Noisy Channel Coding via Privacy Amplification and Information Reconciliation

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...

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Bibliographic Details
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
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Summary: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.
ISSN:0018-9448
1557-9654
DOI:10.1109/TIT.2011.2162226