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.
展开▼
机译：我们表明，在标准核料编码方案中使用时，某些低密度奇偶奇校验（LDPC）代码的双重码在二进制擦除丝网（BEWC）上提供了强烈的保密。这结果铰接在LDPC码的停止集分析与块长度n和周长为⋛。我们表明，如果集合的最小左侧程度为L MIN ，则块误差的预期概率是O（1 / N 1 L MIN K / 2 ⌉-k）当擦除概率ε<ε ef 时，其中ε ef 取决于集合体的程度分布。只要L MIN 和K> 2，该LDPC代码的双重措施在擦除概率的BEWC中提供了强大的保密，大于1-ε EF 。
展开▼
