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

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,k^ℂ (the classical Stiefel surface) manifolds. Using sphere-packing and random coding arguments, the distortion-rate function is bounded within asymptotically tight limits.