Noisy channel coding via privacy amplification and information reconciliation

TL;DR

This paper demonstrates that optimal noisy channel coding protocols for classical and quantum information can be constructed from primitive information-theoretic tools, privacy amplification and information reconciliation, especially in the one-shot setting.

Contribution

It establishes a unified framework showing that all two-terminal protocols can be built from these primitives using smooth min- and max-entropy, simplifying quantum and classical information processing.

Findings

Protocols can be derived from privacy amplification and information reconciliation.

All two-terminal protocols are governed by smooth min- and max-entropy.

Quantum protocols can be constructed from a single primitive due to duality.

Abstract

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 tools: 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.