NDLI: An Extremal Inequality and the Capacity Region of the Degraded Compound Gaussian MIMO Broadcast Channel With Multiple Users

Content Provider	IEEE Xplore Digital Library
Author	Hon-Fah Chong Ying-Chang Liang
Copyright Year	1963
Abstract	The two-user compound Gaussian MIMO broadcast channel models the situation where each user has a finite set of possible realizations. The transmitter sends two messages, one for each user, such that each user must be able to decode its message regardless of the actual realization. This channel also models a broadcast channel (BC) with two groups of users and two messages, with one message intended for each group of users. Weingarten et al. established the capacity region for the degraded case where the realizations/users exhibit a degradedness order. The degradedness order is defined through an additional realization/user where the realizations/users from one set are degraded with respect to him and where he is degraded with respect to the realizations/users from the other set. To show that Gaussian inputs attain the capacity region, they proved a new extremal inequality and employed the use of the channel enhancement technique as well. In this paper, we extend the result to the N-user degraded compound Gaussian MIMO BC, where the N users exhibit a degradedness order similar to the two-user case. We first prove a generalization of the extremal inequality considered by Weingarten et al.; instead of considering the difference between the weighted sum of two sets of conditional differential entropies, we consider the summation of N - 1 sets of such differences, where the conditioning random variables of the N - 1 sets form a Markov chain. Our proof relies on the Gaussian perturbation approach, the necessary KKT conditions as well as a data processing inequality. Finally, we specialize the generalized extremal inequality to characterize the capacity region of the N-user degraded compound Gaussian MIMO BC. By making appropriate use of the necessary KKT conditions, we are able to do away with the use of the channel enhancement technique that was employed in the proof of the capacity region of the two-user case.
Sponsorship	IEEE Information Theory Society
Starting Page	6131
Ending Page	6143
Page Count	13
File Size	281589
File Format	PDF
ISSN	00189448
Volume Number	60
Issue Number	10
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	2014-01-01
Publisher Place	U.S.A.
Access Restriction	One Nation One Subscription (ONOS)
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	MIMO Vectors Compounds Covariance matrices Random variables Gaussian noise Optimization Capacity region compound broadcast channel extremal inequality Gaussian channel Gaussian perturbation
Content Type	Text
Resource Type	Article
Subject	Library and Information Sciences Information Systems Computer Science Applications

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