On subspace structure in source and channel coding

Alyson K. Fletcher, Sundeep Rangan, Vivek K. Goyal

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

The use of subspace structure in source and channel coding is studied. We show that for source coding of an i.i.d. Gaussian source, restriction of the codebook to a union of subspaces need not induce any performance penalty. In fact, in N-dimensional space, a two-stage quantization of first projecting to the nearest of J subspaces of dimension K in a random first-stage codebook of subspaces, followed by quantizing to the nearest of codewords in a second-stage codebook within the K-dimensional subspace induces no performance loss. This structure allows the rate-distortion bound to be approached asymptotically with block length N. The dual results for channel coding are explicitly described: For an additive white Gaussian noise channel, we introduce a particular subspace-based codebook that induces no rate loss, and the Shannon capacity is achieved. While this has complexity exponential in N, it is reduced from an unstructured search.

Original languageEnglish (US)
Title of host publicationProceedings - 2008 IEEE International Symposium on Information Theory, ISIT 2008
Pages1982-1986
Number of pages5
DOIs
StatePublished - 2008
Event2008 IEEE International Symposium on Information Theory, ISIT 2008 - Toronto, ON, Canada
Duration: Jul 6 2008Jul 11 2008

Other

Other2008 IEEE International Symposium on Information Theory, ISIT 2008
CountryCanada
CityToronto, ON
Period7/6/087/11/08

Fingerprint

Channel Coding
Source Coding
Channel coding
Codebook
Subspace
Rate-distortion
Gaussian White Noise
Penalty
Quantization
Union
Restriction

ASJC Scopus subject areas

  • Applied Mathematics
  • Modeling and Simulation
  • Theoretical Computer Science
  • Information Systems

Cite this

Fletcher, A. K., Rangan, S., & Goyal, V. K. (2008). On subspace structure in source and channel coding. In Proceedings - 2008 IEEE International Symposium on Information Theory, ISIT 2008 (pp. 1982-1986). [4595336] https://doi.org/10.1109/ISIT.2008.4595336

On subspace structure in source and channel coding. / Fletcher, Alyson K.; Rangan, Sundeep; Goyal, Vivek K.

Proceedings - 2008 IEEE International Symposium on Information Theory, ISIT 2008. 2008. p. 1982-1986 4595336.

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Fletcher, AK, Rangan, S & Goyal, VK 2008, On subspace structure in source and channel coding. in Proceedings - 2008 IEEE International Symposium on Information Theory, ISIT 2008., 4595336, pp. 1982-1986, 2008 IEEE International Symposium on Information Theory, ISIT 2008, Toronto, ON, Canada, 7/6/08. https://doi.org/10.1109/ISIT.2008.4595336
Fletcher AK, Rangan S, Goyal VK. On subspace structure in source and channel coding. In Proceedings - 2008 IEEE International Symposium on Information Theory, ISIT 2008. 2008. p. 1982-1986. 4595336 https://doi.org/10.1109/ISIT.2008.4595336
Fletcher, Alyson K. ; Rangan, Sundeep ; Goyal, Vivek K. / On subspace structure in source and channel coding. Proceedings - 2008 IEEE International Symposium on Information Theory, ISIT 2008. 2008. pp. 1982-1986
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