Large Deviations Behavior of the Logarithmic Error Probability of Random Codes

Ran Tamir, Neri Merhav, Nir Weinberger, Albert Guillén I Fàbregas

Research output: Contribution to journalArticlepeer-review

Abstract

This work studies the deviations of the error exponent of the constant composition code ensemble around its expectation, known as the error exponent of the typical random code (TRC). In particular, it is shown that the probability of randomly drawing a codebook whose error exponent is smaller than the TRC exponent is exponentially small; upper and lower bounds for this exponent are given, which coincide in some cases. In addition, the probability of randomly drawing a codebook whose error exponent is larger than the TRC exponent is shown to be double-exponentially small; upper and lower bounds to the double-exponential exponent are given. The results suggest that codebooks whose error exponent is larger than the error exponent of the TRC are extremely rare. The key ingredient in the proofs is a new large deviations result of type class enumerators with dependent variables.

Original languageEnglish
Article number9095265
Pages (from-to)6635-6659
Number of pages25
JournalIEEE Transactions on Information Theory
Volume66
Issue number11
DOIs
StatePublished - Nov 2020

Keywords

  • Error exponent
  • expurgated exponent
  • large deviations
  • typical random code

All Science Journal Classification (ASJC) codes

  • Information Systems
  • Computer Science Applications
  • Library and Information Sciences

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