Reconstructing Reed-Solomon Codes from Multiple Noisy Channel Outputs
Abstract
The sequence reconstruction problem, introduced by Levenshtein in 2001, considers a communication setting in which a sender transmits a codeword and the receiver observes K independent noisy versions of this codeword. In this work, we study the problem of efficient reconstruction when each of the outputs is corrupted by a -ary discrete memoryless symmetric (DMS) substitution channel with substitution probability . Focusing on Reed-Solomon (RS) codes, we adapt the Koetter-Vardy soft-decision decoding algorithm to obtain an efficient reconstruction algorithm. For sufficiently large blocklength and alphabet size, we derive an explicit rate threshold, depending only on , such that the transmitted codeword can be reconstructed with arbitrarily small probability of error whenever the code rate lies below this threshold.
Cite
@article{arxiv.2601.09947,
title = {Reconstructing Reed-Solomon Codes from Multiple Noisy Channel Outputs},
author = {Shubhransh Singhvi and Han Mao Kiah and Eitan Yaakobi},
journal= {arXiv preprint arXiv:2601.09947},
year = {2026}
}