Abstract-We show that duals of certain low-density paritycheck (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 l min k/2 −k ) when the erasure probability < ef , where ef depends on the degree distribution of the ensemble. As long as lmin > 2 and k > 2, the dual of this LDPC code provides strong secrecy over a BEWC of erasure probability greater than 1 − ef .
Extending this result, a coset coding scheme is proposed by leveraging the dual of short-cycle-free LDPC code to achieve the strong secrecy on a BEWC in REF .
Strong Secrecy for Erasure Wiretap Channels
2010 IEEE Information Theory Workshop
2010 IEEE Information Theory Workshop
Mathematics Computer Science