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

Abstract

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 $1-{\epsilon }_{\mathrm{th}}$.

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

References in corpus (1)

• Strong Secrecy for Erasure Wiretap Channels

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