On Random-Coding Union Bounds with and Without Erasures

Eli Haim, Yuval Kochman, Uri Erez

Research output: Contribution to journalArticlepeer-review


Upper bounds on the error probability of channel coding are derived for codebooks drawn from random codebook ensembles with various independence and symmetry assumptions. For regular decoding (without an erasure option), the random coding union bound of Polyanskiy et al. is improved by carefully taking ties (equal likelihood scores) into account. It is shown that the improved bound is always better than threshold-decoding based bounds. The framework is extended to the case of decoding with an erasure option, deriving several achievability bounds in the same spirit. In order to exemplify the merits of the approach, the bounds are evaluated for the case of pairwise-independent uniformly-distributed ensembles (e.g., shifted random linear codes).

Original languageAmerican English
Pages (from-to)4294-4308
Number of pages15
JournalIEEE Transactions on Information Theory
Issue number6
StatePublished - Jun 2018

Bibliographical note

Funding Information:
Manuscript received September 13, 2015; revised November 21, 2017; accepted January 30, 2018. Date of publication April 10, 2018; date of current version May 18, 2018. E. Haim and U. Erez was supported by the Israel Science Foundation under Grant 1956/15. E. Haim and Y. Kochman was supported by the Israel Science Foundation under Grant 956/12. Y. Kochman was supported in part by the HUJI Cyber Security Research Center in conjunction with the Israel National Cyber Bureau in the Prime Minister’s Office and in part by the German-Israeli Foundation for Scientific Research and Development. This paper was presented at the 2013 International Symposium on Information Theory.

Publisher Copyright:
© 1963-2012 IEEE.


  • Finite blocklength bounds
  • erasure decoding
  • maximum-likelihood decoding
  • random-coding union bound
  • threshold decoding
  • tie-breaking


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