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arXiv · 1206.2568

LP decoding of expander codes: a simpler proof

Michael Viderman
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Abstract

A code $C \subseteq \F_2^n$ is a $(c,ε,δ)$-expander code if it has a Tanner graph, where every variable node has degree $c$, and every subset of variable nodes $L_0$ such that $|L_0|\leq δn$ has at least $εc |L_0|$ neighbors. Feldman et al. (IEEE IT, 2007) proved that LP decoding corrects $\frac{3ε-2}{2ε-1} \cdot (δn-1)$ errors of $(c,ε,δ)$-expander code, where $ε> 2/3+\frac{1}{3c}$. In this paper, we provide a simpler proof of their result and show that this result holds for every expansion parameter $ε> 2/3$.

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Michael Viderman. 2012-06-12. LP decoding of expander codes: a simpler proof. https://arxiv.org/abs/1206.2568

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