A Survey of Literature Regarding the Multiple Access Channel and Broadcast Channel with Noiseless Feedback

This report is a survey of currently known literature with respect to noiseless (“perfect”) feedback (FB) for the multi–user access channel (MAC, “MISO”) and broadcast channel (BC, “SIMO”), for both the discrete memoryless (DM) case as well as for the additive white gaussian noise (AWGN) case. A motivating example is the FB uplink from a controlling ground terminal to a satellite, where for all practical purposes the signal power can completely dominate the noise and hence the link can be viewed as noiseless. A review of literature on noiseless FB in information theory is provided in the next section. The MAC achievable rates as found in [1] and [2] will be discussed in Section 2.1. The BC achievable rates as found in [3] will be discussed in Section 2.2. Complete determination of the capacity region of some MACs and BCs with FB remain an open problem, e.g. the inner and outer bounds do not coincide.