A. Suresh, A. Subramanian, A. Thangaraj, M. Bloch, S. McLaughlin
{"title":"Strong secrecy for erasure wiretap channels","authors":"A. Suresh, A. Subramanian, A. Thangaraj, M. Bloch, S. McLaughlin","doi":"10.1109/CIG.2010.5592770","DOIUrl":null,"url":null,"abstract":"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 ⋛ for some ⋛. We show that if the minimum left degree of the ensemble is l<inf>min</inf>, the expected probability of block error is O(1/n⌈<sup>l</sup> min<sup>k/2</sup>⌉ −k) when the erasure probability ∊ < ∊<inf>ef</inf>, where ∊<inf>ef</inf> depends on the degree distribution of the ensemble. As long as l<inf>min</inf> and k > 2, the dual of this LDPC code provides strong secrecy over a BEWC of erasure probability greater than 1–∊<inf>ef</inf>.","PeriodicalId":354925,"journal":{"name":"2010 IEEE Information Theory Workshop","volume":"1 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2010-04-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"52","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"2010 IEEE Information Theory Workshop","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1109/CIG.2010.5592770","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 52
Abstract
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 ⋛ for some ⋛. We show that if the minimum left degree of the ensemble is lmin, the expected probability of block error is O(1/n⌈l mink/2⌉ −k) when the erasure probability ∊ < ∊ef, where ∊ef depends on the degree distribution of the ensemble. As long as lmin and k > 2, the dual of this LDPC code provides strong secrecy over a BEWC of erasure probability greater than 1–∊ef.