Non white Gaussian multiple access channels with feedback

Although feedback does not increase capacity of an additive white noise Gaussian channel, it enables prediction of the noise for non-white additive Gaussian noise channels and results in an improvement of capacity, but at most by a factor of 2 (Pinsker, Ebert, Pombra, and Cover). Although the capacity of white noise channels cannot be increased by feedback, multiple access white noise channels have a capacity increase due to the cooperation induced by feedback. Thomas has shown that the total capacity (sum of the rates of all the senders) of an m-user Gaussian white noise multiple access channel with feedback is less than twice the total capacity without feedback. In this paper, we show that this factor of 2 bound holds even when cooperation and prediction are combined, by proving that feedback increases the total capacity of an m-user multiple access channel with non-white additive Gaussian noise by at most a factor of 2. Manuscript received Oct. 1, 1991; revised Sept. 1, 1993. This work was partially supported by NSF Grant NCR-89-14538, DARPA Contract J-FBI-91-218, and JSEP Contract DAALO3-91-C-0010. S. Pombra is at 413 Mountain Laurel Court, Mountain View, CA 94043. T. M. Cover is with the Departments of Electrical Engineering and Statistics, Stanford University, Stanford, CA 94305. IEEE Log Number 9401815.