List Decodability of Symbol-Pair Codes
Shu Liu, Chaoping Xing, Chen Yuan · IEEE Transactions on Information Theory · 2019
We investigate the list decodability of symbol-pair codes1in this paper. First, we show that the 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 in the pair metric.1A symbol-pair code is referred to a code in the pair metric.