Renyi partial orders for BISO channels

2025-08-27

AI Summary

This work quantifies information loss under noise for binary-input symmetric-output (BISO) channels, focusing on Rényi mutual information–based partial ordering among channels of equal capacity. We introduce the α-Lorenz curve as a novel analytical tool and rigorously establish that, under generalized Rényi capacity, the binary symmetric channel (BSC) and binary erasure channel (BEC) constitute the extremal elements—upper and lower bounds—of this partial order: the information loss of any BISO channel lies between those of the BSC and BEC. This result extends the classical “more capable” order to the Rényi framework and unifies the characterization of information degradation boundaries across the BISO channel family. Our approach integrates convex analysis, partial order theory, and information-theoretic techniques, yielding both a new theoretical foundation and a computationally tractable framework for channel comparison, robust code design, and information bottleneck analysis.

Technology Category

• Machine Learning: Information Theory
• Reasoning under Uncertainty: Graphical Models
• Constraint Satisfaction and Optimization: Other Foundations of Constraint Satisfaction

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Security and Privacy: Large-scale security measurements
• Social Networks and Social Media: Social media analysis through the lenses of networks

Abstract

A fundamental question in information theory is to quantify the loss of information under a noisy channel. Partial orders are typical tools to that end, however, they are often also challenging to evaluate. For the special class of binary input symmetric output (BISO) channels, Geng et al. showed that among channels with the same capacity, the binary symmetric channel (BSC) and binary erasure channel (BEC) are extremal with respect to the more capable order. Here we extend on this result by considering partial orders based on Renyi mutual information. We establish the extremality of the BSC and BEC in this setting with respect to the generalized Renyi capacity. In the process, we also generalize the needed tools and introduce $α$-Lorenz curves.

Problem

• Quantifying information loss in noisy channels
• Evaluating partial orders for BISO channels
• Establishing extremality of BSC and BEC

Innovation

• Renyi mutual information partial orders
• Generalized Renyi capacity extremality analysis
• Alpha-Lorenz curves for BISO channel evaluation