Channel Capacity under the Subtractive Dithered Quantization Model

Abstract

We study the capacity of an additive white Gaussian noise (AWGN) channel followed by a subtractive dithered uniform quantizer. Under the Schuchman conditions and with negligible overload probability, the system admits an additive-noise representation in which the effective noise is the sum of Gaussian and uniform components. Capacity bounds are derived for this model where inputs are subject to an average-power constraint as well as a peak-amplitude constraint, where the latter accounts for the limited quantizer dynamic range. Specifically, a computable lower bound is obtained based on the entropy power inequality (EPI), using the maximum-entropy input under the above constraints. Tighter numerical lower bounds are derived using discrete input constellations with finite mass points. Finally, an upper bound is obtained by exploiting the maximum-entropy property of the Gaussian distribution for a given variance. Numerical results show that, for a K-level quantizer, discrete constellations with K mass points already achieve near-optimal rates among the tested families. Moreover, our upper bound is close to the lower bounds in the moderate signal-to-noise ratio (SNR) regime; thus it provides a simple capacity approximation in this regime.