Noisy channel coding via privacy amplification and information reconciliation

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.

8 pages, 2 figures. v2: final version for publication

References in corpus (6)

• The Uncertainty Relation for Smooth Entropies
• Leftover Hashing Against Quantum Side Information
• The mother of all protocols: Restructuring quantum information's family tree
• One-Shot Classical Data Compression with Quantum Side Information and the Distillation of Common Randomness or Secret Keys
• Generalized relative entropies and the capacity of classical-quantum channels
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Cited by in corpus (39)

• Quantum Resource Theories
• Covert Communication over Noisy Channels: A Resolvability Perspective
• One-Shot Classical-Quantum Capacity and Hypothesis Testing
• One-shot coherence distillation
• Finite blocklength converse bounds for quantum channels
• Beyond heat baths: Generalized resource theories for small-scale thermodynamics
• The information-theoretic costs of simulating quantum measurements
• On the power of PPT-preserving and non-signalling codes
• One-Shot Classical Data Compression with Quantum Side Information and the Distillation of Common Randomness or Secret Keys
• Semidefinite programming strong converse bounds for classical capacity
• Quantum Channel Simulation and the Channel's Smooth Max-Information
• Second-Order Asymptotics for the Classical Capacity of Image-Additive Quantum Channels
• One-shot entanglement-assisted quantum and classical communication
• Non-asymptotic entanglement distillation
• A smooth entropy approach to quantum hypothesis testing and the classical capacity of quantum channels
• Position-based coding and convex splitting for private communication over quantum channels
• Non-asymptotic assisted distillation of quantum coherence
• Channel Coding and Lossy Source Coding Using a Constrained Random Number Generator
• Achieving the Capacity of any DMC using only Polar Codes
• Semantic Security via Seeded Modular Coding Schemes and Ramanujan Graphs
• "Pretty strong" converse for the quantum capacity of degradable channels
• Asymmetric Cryptography with Physical Unclonable Keys
• On converse bounds for classical communication over quantum channels
• Entanglement-assisted private communication over quantum broadcast channels
• A decoupling approach to classical data transmission over quantum channels
• Leftover hashing from quantum error correction: Unifying the two approaches to the security proof of quantum key distribution
• One-shot quantum error correction of classical and quantum information
• Dynamical Landauer Principle: Quantifying Information Transmission by Thermodynamics
• Quantum key distribution with finite resources: Taking advantage of quantum noise
• One-shot Capacity bounds on the Simultaneous Transmission of Classical and Quantum Information
• The Physics of Quantum Information: Complementarity, Uncertainty, and Entanglement
• Secure communication over fully quantum Gel'fand-Pinsker wiretap channel
• On privacy amplification, lossy compression, and their duality to channel coding
• Semantic Security for Quantum Wiretap Channels
• "Pretty strong" converse for the private capacity of degraded quantum wiretap channels
• One-Shot Triple-Resource Trade-Off in Quantum Channel Coding
• How Deep the Theory of Quantum Communications Goes: Superadditivity, Superactivation and Causal Activation
• Semantic Security with Infinite Dimensional Quantum Eavesdropping Channel
• Extendibility limits quantum-secured communication and key distillation