This article is cited in 4 papers

Coding Theory

Correcting a single error in feedback channels

I. V. Vorobyev^a, C. Deppe^a, A. V. Lebedev^b, V. S. Lebedev<sup>b

a</sup> Technische Universität München, Munich, Germany
^b Kharkevich Institute for Information Transmission Problems, Russian Academy of Sciences, Moscow, Russia

Abstract: We address the problem of correcting a single error in an arbitrary discrete memoryless channel with error-free instantaneous feedback. For the case of a one-time feedback, we propose a method for constructing optimal transmission strategies. The obtained result allows us to prove that for a binary channel, two feedbacks are sufficient to transmit the same number of messages as in the case of complete feedback. We also apply the developed techniques to a binary asymmetric channel to construct transmission strategies for small lengths.

Keywords: coding with feedback, symmetric channel, asymmetric channel, Hamming bound, linear programming problem.

UDC: 621.391 : 519.72

Received: 20.09.2022
Revised: 28.11.2022
Accepted: 28.11.2022

DOI: 10.31857/S0555292322040040

 English version: Problems of Information Transmission, 2022, 58:4, 329–340