Linear-time Erasure List-decoding of Expander Codes
Linear-time Erasure List-decoding of Expander Codes
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DOI：
10.1109/isit44484.2020.9174325
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发表时间：
2020-02
期刊：
影响因子：
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通讯作者：
Noga Ron-Zewi;Mary Wootters;Gilles Z'emor
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文献类型：
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作者：
Noga Ron-Zewi;Mary Wootters;Gilles Z'emor
我们更精确地给出了一个线性的擦除算法。 expander Graph G g带有n个顶点，我们给出一个算法来列表列表depander代码$ \ mathcal {c} = \ mathcal {c} \ left（{g，{\ mathcal {c} ）长度为nd的$ nd从时间n•poly（d2r/δ）中的大约删除，其中δ和δ分别是相对距离，r'th•r'th•$ {\ mathcal {c} _0} $的广义相对距离据我们所知，这是第一个线性时间算法，可以从其（设计的）距离超出其（设计）距离的删除范围的删除范围，我们证明了类似于（ Hemenway和Wootters，信息和计算，2018年）可用于获得此类擦除列表编码算法，其运行时间对R和δ的依赖性较差。这些参数。
We give a linear-time erasure list-decoding algorithm for expander codes. More precisely, let r > 0 be any integer. Given an inner code ${\mathcal{C}_0}$ 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 $\mathcal{C} = \mathcal{C}\left( {G,{\mathcal{C}_0}} \right)$ of length nd from approximately δδrnd erasures in time n•poly(d2r/δ), where δ and δr are the relative distance and the r’th•generalized relative distance of ${\mathcal{C}_0}$, 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 δ2nd.To obtain our results, we show that an approach similar to that of (Hemenway and 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 δ; then we show how to improve the dependence of the running time on these parameters.