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

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 P_F(n,p²) (the set of positive semi-definite matrices with a trace constraint) and V_n,k ^¿ (the classical Stiefel surface) manifolds. Using sphere-packing and random coding arguments, the distortion-rate function is bounded within asymptotically tight limits.