On the Symmetric Feedback Capacity of the K-user Cyclic Z-Interference Channel

TL;DR

This paper characterizes the symmetric feedback capacity of the K-user cyclic Z-interference channel for both linear deterministic and Gaussian models, revealing how feedback benefits diminish as the number of users increases.

Contribution

It provides a complete characterization of symmetric feedback capacity for the linear deterministic model and an approximate characterization for the Gaussian model, highlighting the impact of user count.

Findings

Feedback capacity decreases as the number of users increases.

Symmetric feedback capacity is a function of the number of users, K.

Feedback provides a constant-gap capacity gain in the Gaussian model.

Abstract

The K-user cyclic Z-interference channel models a situation in which the kth transmitter causes interference only to the (k-1)th receiver in a cyclic manner, e.g., the first transmitter causes interference only to the Kth receiver. The impact of noiseless feedback on the capacity of this channel is studied by focusing on the Gaussian cyclic Z-interference channel. To this end, the symmetric feedback capacity of the linear shift deterministic cyclic Z-interference channel (LD-CZIC) is completely characterized for all interference regimes. Using insights from the linear deterministic channel model, the symmetric feedback capacity of the Gaussian cyclic Z-interference channel is characterized up to within a constant number of bits. As a byproduct of the constant gap result, the symmetric generalized degrees of freedom with feedback for the Gaussian cyclic Z-interference channel are also characterized. These results highlight that the symmetric feedback capacities for both linear and Gaussian channel models are in general functions of K, the number of users. Furthermore, the capacity gain obtained due to feedback decreases as K increases.