Strong secrecy for erasure wiretap channels
Ananda Theertha Suresh, Arunkumar Subramanian, Andrew Thangaraj, Matthieu R. Bloch, Stephen McLaughlin · 2010
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 ≥ 2k for some k ≥ 2. We show that if the minimum left degree of the ensemble is lmin, the expected probability of block error is O(1/n⌈lmink/2⌉ -k) when the erasure probability ϵef, where ϵefdepends on the degree distribution of the ensemble. As long as lminand k > 2, the dual of this LDPC code provides strong secrecy over a BEWC of erasure probability greater than 1-ϵef.