NDLI: MIMO MAC-BC Duality With Linear-Feedback Coding Schemes

Content Provider	IEEE Xplore Digital Library
Author	Belhadj Amor, S. Steinberg, Y. Wigger, M.
Copyright Year	1963
Abstract	We show that the rate regions achieved by linear-feedback coding schemes over dual multi-antenna Gaussian multi-access channels (MACs) and broadcast channels (BCs) with independent noises coincide. By dual here we mean: (1) the channel matrices of the MAC and the BC are transposes of each other and (2) the same total input-power constraint P is imposed on both the channels. We also present multi-letter expressions for the linear-feedback capacity regions of the two channels, i.e., for the set of all rates that are achievable with the linear-feedback coding schemes. We identify a sub-class of MAC and BC linear-feedback coding schemes that achieve the respective linear-feedback capacity regions, and within these subclasses, we identify pairs of MAC and BC coding schemes that achieve the same rate regions. In the two-user case, when the transmitters or the receiver are single-antenna, the capacity region for the Gaussian MAC is known [20], [15] and the capacity-achieving scheme is a linear-feedback coding scheme. With our results, we can thus determine the linear-feedback capacity region of the two-user Gaussian BC when either transmitter or receivers are single-antenna and we can identify the corresponding linear-feedback capacity-achieving coding schemes. Our results show that the control-theory inspired linear-feedback coding scheme by Elia [11], Wu et al. [30], and Ardestanizadeh et al. [1] is sumrate optimal among all the linear-feedback coding schemes for the symmetric single-antenna Gaussian BC with equal channel gains. More generally, we show that the linear-feedback sum-capacity of the scalar Gaussian BC with independent noises is achieved using a simple rearrangement of Ozarow's MAC encodings and decodings. In the K 3-user case, Kramer [16] and Ardestanizadeh et al. [2] determined the linear-feedback sum-capacity for the symmetric single-antenna Gaussian MAC with equal channel gains. Using our duality result, in this paper, we identify the linear-feedback sum-capacity for the K 3-user single-antenna Gaussian BC with equal channel gains. It is equal to the sum-rate achieved by Ardestanizadeh et al.'s linear-feedback coding scheme [1].
Sponsorship	IEEE Information Theory Society
Starting Page	5976
Ending Page	5998
Page Count	23
File Size	1328992
File Format	PDF
ISSN	00189448
Volume Number	61
Issue Number	11
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	2015-01-01
Publisher Place	U.S.A.
Access Restriction	One Nation One Subscription (ONOS)
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	Encoding Receivers MIMO Transmitters Noise Decoding Noise measurement multiple-input multiple-output (MIMO) channels Broadcast channel (BC) multiple-access channel (MAC) Gaussian noise channel capacity duality linear-feedback coding schemes perfect feedback
Content Type	Text
Resource Type	Article
Subject	Library and Information Sciences Information Systems Computer Science Applications

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4	Project PI / Joint PI	Principal Investigator and Joint Principal Investigators of the project	Dr. B. Sutradhar bsutra@ndl.gov.in Prof. Saswat Chakrabarti will be added soon
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