List Decodability of Symbol-Pair Codes

Chaoping Xing; Chen Yuan; Shu Liu

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List Decodability of Symbol-Pair Codes

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arxiv 1806.08992 v1 pith:GGW7RQRJ submitted 2018-06-23 cs.IT math.IT

List Decodability of Symbol-Pair Codes

Shu Liu , Chaoping Xing , Chen Yuan This is my paper

classification cs.IT math.IT

keywords listboundsymbol-paircodesdecodabilitycodedecodinggilbert-varshamov

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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.

List Decodability of Symbol-Pair Codes

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