Coding Theorems for Compound Problems via Quantum Rényi Divergences

Research output: Contribution to journalArticle

15 Citations (Scopus)

Abstract

Recently, a new notion of quantum Rényi divergences has been introduced by Müller-Lennert, Dupuis, Szehr, Fehr, and Tomamichel and Wilde, Winter, and Yang, which found a number of applications in strong converse theorems. Here, we show that these new Rényi divergences are also useful tools to obtain coding theorems in the direct domain of various problems. We demonstrate this by giving new and considerably simplified proofs for the achievability parts of Stein's lemma with composite null-hypothesis, universal state compression, and the classical capacity of compound classical-quantum channels, based on single-shot error bounds already available in the literature and simple properties of the quantum Rényi divergences. The novelty of our proofs is that the composite/compound coding theorems can be almost directly obtained from the single-shot error bounds, essentially with the same effort as for the case of simple null-hypothesis/single source/single channel.

Original languageEnglish
Article number7086060
Pages (from-to)2997-3012
Number of pages16
JournalIEEE Transactions on Information Theory
Volume61
Issue number6
DOIs
Publication statusPublished - Jun 1 2015

Keywords

  • Channel coding
  • channel capacity
  • information entropy
  • source coding

ASJC Scopus subject areas

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

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