Comparison-limited Vector Quantization

A variation of the classic vector quantization problem is considered, in which the analog-to-digital (A2D) conversion is not constrained by the cardinality of the output but rather by the number of comparators available for quantization. More specifically, we consider the scenario in which a vector quantizer of dimension d is comprised of k comparators, each receiving a linear combination of the inputs and producing zero/one when this signal is above/below a threshold. Given a distribution of the inputs and a distortion criterion, the value of the linear combinations and thresholds are to be configured so as to minimize the distortion between the quantizer input and its reconstruction. This vector quantizer architecture naturally arises in many A2D conversion scenarios in which the quantizer's cost and energy consumption are severely restricted. For this novel vector quantizer architecture, we propose an algorithm to determine the optimal configuration and provide the first performance evaluation for the case of uniform and Gaussian sources.