NDLI: Degrees of Freedom of a Communication Channel: Using DOF Singular Values

Content Provider	IEEE Xplore Digital Library
Author	Somaraju, R. Trumpf, J.
Copyright Year	1963
Abstract	A fundamental problem in any communication system is: given a communication channel between a transmitter and a receiver, how many ¿independent¿ signals can be exchanged between them? Arbitrary communication channels that can be described by linear compact channel operators mapping between normed spaces are examined in this paper. The (well-known) notions of degrees of freedom (DOF) at level ¿ and essential dimension of such channels are developed in this general setting. We argue that the DOF at level ¿ and the essential dimension fundamentally limit the number of independent signals that can be exchanged between the transmitter and the receiver. We also generalize the concept of singular values of compact operators to be applicable to compact operators defined on arbitrary normed spaces which do not necessarily carry a Hilbert space structure. We show how these generalized singular values, which we call DOF singular values, can be used to calculate the DOF at level ¿ and the essential dimension of compact operators that describe communication channels. We describe physically realistic channels that require such general channel models.
Sponsorship	IEEE Information Theory Society
Starting Page	1560
Ending Page	1573
Page Count	14
File Size	307150
File Format	PDF
ISSN	00189448
Volume Number	56
Issue Number	4
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	2010-04-01
Publisher Place	U.S.A.
Access Restriction	One Nation One Subscription (ONOS)
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	Communication channels Hilbert space Australia Communication systems Transmitters Channel capacity MIMO Receiving antennas Transmitting antennas singular values Degrees of freedom (DOF) essential dimension modes of communication operator channels
Content Type	Text
Resource Type	Article
Subject	Library and Information Sciences Information Systems Computer Science Applications

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