Rate-distance tradeoff for codes above graph capacity

Daniel Cullina, Marco Dalai, Yury Polyanskiy

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

1 Scopus citations


The capacity of a graph is defined as the rate of exponential growth of independent sets in the strong powers of the graph. In the strong power an edge connects two sequences if at each position their letters are equal or adjacent. We consider a variation of the problem where edges in the power graphs are removed between sequences which differ in more than a fraction δ of coordinates. The proposed generalization can be interpreted as the problem of determining the highest rate of zero undetected-error communication over a link with adversarial noise, where only a fraction δ of symbols can be perturbed and only some substitutions are allowed. We derive lower bounds on achievable rates by combining graph homomorphisms with a graph-theoretic generalization of the Gilbert-Varshamov bound. We then give an upper bound, based on Delsarte's linear programming approach, which combines Lovász' theta function with the construction used by McEliece et al. for bounding the minimum distance of codes in Hamming spaces.

Original languageEnglish (US)
Title of host publicationProceedings - ISIT 2016; 2016 IEEE International Symposium on Information Theory
PublisherInstitute of Electrical and Electronics Engineers Inc.
Number of pages5
ISBN (Electronic)9781509018062
StatePublished - Aug 10 2016
Event2016 IEEE International Symposium on Information Theory, ISIT 2016 - Barcelona, Spain
Duration: Jul 10 2016Jul 15 2016

Publication series

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


Other2016 IEEE International Symposium on Information Theory, ISIT 2016

All Science Journal Classification (ASJC) codes

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


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