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List Decoding Bounds for Binary Codes with Noiseless Feedback

Authors Meghal Gupta , Rachel Yun Zhang

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Author Details

Meghal Gupta
  • University of California Berkeley, CA, USA
Rachel Yun Zhang
  • Massachusetts Institute of Technology, Cambridge, MA, USA

Funding

  • Gupta, Meghal: Supported by a NSF GFRP Fellowship.
  • Zhang, Rachel Yun: Supported by NSF Graduate Research Fellowship 2141064. Supported in part by DARPA under Agreement No. HR00112020023 and by an NSF grant CNS-2154149.

Cite As Get BibTex

Meghal Gupta and Rachel Yun Zhang. List Decoding Bounds for Binary Codes with Noiseless Feedback. In 16th Innovations in Theoretical Computer Science Conference (ITCS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 325, pp. 60:1-60:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025) https://doi.org/10.4230/LIPIcs.ITCS.2025.60

Abstract

In an error-correcting code, a sender encodes a message x ∈ {0, 1}^k such that it is still decodable by a receiver on the other end of a noisy channel. In the setting of error-correcting codes with feedback, after sending each bit, the sender learns what was received at the other end and can tailor future messages accordingly. 
While the unique decoding radius of feedback codes has long been known to be 1/3, the list decoding capabilities of feedback codes is not well understood. In this paper, we provide the first nontrivial bounds on the list decoding radius of feedback codes for lists of size 𝓁. For 𝓁 = 2, we fully determine the 2-list decoding radius to be 3/7. For larger values of 𝓁, we show an upper bound of 1/2 - 1/{2^(𝓁+2) - 2}, and show that the same techniques for the 𝓁 = 2 case cannot match this upper bound in general.

Subject Classification

ACM Subject Classification
  • Mathematics of computing → Coding theory
Keywords
  • error-correcting codes
  • feedback
  • list decoding

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