We investigate the list decodability of symbol-pair codes 1 in 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. 1

A symbol-pair code is referred to a code is the pair metric.

Additional Metadata
Keywords Block code, List decoding, Symbol-pair metric code
Persistent URL dx.doi.org/10.1109/TIT.2019.2904998
Journal IEEE Transactions on Information Theory
Citation
Liu, S, Xing, C, & Yuan, C. (2019). List decodability of symbol-pair codes. IEEE Transactions on Information Theory, 65(8), 4815–4821. doi:10.1109/TIT.2019.2904998