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arXiv · 2006.11516

Systematic Single-Deletion Multiple-Substitution Correcting Codes

Wentu Song·Nikita Polyanskii·Kui Cai·Xuan He
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Abstract

Recent work by Smagloy et al. (ISIT 2020) shows that the redundancy of a single-deletion $s$-substitution correcting code is asymptotically at least $(s+1)\log n+o(\log n)$, where $n$ is the length of the codes. They also provide a construction of single-deletion and single-substitution codes with redundancy $6\log n+8$. In this paper, we propose a family of systematic single-deletion $s$-substitution correcting codes of length $n$ with asymptotical redundancy at most $(3s+4)\log n+o(\log n)$ and polynomial encoding/decoding complexity, where $s\geq 2$ is a constant. Specifically, the encoding and decoding complexity of the proposed codes are $O(n^{s+3})$ and $O(n^{s+2})$, respectively.

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Wentu Song, Nikita Polyanskii, Kui Cai, Xuan He. 2020-06-20. Systematic Single-Deletion Multiple-Substitution Correcting Codes. https://arxiv.org/abs/2006.11516

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