Rate-distance tradeoff for codes above graph capacity
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Polyanskiy_Rate-distance.pdf
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294.9 KB
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Author(s)
Cullina, Daniel
Dalai, Marco
Polyanskiy, Yury
Date Issued
July 2016
Journal
2016 IEEE International Symposium on Information Theory (ISIT)
Publisher
Institute of Electrical and Electronics Engineers (IEEE)
Citation
Cullina, Daniel et al. “Rate-Distance Tradeoff for Codes Above Graph Capacity.” 2016 IEEE International Symposium on Information Theory (ISIT), July 10-15 2016, Barcelona, Spain, Institute of Electrical and Electronics Engineers (IEEE), July 2016: 1331-1335 © 2016 Institute of Electrical and Electronics Engineers (IEEE)
Version
Author's final manuscript
Abstract
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.
MIT Department
Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
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Creative Commons Attribution-Noncommercial-Share Alike
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DOI of Published Version
https://doi.org/10.1109/ISIT.2016.7541515
