List Decodability of Symbol-Pair Codes
Information Theory
2018-06-26 v1 math.IT
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.
Cite
@article{arxiv.1806.08992,
title = {List Decodability of Symbol-Pair Codes},
author = {Shu Liu and Chaoping Xing and Chen Yuan},
journal= {arXiv preprint arXiv:1806.08992},
year = {2018}
}