A noisy feedback encoding scheme for the Gaussian channel

In certain communications systems, it is a reasonable to assume the presence of a noisy feedback channel. The ability to send data from receiver back to transmitter opens new doors in the way of modulation schemes. In this paper, we investigate the class of linear feedback encoding schemes in which the transmitter linearly encodes the feedback information along with the message to be sent. Given a general framework, we propose a new scheme and compare it to a well-known linear encoding method - the Schalkwijk-Kailath scheme. The new technique is then optimized based on power allocation requirements.