Quantization strategies for low-power communications

Power reduction in digital communication systems can be achieved in many ways. Reduction of the wordlengths used to represent data and control variables in the digital circuits comprising a communication system is an effective strategy, as register power consumption increases with wordlength. Another strategy is the reduction of the required data transmission rate, and hence speed of the digital circuits, by efficient source encoding. In this dissertation, applications of both of these power reduction strategies are investigated.; The LMS adaptive filter, for which a myriad of applications exists in digital communication systems, is optimized for performance with a power consumption constraint. This optimization is achieved by an analysis of the effects of wordlength reduction on both performance—transient and steady-state—as well as power consumption. Analytical formulas for the residual steady-state mean square error (MSE) due to quantization versus wordlength of data and coefficient registers are used to determine the optimal allocation of bits to data versus coefficients under a power constraint. A condition on the wordlengths is derived under which the potentially hazardous transient “slowdown” phenomenon is avoided. The algorithm is then optimized for no slowdown and minimum MSE. Numerical studies are presented for the case of LMS channel equalization.; Next, source encoding by vector quantization is studied for distributed hypothesis testing environments with simple binary hypotheses. It is shown that, in some cases, low-rate quantizers exist that cause no degradation in hypothesis testing performance. These cases are, however, uncommon. For the majority of cases, in which quantization necessarily degrades performance, optimal many-cell vector quantizers are derived that minimize the performance loss. These quantizers are optimized using objective functions based on the Kullback-Leibler statistical divergence, or discrimination, and large deviations theory. Motivated by Stein's lemma, the loss in discrimination between two sources due to quantization is minimized. Next, formulas for the losses in discrimination between the hypothesized sources and the so-called “tilted” source are determined. These formulas are used to design quantizers that maximize the area under an analog to the receiver operating characteristic (ROC) curve. The optimal quantizer is shown to have fine resolution in areas where the log-likelihood ratio gradient is large in magnitude. The techniques are extended to the design of quantizers optimal for mixed detection-estimation objectives.