Correcting One Error in Non-Binary Channels with Feedback

05/11/2023

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by   Ilya Vorobyev, et al.

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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≤ q+1, which can be seen as an analog for Reed-Solomon codes.