Coding Theorems for Compound Problems via Quantum Rényi Divergences

Milán Mosonyi

    Research output: Contribution to journalArticleResearchpeer-review

    16 Citations (Scopus)

    Abstract

    © 2015 IEEE. 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
    JournalIEEE Transactions on Information Theory
    Volume61
    Issue number6
    DOIs
    Publication statusPublished - 1 Jun 2015

    Keywords

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

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