By Topic

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

Sign In

Cookies must be enabled to login.After enabling cookies , please use refresh or reload or ctrl+f5 on the browser for the login options.

Formats Non-Member Member
$33 $13
Learn how you can qualify for the best price for this item!
Become an IEEE Member or Subscribe to
IEEE Xplore for exclusive pricing!
close button

puzzle piece

IEEE membership options for an individual and IEEE Xplore subscriptions for an organization offer the most affordable access to essential journal articles, conference papers, standards, eBooks, and eLearning courses.

Learn more about:

IEEE membership

IEEE Xplore subscriptions

2 Author(s)
Somaraju, R. ; Sch. of Inf. Technol. & Electr. Eng., Univ. of New South Wales at ADFA, Canberra, ACT, Australia ; Trumpf, J.

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.

Published in:

Information Theory, IEEE Transactions on  (Volume:56 ,  Issue: 4 )