Approximate feedback capacity of the Gaussian multicast channel

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 nonfeedback 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 deterministic model, from which we make the observation that feedback can also be beneficial for function computation.