Noisy Channel Coding via Privacy Amplification and Information Reconciliation

• Published in: IEEE transactions on information theory 2011-11, Vol.57 (11), p.7377-7385
• Main Authors: Renes, J. M., Renner, R.
• Format: Article
• Language: English
• Subjects: Amplification; Applied sciences; Channel coding; Channels; Classical and quantum physics: mechanics and fields; Coding; Coding, codes; Construction; Data compression; Decoding; Electric noise; Entropy; Error probability; Exact sciences and technology; information reconciliation; Information theory; Information, signal and communications theory; Markov processes; Optimization; Physics; Privacy; privacy amplification; Protocol; Quantum information; Random variables; Signal and communications theory; Slepian-Wolf coding; smooth entropies; Telecommunications and information theory
• ISSN: 0018-9448; 1557-9654
• DOI: 10.1109/TIT.2011.2162226

We show that optimal protocols for noisy channel coding of public or private information over either classical or quantum channels can be directly constructed from two more primitive information-theoretic protocols: privacy amplification and information reconciliation, also known as data compression with side information. We do this in the one-shot scenario of structureless resources, and formulate our results in terms of the smooth min- and max-entropy. In the context of classical information theory, this shows that essentially all two-terminal protocols can be reduced to these two primitives, which are in turn governed by the smooth min- and max-entropies, respectively. In the context of quantum information theory, the recently-established duality of these two protocols means essentially all two-terminal protocols can be constructed using just a single primitive. As an illustration, we show how optimal noisy channel coding protocols can be constructed solely from privacy amplification.