Sum Capacity of K User Gaussian Degraded Interference Channels

TL;DR

This paper introduces a new outer bounding technique for K-user Gaussian interference channels, deriving the sum capacity in closed-form for degraded cases and demonstrating the effectiveness of successive interference cancellation.

Contribution

It proposes a novel genie-MAC outer bound approach and extends the sum-capacity result from two-user to K-user Gaussian degraded interference channels.

Findings

Closed-form sum capacity for K-user Gaussian degraded interference channels.

Successive interference cancellation achieves the sum capacity.

Generalization of two-user results to K-user scenarios.

Abstract

This paper studies a family of genie-MAC (multiple access channel) outer bounds for K-user Gaussian interference channels. This family is inspired by existing genie-aided bounding mechanisms, but differs from current approaches in its optimization problem formulation and application. The fundamental idea behind these bounds is to create a group of genie receivers that form multiple access channels that can decode a subset of the original interference channel's messages. The MAC sum capacity of each of the genie receivers provides an outer bound on the sum of rates for this subset. The genie-MAC outer bounds are used to derive new sum-capacity results. In particular, this paper derives sum-capacity in closed-form for the class of K-user Gaussian degraded interference channels. The sum-capacity achieving scheme is shown to be a successive interference cancellation scheme. This result generalizes a known result for two-user channels to K-user channels.