Sum-Capacity and the Unique Separability of the Parallel Gaussian MAC-Z-BC Network

TL;DR

This paper characterizes the unique class of Gaussian interference networks, specifically the MAC-Z-BC network, that are always separable for sum-capacity, providing explicit capacity results and highlighting the non-separability of other networks.

Contribution

It proves that the MAC-Z-BC network is the only interference network always separable for sum-capacity and explicitly characterizes its capacity.

Findings

MAC-Z-BC network is always separable for sum-capacity

Explicit sum-capacity of the MAC-Z-BC network is derived

Other interference networks are not always separable

Abstract

It is known that the capacity of parallel (e.g., multi-carrier) Gaussian point-to-point, multiple access and broadcast channels can be achieved by separate encoding for each subchannel (carrier) subject to a power allocation across carriers. Recent results have shown that parallel interference channels are not separable, i.e., joint coding is needed to achieve capacity in general. This work studies the separability, from a sum-capacity perspective, of single hop Gaussian interference networks with independent messages and arbitrary number of transmitters and receivers. The main result is that the only network that is always (for all values of channel coefficients) separable from a sum-capacity perspective is the MAC-Z-BC network, i.e., a network where a MAC component and a BC component are linked by a Z component. The sum capacity of this network is explicitly characterized.