Generalized sphere-packing upper bounds on the size of codes for combinatorial channels

Daniel Cullina, Negar Kiyavash

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

4 Citations (Scopus)

Abstract

A code for a combinatorial channel is a feasible point in an integer linear program derived from that channel. Sphere-packing upper bounds are closely related to the fractional relaxation of this program. When bounding highly symmetric channels, this formulation can often be avoided, but it is essential in less symmetric cases. We present a few low-complexity upper bounds on the value of the relaxed linear program. We also discuss a more general bound derived from the codeword constraint graph for the channel. This bound is not necessarily computationally tractable. When there is a family of channels with the same constraint graph, tractable bounds can be applied to each channel and the best bound will apply to the whole family.

Original languageEnglish (US)
Title of host publication2014 IEEE International Symposium on Information Theory, ISIT 2014
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages1266-1270
Number of pages5
ISBN (Print)9781479951864
DOIs
StatePublished - Jan 1 2014
Event2014 IEEE International Symposium on Information Theory, ISIT 2014 - Honolulu, HI, United States
Duration: Jun 29 2014Jul 4 2014

Publication series

NameIEEE International Symposium on Information Theory - Proceedings
ISSN (Print)2157-8095

Other

Other2014 IEEE International Symposium on Information Theory, ISIT 2014
CountryUnited States
CityHonolulu, HI
Period6/29/147/4/14

Fingerprint

Sphere packing
Upper bound
Linear Program
Integer Program
Graph in graph theory
Low Complexity
Fractional
Formulation
Family

All Science Journal Classification (ASJC) codes

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

Cite this

Cullina, D., & Kiyavash, N. (2014). Generalized sphere-packing upper bounds on the size of codes for combinatorial channels. In 2014 IEEE International Symposium on Information Theory, ISIT 2014 (pp. 1266-1270). [6875036] (IEEE International Symposium on Information Theory - Proceedings). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/ISIT.2014.6875036
Cullina, Daniel ; Kiyavash, Negar. / Generalized sphere-packing upper bounds on the size of codes for combinatorial channels. 2014 IEEE International Symposium on Information Theory, ISIT 2014. Institute of Electrical and Electronics Engineers Inc., 2014. pp. 1266-1270 (IEEE International Symposium on Information Theory - Proceedings).
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Cullina, D & Kiyavash, N 2014, Generalized sphere-packing upper bounds on the size of codes for combinatorial channels. in 2014 IEEE International Symposium on Information Theory, ISIT 2014., 6875036, IEEE International Symposium on Information Theory - Proceedings, Institute of Electrical and Electronics Engineers Inc., pp. 1266-1270, 2014 IEEE International Symposium on Information Theory, ISIT 2014, Honolulu, HI, United States, 6/29/14. https://doi.org/10.1109/ISIT.2014.6875036

Generalized sphere-packing upper bounds on the size of codes for combinatorial channels. / Cullina, Daniel; Kiyavash, Negar.

2014 IEEE International Symposium on Information Theory, ISIT 2014. Institute of Electrical and Electronics Engineers Inc., 2014. p. 1266-1270 6875036 (IEEE International Symposium on Information Theory - Proceedings).

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

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Cullina D, Kiyavash N. Generalized sphere-packing upper bounds on the size of codes for combinatorial channels. In 2014 IEEE International Symposium on Information Theory, ISIT 2014. Institute of Electrical and Electronics Engineers Inc. 2014. p. 1266-1270. 6875036. (IEEE International Symposium on Information Theory - Proceedings). https://doi.org/10.1109/ISIT.2014.6875036