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Error Correcting Codes for Uncompressed Messages

Authors Ofer Grossman, Justin Holmgren

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Author Details

Ofer Grossman
  • MIT, Cambridge, MA, USA
Justin Holmgren
  • NTT Research, Palo Alto, CA, USA

Funding

Work done in part while generously hosted by the Simons Institute.
  • Grossman, Ofer: Supported by a Fannie and John Hertz Foundation Fellowship and a NSF GRFP fellowship.
  • Holmgren, Justin: Work done in part while at Princeton University, supported by the Simons Collaboration on Algorithms and Geometry and National Science Foundation grant No. CCF-1714779.

Acknowledgements

We thank Elad Haramaty and Madhu Sudan for many very fruitful discussions in the early stages of this work. We also thank Venkat Guruswami and Lijie Chen for helpful discussions, and Shafi Goldwasser for her encouragement and her feedback on an earlier version of this work. We also thank anonymous reviewers for many useful comments on earlier versions of this work.

Cite As Get BibTex

Ofer Grossman and Justin Holmgren. Error Correcting Codes for Uncompressed Messages. In 12th Innovations in Theoretical Computer Science Conference (ITCS 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 185, pp. 43:1-43:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021) https://doi.org/10.4230/LIPIcs.ITCS.2021.43

Abstract

Most types of messages we transmit (e.g., video, audio, images, text) are not fully compressed, since they do not have known efficient and information theoretically optimal compression algorithms. When transmitting such messages, standard error correcting codes fail to take advantage of the fact that messages are not fully compressed.
We show that in this setting, it is sub-optimal to use standard error correction. We consider a model where there is a set of "valid messages" which the sender may send that may not be efficiently compressible, but where it is possible for the receiver to recognize valid messages. In this model, we construct a (probabilistic) encoding procedure that achieves better tradeoffs between data rates and error-resilience (compared to just applying a standard error correcting code).
Additionally, our techniques yield improved efficiently decodable (probabilistic) codes for fully compressed messages (the standard setting where the set of valid messages is all binary strings) in the high-rate regime.

Subject Classification

ACM Subject Classification
  • Theory of computation → Error-correcting codes
Keywords
  • Coding Theory
  • List Decoding

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References

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