Stronger communication limits found using refined data processing methods
Beyond Hypercontractivity: Stronger Communication Converses via Rényi Contraction
Information Theory
Summary
The paper improves how we understand limits on communication by studying a mathematical concept called Rényi divergence. It shows a new way to measure how information shrinks when passed through certain processes, which is stronger than previous methods relying on hypercontractivity. The authors use this to better estimate the minimum communication needed for processes like agreement between parties. They demonstrate their improvements with examples involving specific communication channels.
What this means in practice
- •For communication system engineers: Design tighter protocols for one-way communication by understanding stronger lower bounds on message exchange.
- •For network security teams: Assess security guarantees in communication channels where information leakage and agreement protocols depend on refined data-processing limits.
A theory result. No direct application yet.
Authors
Ryo Hommura Moore, Amedeo Roberto Esposito
Abstract
We study the relationship between strong data-processing inequalities for Rényi divergences and hypercontractivity. For Rényi divergences of order greater than one, we characterize the contraction of Rényi divergences through a property of the dual Markov operator that we name power contraction. Using the contraction coefficient, we derive an upper bound on rectangle probabilities in terms of their marginals that is at least as strong as the corresponding bound obtained via hypercontractivity. Combining this result with inversion of the binary Rényi divergence, we derive communication lower bounds for one-way communication-assisted agreement distillation. Examples involving binary symmetric and rare-event Z-channels illustrate the improvements over standard hypercontractive converses.