Capacity Regions and Bounds for a Class of Z-interference Channels

TL;DR

This paper introduces a new upper bound on the capacity region for a specific class of Z-interference channels, demonstrating cases where this bound is tight and capacity is achieved with superposition coding.

Contribution

The paper derives a novel upper bound for Z-interference channels using a technique by Korner and Marton, and identifies conditions where this bound is tight and capacity-achieving.

Findings

The new bound is tight for some Z-interference channels.

Superposition encoding with partial decoding is optimal for certain channels.

The capacity region can be characterized with a single-letter formula under specific conditions.

Abstract

We define a class of Z-interference channels for which we obtain a new upper bound on the capacity region. The bound exploits a technique first introduced by Korner and Marton. A channel in this class has the property that, for the transmitter-receiver pair that suffers from interference, the conditional output entropy at the receiver is invariant with respect to the transmitted codewords. We compare the new capacity region upper bound with the Han/Kobayashi achievable rate region for interference channels. This comparison shows that our bound is tight in some cases, thereby yielding specific points on the capacity region as well as sum capacity for certain Z-interference channels. In particular, this result can be used as an alternate method to obtain sum capacity of Gaussian Z-interference channels. We then apply an additional restriction on our channel class: the transmitter-receiver pair that suffers from interference achieves its maximum output entropy with a single input distribution irrespective of the interference distribution. For these channels we show that our new capacity region upper bound coincides with the Han/Kobayashi achievable rate region, which is therefore capacity-achieving. In particular, for these channels superposition encoding with partial decoding is shown to be optimal and a single-letter characterization for the capacity region is obtained.