Joint Source and Channel Coding for MIMO Systems: Is it Better to be Robust or Quick?

A framework is developed for optimizing the tradeoff between diversity, multiplexing, and delay in multiple-input multiple-output (MIMO) systems to minimize end-to-end distortion. The goal is to find the optimal balance between the increased data rate provided by antenna multiplexing, the reduction in transmission errors provided by antenna diversity and automatic repeat request (ARQ), and the delay introduced by ARQ. First, closed-form analytical results are developed to minimize end-to-end distortion of a vector quantizer concatenated with a space-time MIMO channel code in the high SNR regime. The minimization determines the optimal point on the diversity-multiplexing tradeoff curve. For large but finite SNR this optimal point is found via convex optimization, which is illustrated with an example of a practical joint source-channel code design. It is then shown that for MIMO systems with ARQ retransmission, sources without a delay constraint have distortion minimized by maximizing the ARQ window size. This results in a new multiplexing-diversity tradeoff region enhanced by ARQ. However, under a source delay constraint the problem formulation changes to account for delay distortion associated with random message arrival and random ARQ completion times. In this case, the simplifications associated with a high SNR assumption break down, and a dynamic programming formulation is required to capture the channel diversity-multiplexing tradeoff as well as the random arrival and retransmission dynamics. Results based on this formulation show that a delay-sensitive system obtains significant performance gains by adapting its operating point on the diversity-multiplexing-delay region to system dynamics.