Feedback in Multi-terminal networks

Multiple Access Channels
For a two-user multiple-access channel, the feedback code $$ (2^{nR_1}, 2^{nR_2}, n) $$ is defined as a sequence of mappings $$ x_{1i} (W_1, Y^{i-1}), x_{2i} (W_2, Y^{i-1}) $$ where $$ x_{1i} $$ and $$ x_{2i} $$ are a functions of previously received symbol $$ Y_1, Y_2, \ldots Y_{i-1} $$ and messages $$ W_1 $$ and $$ W_2$$. The messages $$ W_1 \in 2^{nR_1} $$ and $$ W_2 \in 2^{nR_2}$$

In multiple access channels, feedback enlarges the capacity region. For the Gaussian channels, this has been shown in [1] and [2], where [1] is an exact capacity region result for the two user multiple access channel.

Broadcast Channels
For broadcast channels, the encoded message is a function of the received message at one or both the receivers. One interesting aspect of feedback [sum-capacity] is that it is the same whether the encoding at the source is function of the received message at one or both the receivers.

Interference Channels
For the Gaussian interference channel, feedback has been shown to provide potentially unbounded gains in the capacity region. Improvement over the case without feedback was shown for the general K user interference channel in [2]. For the symmetric two user Gaussian interference channel with perfect feedback, it was shown that as the SNR tends to infinity, the gap between the capacity region with and without feedback grows without bound [3].