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Error Correction for Message Streams

Authors Meghal Gupta , Rachel Yun Zhang

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Subject Classification

ACM Subject Classification
  • Mathematics of computing → Coding theory
Keywords
  • error-correcting codes
  • streaming algorithms
  • space-efficient algorithms

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Abstract

In the setting of error correcting codes, Alice wants to send a message x ∈ {0,1}ⁿ to Bob via an encoding enc(x) that is resilient to error. In this work, we investigate the scenario where Bob is a low space decoder. More precisely, he receives Alice’s encoding enc(x) bit-by-bit and desires to compute some function f(x) in low space. A generic error-correcting code does not accomplish this because decoding is a very global process and requires at least linear space. Locally decodable codes partially solve this problem as they allow Bob to learn a given bit of x in low space, but not compute a generic function f. 
Our main result is an encoding and decoding procedure where Bob is still able to compute any such function f in low space when a constant fraction of the stream is corrupted. More precisely, we describe an encoding function enc(x) of length poly(n) so that for any decoder (streaming algorithm) A that on input x computes f(x) in space s, there is an explicit decoder B that computes f(x) in space s ⋅ polylog(n) as long as there were not more than 1/4 - ε fraction of (adversarial) errors in the input stream enc(x).

Cite As Get BibTex

Meghal Gupta and Rachel Yun Zhang. Error Correction for Message Streams. In 16th Innovations in Theoretical Computer Science Conference (ITCS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 325, pp. 59:1-59:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025) https://doi.org/10.4230/LIPIcs.ITCS.2025.59

Author Details

Meghal Gupta
  • University of California Berkeley, CA, USA
Rachel Yun Zhang
  • MIT, Cambridge, MA, USA

Funding

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

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