Correcting One Error in Non-Binary Channels with Feedback

2023/05/11 by Vorobyev, Ilya, Lebedev, Vladimir, Lebedev, Alexey
#Combinatorics (math.CO) #FOS: Computer and information sciences #FOS: Mathematics #Information Theory (cs.IT)

paper · doi:10.48550/arxiv.2305.06691

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

Related

• Correcting one error in channels with feedback
• Algorithms for q-ary Error-Correcting Codes with Limited Magnitude and\n Feedback
• Non--binary error correcting codes with noiseless feedback, localized errors, or both
• Coding with Noiseless Feedback over the Z-channel
• Adversarial Channels with O(1)-Bit Partial Feedback