Correcting One Error in Non-Binary Channels with Feedback
Information Theory
2023-05-12 v1 Combinatorics
math.IT
Abstract
In this paper, the problem of correction of a single error in -ary symmetric channel with noiseless feedback is considered. We propose an algorithm to construct codes with feedback inductively. For all prime power we prove that two instances of feedback are sufficient to transmit over the -ary symmetric channel the same number of messages as in the case of complete feedback. Our other contribution is the construction of codes with one-time feedback with the same parameters as Hamming codes for that is not a prime power. We also construct single-error-correcting codes with one-time feedback of size for arbitrary and , which can be seen as an analog for Reed-Solomon codes.
Cite
@article{arxiv.2305.06691,
title = {Correcting One Error in Non-Binary Channels with Feedback},
author = {Ilya Vorobyev and Vladimir Lebedev and Alexey Lebedev},
journal= {arXiv preprint arXiv:2305.06691},
year = {2023}
}