On Random-Coding Union Bounds with and Without Erasures

Eli Haim, Yuval Kochman, Uri Erez

Research output: Contribution to journalArticlepeer-review

Abstract

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 languageEnglish
Pages (from-to)4294-4308
Number of pages15
JournalIEEE Transactions on Information Theory
Volume64
Issue number6
DOIs
StatePublished - Jun 2018

Keywords

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

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