Linear sum capacity for Gaussian multiple access channel with feedback

This paper studies the class of generalized linear feedback codes for additive white Gaussian noise multiple access channel. This class includes (nonlinear) nonfeedback codes at one extreme and linear feedback codes by Schalkwijk and Kailath, Ozarow, and Kramer at the other extreme. The linear sum capacity C_L(P), the maximum sum-rate achieved by the generalized linear feedback codes, is characterized under symmetric block power constraints P for all the senders. In particular, it is shown that the Kramer linear code achieves C_L(P). Based on the properties of the conditional maximal correlation, an extension of the Hirschfeld-Gebelein-Renyi maximal correlation, it is conjectured that Kramer's linear code achieves not only the linear sum capacity, but also the general sum capacity, i.e., the maximum sum-rate achieved by arbitrary feedback codes.