Strong Secrecy on the Binary Erasure Wiretap Channel Using Large-Girth LDPC Codes

Details Strong Secrecy on the Binary Erasure Wiretap Channel Using Large-Girth LDPC Codes Strong Secrecy on the Binary Erasure Wiretap Channel Using Large-Girth LDPC Codes

2010-09-16

arxiv.org/abs/1009.3130v3

Computer Science

Information Theory

11 pages, 4 figures. Submitted to the IEEE Transactions on Information Forensics and Security

Scientific paper

For an arbitrary degree distribution pair (DDP), we construct a sequence of low-density parity-check (LDPC) code ensembles with girth growing logarithmically in block-length using Ramanujan graphs. When the DDP has minimum left degree at least three, we show using density evolution analysis that the expected bit-error probability of these ensembles, when passed through a binary erasure channel with erasure probability $\epsilon$, decays as $\mathcal{O}(\exp(-c_1 n^{c_2}))$ with the block-length $n$ for positive constants $c_1$ and $c_2$, as long as $\epsilon$ is lesser than the erasure threshold $\epsilon_\mathrm{th}$ of the DDP. This guarantees that the coset coding scheme using the dual sequence provides strong secrecy over the binary erasure wiretap channel for erasure probabilities greater than $1 - \epsilon_\mathrm{th}$.

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