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Paper Detail

Paper IDC.5.2
Paper Title Linear-Time Erasure List-Decoding of Expander Codes
Authors Noga Ron-Zewi, University of Haifa, Israel; Mary Wootters, Stanford University, United States; Gilles Zemor, Universite de Bordeaux, France
Session C.5: List Decoding
Presentation Lecture
Track Coding for Communications
Manuscript  Click here to download the manuscript
Virtual Presentation  Click here to watch in the Virtual Symposium
Abstract We give a linear-time erasure list-decoding algorithm for expander codes. More precisely, let $r > 0$ be any integer. Given a linear inner code $\cC_0$ of length $d$, and a $d$-regular bipartite expander graph $G$ with $n$ vertices on each side, we give an algorithm to list-decode the expander code $\cC = \cC(G, \cC_0)$ of length $nd$ from approximately $\delta \delta_r nd$ erasures in time $n \cdot \poly(d2^r / \delta)$, where $\delta$ and $\delta_r$ are the relative distance and $r$'th generalized relative distance of $\cC_0$, respectively. To the best of our knowledge, this is the first linear-time algorithm that can list-decode expander codes from erasures beyond their (designed) distance of approximately $\delta^2 nd$. To obtain our results, we show that an approach similar to that of (Hemenway, Wootters, Information and Computation, 2018) can be used to obtain such an erasure-list-decoding algorithm with an exponentially worse dependence of the running time on $r$ and $\delta$; then we show how to improve the dependence of the running time on these parameters.

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2021 IEEE International Symposium on Information Theory

11-16 July 2021 | Melbourne, Victoria, Australia

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