Joint source and channel coding for MIMO systems: Is it better to be   robust or quick?
  We develop a framework to optimize the tradeoff between diversity, multiplexing, and delay in MIMO systems to minimize end-to-end distortion. We first focus on the diversity-multiplexing tradeoff in MIMO systems, and develop analytical results to minimize distortion of a vector quantizer concatenated with a space-time MIMO channel code. In the high SNR regime we obtain a closed-form expression for the end-to-end distortion as a function of the optimal point on the diversity-multiplexing tradeoff curve. For large but finite SNR we find this optimal point via convex optimization. We then consider MIMO systems using ARQ retransmission to provide additional diversity at the expense of delay. For sources without a delay constraint, distortion is minimized by maximizing the ARQ window size. This results in an ARQ-enhanced multiplexing-diversity tradeoff region, with distortion minimized over this region in the same manner as without ARQ. Under a source delay constraint the problem formulation changes to account for delay distortion associated with random message arrival and random ARQ completion times. We use a dynamic programming formulation to capture the channel diversity-multiplexing tradeoff at finite SNR as well as the random arrival and retransmission dynamics; we solve for the optimal multiplexing-diversity-delay tradeoff to minimize end-to-end distortion associated with the source encoder, channel, and ARQ retransmissions. Our results show that a delay-sensitive system should adapt its operating point on the diversity-multiplexing-delay tradeoff region to the system dynamics. We provide numerical results that demonstrate significant performance gains of this adaptive policy over a static allocation of diversity/multiplexing in the channel code and a static ARQ window size. 
Tim Holliday, Andrea J. Goldsmith, and H. Vincent Poor