LQG control approach for Gaussian MAC with feedback

Abstract

Abstract-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-topoint AWGN channel which could be useful in other contexts.