Sequential linear coding for multi user Gaussian channels with active noisy feedback

Shannon considered the point-to-point channel with feedback in 1956 and showed that feedback does not increase the capacity of the channel. Since then, it has been shown that (noiseless) feedback can provide better error exponents and simplify coding/decoding. Moreover, feedback has indeed been shown to increase the capacity of multi user channels such as MAC. However, very little is known about channels with noisy feedback, primarily because it is a problem of decentralized control without any common information, which is vastly a challenging and unknown territory. In this talk, we will start with a point to point channel with (passive) noisy feedback and present a new idea and consequently, a new mathematical framework to study this channel. Based on this framework, we will study various multi user Gaussian channels with active noisy feedback, such as point to point channel, two way channel, MAC, broadcast, relay, MIMO, and interference channels, where there is hardly any theoretical framework, if any at all, to study these channels so far.