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arXiv · 1806.08992

List Decodability of Symbol-Pair Codes

Shu Liu·Chaoping Xing·Chen Yuan
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Abstract

We investigate the list decodability of symbol-pair codes in the present paper. Firstly, we show that list decodability of every symbol-pair code does not exceed the Gilbert-Varshamov bound. On the other hand, we are able to prove that with high probability, a random symbol-pair code can be list decoded up to the Gilbert-Varshamov bound. Our second result of this paper is to derive the Johnson-type bound, i.e., a lower bound on list decoding radius in terms of minimum distance. Finally, we present a list decoding algorithm of Reed-Solomon codes beyond the Johnson-type bound.

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Shu Liu, Chaoping Xing, Chen Yuan. 2018-06-23. List Decodability of Symbol-Pair Codes. https://arxiv.org/abs/1806.08992

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