🤖 AI Summary
This work investigates the channel capacity of an additive white Gaussian noise (AWGN) channel followed by a subtractive dithered uniform quantizer under both average power and peak amplitude constraints. By invoking the Schuchman condition, the system is modeled as an effective additive noise channel with noise distributed as the sum of Gaussian and uniform components. Leveraging the entropy power inequality and constructing a maximum-entropy input distribution, a computable lower bound on capacity is derived. A tighter lower bound is then obtained by optimizing K-point discrete constellations, leading to a concise capacity approximation suitable for moderate signal-to-noise ratios (SNR). Numerical results demonstrate that with K-level quantization, only K mass points are sufficient to closely approach the optimal rate, and the proposed upper and lower bounds exhibit excellent agreement in the moderate-SNR regime.
📝 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 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.