LQG control approach for Gaussian MAC with feedback

The communication problem over the N-sender additive white Gaussian noise (AWGN) multiple access channel (MAC) with feedback is considered. It is shown that Kramer´s code, which is known to be sum rate optimal in the class of generalized linear feedback codes, can be obtained by solving a linear quadratic Gaussian (LQG) control problem. This generalizes the previous result of Elia, which recovers Ozarow´s code (a special case of Kramer´s code for N = 2) using different approach based on Youla parametrization. Our construction is based on a general correspondence between AWGN-MAC and a linear time invariant (LTI) system controlled over a point-to-point AWGN channel which could be useful in other contexts.