Gaussian interference networks with feedback: Duality, sum capacity and dynamic team problems

This paper utilizes and extends the existing control-infor mation theoretic interdisciplinary framework for analyzing multi-user systems with feedback. The result s derived in this paper using this framework are: Generalization of the capacity region of the multiple-acce ss channel (MAC) with feedback with two users to multiple (greater than two) users; and, sum-rate duality between the MAC and broadcast channel (BC) with feedback, which is akin to the estimation-control dual ity. I. I NTRODUCTION Characterization of the capacity of multiuser channels with feedback is gaining value as feed back from the receiver(s) to the transmitter(s) becomes a viable proposition in modern wireless systems. However, obtaining such a characterization is far from stra ightforward. Unfortunately, even when the capacity of the channel is known without feedback, it doe s little to help our understanding of its capacity with feedback. One of the successes in our understanding of the feedback cha nnel is in the case of Gaussian single user channels, where it is well known that there are no capacity gains, but the Schalkwijk and Kailath’s (SK) coding scheme [18], [19] can significantly re duce encoding and decoding complexity. This scheme has been successfully extended to the Gaussian M AC, BC and interference channel (IFC) with feedback [10], [12]–[15]. The MAC with feedback wh en there are two users in the system has seen a particularly successful application of SK coding by Ozarow [14], as a converse can be shown for the achievable region obtained. However, fo r all the other channels, including the MAC with feedback where the number of transmitters is greate r than two, the achievable rates in literature do not meet known outer bounds. Recently, interdisciplinary research in the fields of closed -loop control and communications has gained prominence, providing us with new tools with which to study feedback systems. Specifically, the techniques introduced by Elia [4] have been of particula r help in obtaining new achievable regions for feedback channels. In this paper, we build on Eli a’s work by generalizing the results obtained for two-user systems to systems with greater than t wo users. We apply this to the MAC with feedback, where we determine its capacity 1. Also, we apply it to the BC with feedback and the sum-rate thus obtained is found to be a dual of the sum-cap acity of the MAC with feedback. Finally, we apply this technique to the IFC with feedback. Next, we provide a detailed explanation of the SK coding sche me. Section II introduces the modeling and notations of the Gaussian interference networ ks. In section III, a generalized control theoretic coding scheme is provided. In section IV, we show t hat he sum-rate capacity of MAC with feedback can be achieved by the coding scheme and the ach i v ble rate region of BC with feedback is sum-rate dual to the sum-rate capacity of the dua l BC channel. For the interference channel with feedback, our coding scheme leads to solve a LQG team problem and a sub-optimal linear solution is briefly discussed in section V. A. Schalkwijk and Kailath’s coding scheme and its extensions Proposed for single user Gaussian channels in [18], [19], th e SK coding scheme maps the transmitter’s message to a point θ on the real line. The receiver’s goal is to correct its linear mean squared estimation (LMMSE) estimatê θ(k) at time k of θ. The transmitter aids this correction The authors are with Wireless Networking and Communications Group, Dep artment of Electrical and Computer Engineering, The University of Texas at Austin, Austin, TX 78712, USA (e-mail: wwu@ece .ut xas.edu; sriram@ece.utexas.edu; ari@ece.utexas.edu). Note that the generalization from 2 to greater than 2 is not a straightforward extension of [14].