this work, a notion of coverable stopping sets is defined. In order to achieve maximum-likelihood performance under iterative decoding over the BEC, the parity-check matrix should contain no coverable stopping sets of size $\\ell$, for $1 \\le \\ell \\le n-k$, where $n$ is the code length, $k$ is the code dimension. By estimating th"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1804.06770","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"}