Asymptotic quantization for signal estimation with noisy channels

The authors consider signal estimation using a communication system which consists of a quantizer, a noisy channel, and a decision device. By assuming that the lengths of the quantization intervals become arbitrarily small, they derive the asymptotic signal estimation error for the communication system. The asymptotic error consists of an interaction term which depends on both the quantization error and the channel error. The most significant property of the interaction term is that it can be negative. Next, the authors use the companding approach to find the optimal uniform quantizer. They then suggest using a suboptimal piecewise uniform quantizer to approximate the optimal nonuniform quantizer. Finally, they present several analytic and numerical results to justify the validity of the obtained asymptotic expression