Robust quantization and coding for multidimensional linear systems under data rate constraints

Recently we reported results on coding strategies for scalar feedback systems with data-rate-limited feedback channels in which the data-rate constraints are time varying. Such rate-varying channels are typically encountered in communications networks in which links between nodes are subject to noise, congestion, and intermittent disruption. The present paper describes results of extending this research into the multidimensional domain. An important consideration is that for systems of dimension greater than one, many classical feedback designs cannot be realized for operation near the theoretical minimum possible data-rate. A novel control coding scheme is presented, and in terms of this, it is shown that the advantages of coarse signal quantization that had earlier been reported for scalar systems remain in the multidimensional case. The key is to allocate the communication bandwidth efficiently among faster and slower modes. We introduce a technique that allocates bandwidth by assigning time slots. The merit of this technique is discussed in terms of its robustness with respect to time-varying communications bandwidth constraints and also in terms of how well it operates when the feedback channel capacity is near the theoretical minimum data rate.