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arXiv · 2305.06691

Correcting One Error in Non-Binary Channels with Feedback

Ilya Vorobyev·Vladimir Lebedev·Alexey Lebedev
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Abstract

In this paper, the problem of correction of a single error in $q$-ary symmetric channel with noiseless feedback is considered. We propose an algorithm to construct codes with feedback inductively. For all prime power $q$ we prove that two instances of feedback are sufficient to transmit over the $q$-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 $q$ that is not a prime power. We also construct single-error-correcting codes with one-time feedback of size $q^{n-2}$ for arbitrary $q$ and $n\leq q+1$, which can be seen as an analog for Reed-Solomon codes.

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Ilya Vorobyev, Vladimir Lebedev, Alexey Lebedev. 2023-05-11. Correcting One Error in Non-Binary Channels with Feedback. https://arxiv.org/abs/2305.06691

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