List decoding - Random coding exponents and expurgated exponents

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Abstract

New results are derived concerning random coding error exponents and expurgated exponents for list decoding with a deterministic list size L. Two asymptotic regimes are considered, the fixed list-size regime, where L is fixed independently of the block length n, and the exponential list-size, where L grows exponentially with n. We first derive a general upper bound on the list-decoding average error probability, which is suitable for both regimes. This bound leads to more specific bounds in the two regimes. In the fixed list-size regime, the bound is related to known bounds and we establish its exponential tightness. In the exponential list-size regime, we establish the achievability of the well known sphere packing lower bound. An immediate byproduct of our analysis in both regimes is the universality of the maximum mutual information (MMI) list decoder in the error exponent sense. Finally, we consider expurgated bounds at low rates, using the Csiszár-Körner- Marton approach. This expurgated bound, which involves the notion of multi-information, is also modified to apply to continuous alphabet channels, and in particular, to the Gaussian memoryless channel, where the expression of the expurgated bound becomes quite explicit.

Original languageEnglish
Title of host publication2014 IEEE International Symposium on Information Theory, ISIT 2014
Pages2459-2463
Number of pages5
DOIs
StatePublished - 2014
Event2014 IEEE International Symposium on Information Theory, ISIT 2014 - Honolulu, HI, United States
Duration: 29 Jun 20144 Jul 2014

Publication series

NameIEEE International Symposium on Information Theory - Proceedings

Conference

Conference2014 IEEE International Symposium on Information Theory, ISIT 2014
Country/TerritoryUnited States
CityHonolulu, HI
Period29/06/144/07/14

All Science Journal Classification (ASJC) codes

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

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