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For K-level subtractive dithered quantizers, discrete inputs with exactly K mass points achieve near-optimal rates under power constraints.

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2026-06-30 08:40 UTC pith:HHQLEFMV

load-bearing objection The paper gives computable EPI-based bounds on capacity for AWGN with subtractive dithered quantization under joint power and peak constraints, with the main numerical observation that K-point discrete inputs perform well.

arxiv 2606.28842 v1 pith:HHQLEFMV submitted 2026-06-27 cs.IT eess.SPmath.IT

Channel Capacity under the Subtractive Dithered Quantization Model

Hossein Atrsaei , Mireille Sarkiss , Mich\`ele Wigger This is my paper
classification cs.IT eess.SPmath.IT
keywords channel capacitysubtractive ditheruniform quantizationAWGN channelcapacity boundsdiscrete constellationsentropy power inequalitypeak power constraint
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper derives capacity bounds for an AWGN channel followed by subtractive dithered uniform quantization. Under the model conditions, the effective noise becomes the sum of Gaussian and uniform components. A lower bound follows from the entropy power inequality applied to the maximum-entropy input, while tighter numerical lower bounds use finite discrete constellations. An upper bound exploits the maximum-entropy property of Gaussians under a variance constraint. Numerical evaluation shows that K-mass-point discrete inputs already come close to the best rates tested, and the upper bound tracks the lower bounds closely at moderate SNR.

Core claim

Under the subtractive dithered quantization model that admits an additive Gaussian-plus-uniform noise representation, capacity under average-power and peak-amplitude constraints is bounded from below by rates achieved with discrete constellations having K mass points for a K-level quantizer; an upper bound obtained by replacing the effective noise entropy with that of a Gaussian of equal variance lies close to these lower bounds in the moderate-SNR regime and therefore supplies a simple capacity approximation.

What carries the argument

The additive-noise representation in which effective noise equals the sum of the original Gaussian noise and a uniform dither component; this representation enables direct application of the entropy power inequality for the lower bound and Gaussian entropy maximization for the upper bound.

Load-bearing premise

The Schuchman conditions hold and overload probability remains negligible so that the system exactly reduces to an additive Gaussian-plus-uniform noise channel.

What would settle it

A direct computation of mutual information for the original quantized channel (without invoking the additive-noise model) that yields rates materially below the derived upper bound at moderate SNR would falsify the approximation quality claimed for that regime.

Watch this falsifier — get emailed when new claim-graph text bears on it.

If this is right

  • For any K-level quantizer, discrete inputs limited to K mass points already attain rates close to the highest values obtained from the families examined.
  • The upper bound based on Gaussian entropy maximization serves as a simple and accurate capacity estimate precisely when SNR is moderate.
  • Tighter lower bounds are obtained by optimizing over discrete constellations with a finite number of mass points subject to the power constraints.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The results imply that, once dither is subtracted, the uniform noise component does not force the optimal input away from simple discrete supports whose size matches the quantizer resolution.
  • Because the upper bound is tight at moderate SNR, system designers could use it directly for link-budget calculations instead of running full mutual-information optimizations.
  • The same bounding technique may extend to vector channels or to cases where the quantizer levels are nonuniform, provided the additive-noise representation still holds.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit.

Referee Report

0 major / 2 minor

Summary. The manuscript studies the capacity of an AWGN channel followed by a subtractive dithered uniform quantizer. Under Schuchman conditions and negligible overload probability, it models the effective noise as the sum of Gaussian and uniform components. Capacity bounds are derived under average-power and peak-amplitude constraints: an EPI-based lower bound using the maximum-entropy input, tighter numerical lower bounds with discrete K-point constellations, and an upper bound based on Gaussian maximum entropy. Numerical results claim that K-mass-point inputs achieve near-optimal rates for K-level quantizers and that the upper bound approximates the lower bounds in moderate SNR.

Significance. The work applies standard information-theoretic tools (EPI, max-entropy distributions) to a practical quantization model, providing bounds and an approximation that could be useful for system design. The finding that discrete constellations with K mass points suffice is a strength, as it suggests simple inputs are sufficient. Credit is given for the explicit use of established properties without introducing new parameters or circular arguments.

minor comments (2)
  1. The abstract states that 'discrete constellations with K mass points already achieve near-optimal rates among the tested families,' but the specific families tested and the definition of 'near-optimal' (e.g., gap to upper bound) should be clarified in the numerical results section.
  2. The peak-amplitude constraint is introduced to account for limited quantizer dynamic range, but the exact formulation of this constraint and how it interacts with the average-power constraint could be stated more explicitly.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for the positive assessment and the recommendation of minor revision. The referee summary correctly captures the scope and results of the manuscript. No major comments appear in the report.

Circularity Check

0 steps flagged

No significant circularity identified

full rationale

The paper derives capacity bounds for the subtractive dithered quantization model using the entropy power inequality for a lower bound (via maximum-entropy input under joint power and peak constraints) and the Gaussian maximum-entropy property for an upper bound on output entropy. These are standard, externally established results independent of the paper. Discrete constellation lower bounds are obtained by direct numerical evaluation. No step reduces by construction to a fitted parameter, self-definition, or self-citation chain; the numerical claim that K-mass-point inputs are near-optimal follows from explicit computation on the additive Gaussian-plus-uniform noise model without internal reduction.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The additive-noise representation and all subsequent bounds rest on the Schuchman conditions plus the modeling choice of negligible overload probability; no free parameters or invented entities are introduced in the abstract.

axioms (1)
  • domain assumption Schuchman conditions hold and overload probability is negligible
    Invoked to obtain the Gaussian-plus-uniform additive-noise model that underpins every capacity bound.

pith-pipeline@v0.9.1-grok · 5735 in / 1188 out tokens · 31251 ms · 2026-06-30T08:40:19.887765+00:00 · methodology

0 comments
read the original 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.

Figures

Figures reproduced from arXiv: 2606.28842 by Hossein Atrsaei, Mich\`ele Wigger, Mireille Sarkiss.

Figure 1
Figure 1. Figure 1: Block diagram of the communication system model with subtractive dithered quantization at the receiver. [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Capacity bounds for K = 4 quantization levels. Top: high-SNR regime. Bottom: low-SNR regime in logarithmic scale. average-power constraints, leading to a sequence of increas￾ingly tight lower bounds on the capacity C(A, P0). Remark 2. The effective noise W¯ has a continuous density with finite variance and admits an analytic extension. Under such regularity conditions, the capacity-achieving input distri￾b… view at source ↗
Figure 5
Figure 5. Figure 5: Capacity of a one-bit sign quantizer under an average power [PITH_FULL_IMAGE:figures/full_fig_p005_5.png] view at source ↗

discussion (0)

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Forward citations

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Reference graph

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