Constant Compositions in the Sphere Packing Bound for Classical-Quantum Channels

Abstract

The sphere packing bound, in the form given by Shannon, Gallager and Berlekamp, was recently extended to classical-quantum channels, and it was shown that this creates a natural setting for combining probabilistic approaches with some combinatorial ones such as the Lovász theta function. In this paper, we extend the study to the case of constant composition codes. We first extend the sphere packing bound for classical-quantum channels to this case, and we then show that the obtained result is related to a variation of the Lovász theta function studied by Marton. We then propose a further extension to the case of varying channels and codewords with a constant conditional composition given a particular sequence. This extension is then applied to auxiliary channels to deduce a bound which can be interpreted as an extension of the Elias bound.

Extended version of arXiv:1401.6039v2

References in corpus (7)

• Quantum Information Processing with Finite Resources -- Mathematical Foundations
• The Chernoff lower bound for symmetric quantum hypothesis testing
• Strong converse exponent for classical-quantum channel coding
• The Converse Part of The Theorem for Quantum Hoeffding Bound
• No-Signalling Assisted Zero-Error Capacity of Quantum Channels and an Information Theoretic Interpretation of the Lovasz Number
• Constant Compositions in the Sphere Packing Bound for Classical-Quantum Channels
• Elias Bound for General Distances and Stable Sets in Edge-Weighted Graphs

Cited by in corpus (8)

• Quantum Sphere-Packing Bounds with Polynomial Prefactors
• Non-Asymptotic Classical Data Compression with Quantum Side Information
• Divergence radii and the strong converse exponent of classical-quantum channel coding with constant compositions
• The Sphere Packing Bound via Augustin's Method
• A Simple Derivation of the Refined Sphere Packing Bound Under Certain Symmetry Hypotheses
• On the Existence of the Augustin Mean
• Reliable Simulation of Quantum Channels: the Error Exponent
• Minimizing Quantum Renyi Divergences via Mirror Descent with Polyak Step Size