Channel Capacity under the Subtractive Dithered Quantization Model

Hossein Atrsaei, Mireille Sarkiss, Michèle Wigger

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 when 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 fact that Gaussian distributions maximize entropy under a variance constraint. 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-SNR regime; it thus represents a good and simple capacity approximation in this regime.