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      An upper bound on the capacity of non-binary deletion channels

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      Author
      Rahmati, M.
      Duman, Tolga M.
      Date
      2013
      Source Title
      2013 IEEE International Symposium on Information Theory
      Print ISSN
      157-8095
      Publisher
      IEEE
      Pages
      2940 - 2944
      Language
      English
      Type
      Conference Paper
      Item Usage Stats
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      Abstract
      We derive an upper bound on the capacity of non-binary deletion channels. Although binary deletion channels have received significant attention over the years, and many upper and lower bounds on their capacity have been derived, such studies for the non-binary case are largely missing. The state of the art is the following: as a trivial upper bound, capacity of an erasure channel with the same input alphabet as the deletion channel can be used, and as a lower bound the results by Diggavi and Grossglauser in [1] are available. In this paper, we derive the first non-trivial non-binary deletion channel capacity upper bound and reduce the gap with the existing achievable rates. To derive the results we first prove an inequality between the capacity of a 2K-ary deletion channel with deletion probability d, denoted by C2K(d), and the capacity of the binary deletion channel with the same deletion probability, C2(d), that is, C2K(d) ≤ C2(d)+(1-d) log(K). Then by employing some existing upper bounds on the capacity of the binary deletion channel, we obtain upper bounds on the capacity of the 2K-ary deletion channel. We illustrate via examples the use of the new bounds and discuss their asymptotic behavior as d → 0. © 2013 IEEE.
      Keywords
      Asymptotic behaviors
      Deletion channels
      Erasure channels
      Lower bounds
      Non-trivial
      State of the art
      Upper and lower bounds
      Upper Bound
      Information theory
      Permalink
      http://hdl.handle.net/11693/27887
      Published Version (Please cite this version)
      http://dx.doi.org/10.1109/ISIT.2013.6620764
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      • Department of Electrical and Electronics Engineering 3524
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