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A Control Theoretic Interpretation for the Capacity Region of the MAC with Feedback

Summary: 1
A Control Theoretic Interpretation for the
Capacity Region of the MAC with Feedback
Kihyuk Sohn and Achilleas Anastasopoulos
EECS Department, University of Michigan
We consider the problem of communication over a discrete memoryless multiple access channel (DM-MAC) with
noiseless feedback. A single-letter characterization of the capacity of this channel is not currently known. Several
inner and outer bounds exist in the literature that provide expressions involving a number of auxiliary variables. In this
paper we formulate the MAC with feedback capacity problem as a distributed stochastic control problem. Through
this interpretation a single-letter outer bound is derived. Although this bound is larger than existing outer bounds in
general, for the special class of channels for which the capacity is known to be the Cover and Leung region, the
bound is tight. Furthermore, the new formulation provides an interpretation of the auxiliary random variables that
usually appear in relevant inner and outer bounds.
Shannon showed in his early work [1] that the capacity of single-user discrete memoryless channel (DMC) does
not increase with output feedback. Feedback, however, was shown to be useful in the sense of improving the error
performance or simplifying the transmission scheme. When it comes to the multiple-access channels (MACs), the
improvement becomes more dramatic since Gaarder and Wolf [2] showed that the capacity region can be expanded
with output feedback. Subsequently, the capacity region for the MAC with feedback has been studied. Cover and


Source: Anastasopoulos, Achilleas - Department of Electrical Engineering and Computer Science, University of Michigan


Collections: Engineering; Computer Technologies and Information Sciences