License: Creative Commons Attribution 3.0 Unported license (CC BY 3.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.ITCS.2021.43
URN: urn:nbn:de:0030-drops-135828
URL: https://drops.dagstuhl.de/opus/volltexte/2021/13582/
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Grossman, Ofer ; Holmgren, Justin

Error Correcting Codes for Uncompressed Messages

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LIPIcs-ITCS-2021-43.pdf (0.6 MB)


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.

BibTeX - Entry

@InProceedings{grossman_et_al:LIPIcs.ITCS.2021.43,
  author =	{Ofer Grossman and Justin Holmgren},
  title =	{{Error Correcting Codes for Uncompressed Messages}},
  booktitle =	{12th Innovations in Theoretical Computer Science Conference (ITCS 2021)},
  pages =	{43:1--43:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-177-1},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{185},
  editor =	{James R. Lee},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2021/13582},
  URN =		{urn:nbn:de:0030-drops-135828},
  doi =		{10.4230/LIPIcs.ITCS.2021.43},
  annote =	{Keywords: Coding Theory, List Decoding}
}

Keywords: Coding Theory, List Decoding
Collection: 12th Innovations in Theoretical Computer Science Conference (ITCS 2021)
Issue Date: 2021
Date of publication: 04.02.2021
Supplementary Material: The code used to generate the figures and tables in this paper can be found at https://github.com/jnhnum1/contextual_codes.


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