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arXiv · 2411.08258

Efficient encoding and decoding algorithm for a class of perfect single-deletion-correcting permutation codes

Minhan Gao·Kenneth W. Shum
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Abstract

A permutation code is a nonlinear code whose codewords are permutation of a set of symbols. We consider the use of permutation code in the deletion channel, and consider the symbol-invariant error model, meaning that the values of the symbols that are not removed are not affected by the deletion. In 1992, Levenshtein gave a construction of perfect single-deletion-correcting permutation codes that attain the maximum code size. Furthermore, he showed in the same paper that the set of all permutations of a given length can be partitioned into permutation codes so constructed. This construction relies on the binary Varshamov-Tenengolts codes. In this paper we give an independent and more direct proof of Levenshtein's result that does not depend on the Varshamov-Tenengolts code. Using the new approach, we devise efficient encoding and decoding algorithms that correct one deletion.

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Minhan Gao, Kenneth W. Shum. 2024-11-13. Efficient encoding and decoding algorithm for a class of perfect single-deletion-correcting permutation codes. https://arxiv.org/abs/2411.08258

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