Dependence Balance and Capacity Bounds for Multiterminal Communication and Wiretap Channels

TL;DR

This paper introduces a new dependence balance inequality based on fractional partitions, providing improved capacity bounds for multiterminal and wiretap channels, especially Gaussian channels.

Contribution

It develops a novel dependence balance inequality and applies it to derive tighter upper bounds on communication and secret rates in multiterminal channels.

Findings

New upper bound on shared randomness rate among terminals.

Bounds are optimized by Gaussian distributions for Gaussian channels.

Improved cut-set bounds for scalar Gaussian channels and relay channels.

Abstract

An information measure based on fractional partitions of a set is used to derive a general dependence balance inequality for communication. This inequality is used to obtain new upper bounds on reliable and secret rates for multiterminal channels. For example, we obtain a new upper bound on the rate of shared randomness generated among terminals, a counterpart of the cut-set bound for reliable communication. The bounds for reliable communication use the concept of auxiliary receivers, and we show that they are optimized by Gaussian distributions for Gaussian channels. The bounds are applied to multiaccess channels with generalized feedback and relay channels, and improve the cut-set bound for scalar Gaussian channels. The improvement for Gaussian relay channels complements results obtained with other methods.