Quantization for LTI systems with noiseless channels

This paper studies the rate requirements for achieving a monotonic bounded estimation error sequence and stability achieving communication schemes, recursive and forward-looking, for LTI systems where the controller and the plant are connected via a noiseless digital channel. Using information theoretic arguments, quantizers are designed under two different criteria, both of which use the mean-square estimation error measure. For the monotonic boundedness of the uncertainty, which is measured in terms of the mean-square error or the entropy power, it is shown that in noiseless systems recursive schemes entail no loss of performance as compared with forward-looking schemes, whereas in noisy systems recursiveness in quantization leads to higher bit rate requirements. For noiseless systems, uniform quantization noise is shown to be the effective one and distortion constrained entropy minimizing quantization is introduced as a time invariant stable quantization method.