On the achievable rate of the additive Gaussian noise channel with noisy feedback

Communications systems operating over additive Gaussian noise channels with no feedback or ideal channel output feedback are now well studied. However, these set-ups model extreme cases and fail to provide much insight into more practical feedback systems. Therefore, in this paper, a noisy feedback communication system is considered. We study the application of linear multi-dimensional coding of the feedback and data signal. Upper bounds on the achievable rate for our set-up, that are functions of the open-loop capacity and ideal feedback capacity, are derived.