{"paper":{"title":"Strong Secrecy for Erasure Wiretap Channels","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Ananda T. Suresh, Andrew Thangaraj, Arunkumar Subramanian, Matthieu Bloch, Steven McLaughlin","submitted_at":"2010-04-30T14:36:50Z","abstract_excerpt":"We show that duals of certain low-density parity-check (LDPC) codes, when used in a standard coset coding scheme, provide strong secrecy over the binary erasure wiretap channel (BEWC). This result hinges on a stopping set analysis of ensembles of LDPC codes with block length $n$ and girth $\\geq 2k$, for some $k \\geq 2$. We show that if the minimum left degree of the ensemble is $l_\\mathrm{min}$, the expected probability of block error is $\\calO(\\frac{1}{n^{\\lceil l_\\mathrm{min} k /2 \\rceil - k}})$ when the erasure probability $\\epsilon < \\epsilon_\\mathrm{ef}$, where $\\epsilon_\\mathrm{ef}$ depe"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1004.5540","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"}