We characterize the capacity region to within log {2(M − 1)} bits/s/Hz for the M -transmitter K -receiver Gaus- sian 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 deterministic model, from which we make the observation that feedback can also be beneficial for function computation.
Marco Pizzolato, Tim Bjørn Dyrby
Colin Neil Jones, Ye Pu, Andrea Alessandretti, Francisco Fernandes Castro Rego
Luis Guillermo Villanueva Torrijo