Approximate Feedback Capacity of the Gaussian Multicast Channel

TL;DR

This paper characterizes the approximate capacity of the Gaussian multicast channel with feedback, showing that feedback significantly improves capacity and providing exact results for a deterministic model.

Contribution

It extends existing feedback schemes to the multicast setting, achieving near-optimal capacity bounds and demonstrating feedback's benefits for capacity and function computation.

Findings

Feedback improves capacity beyond non-feedback limits.

The generalized scheme achieves within log{2(M-1)} bits of the outer bound.

Exact feedback capacity is established for the deterministic model.

Abstract

We characterize the capacity region to within log{2(M-1)} bits/s/Hz for the M-transmitter K-receiver Gaussian multicast channel with feedback where each receiver wishes to decode every message from the M transmitters. Extending Cover-Leung's achievable scheme intended for (M,K)=(2,1), we show that this generalized scheme achieves the cutset-based outer bound within log{2(M-1)} bits per transmitter for all channel parameters. In contrast to the capacity in the non-feedback case, the feedback capacity improves upon the naive intersection of the feedback capacities of K individual multiple access channels. We find that feedback provides unbounded multiplicative gain at high signal-to-noise ratios as was shown in the Gaussian interference channel. To complement the results, we establish the exact feedback capacity of the Avestimehr-Diggavi-Tse (ADT) deterministic model, from which we make the observation that feedback can also be beneficial for function computation.