Distortion-rate tradeoff of a source uniformly distributed over the composite PF(N) and the Composite Stiefel manifolds

Authors:
Rajesh T. Krishnamachari;Mahesh K. Varanasi
Affiliations:
Department of Electrical and Computer Engineering, University of Colorado, Boulder, CO;Department of Electrical and Computer Engineering, University of Colorado, Boulder, CO
Venue:
ISIT'09 Proceedings of the 2009 IEEE international conference on Symposium on Information Theory - Volume 1
Year:
2009

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Abstract

To model the benefit accrued due to limited rate feedback on the information transfer of optimal 'input covariance matrices' from a channel-aware receiver to the transmitting users in a multiple-access channel, we study the distortion-rate tradeoff of a source uniformly distributed over multivariate generalizations of PF(n,p2) (the set of positive semi-definite matrices with a trace constraint) and Vn,kC (the classical Stiefel surface) manifolds. Using sphere-packing and random coding arguments, the distortion-rate function is bounded within asymptotically tight limits.