Simultaneous SDR optimality via a joint matrix decomposition

This work considers the joint source-channel problem of transmitting a Gaussian source over a two-user multiple-input multiple-output (MIMO) broadcast channel. We show the existence of non-trivial channels, where the optimal distortion pair (which for high signal-to-noise ratios equals the point-to-point distortions of the individual users) may be achieved. A condition for existence of a joint triangularization of the MIMO channels which shapes the ratio of the diagonals to a desired form is derived. Whenever possible, all diagonal elements but one are made equal. We then employ a hybrid digital-analog scheme to the source, where the digital part is sent over the equal subchannels and the analog refinement is sent over the remaining one.