The AWGN BC with MAC feedback: A reduction to noiseless feedback via interaction

We consider the problem of communication over a two-user Additive White Gaussian Noise Broadcast Channel (AWGN-BC) with an AWGN Multiple Access (MAC) active feedback. We describe a constructive reduction from this setup to the well-studied setup of linear-feedback coding over the AWGN-BC with noiseless feedback (and different parameters). This reduction facilitates the design of linear-feedback coding schemes in the (passive) noiseless feedback regime, which can then be easily and constructively transformed into coding schemes in the MAC feedback regime that attain the exact same rates. Our construction introduces an element of interaction into the coding protocol, and is based on modulo-lattice operations. As an example, we apply our method to the Ozarow-Leung scheme, and demonstrate how MAC feedback can be used to enlarge the capacity region of the AWGN-BC.