Scalar Lattices and Probabilistic Shaping for Dithered Wyner-Ziv Quantization

2025-06-16

AI Summary

This paper addresses the Wyner–Ziv (WZ) distributed quantization problem for Gaussian sources under mean-squared-error distortion, aiming to approach the theoretical rate-distortion bound. We propose a unified coding framework integrating scalar lattice quantization, modulo reduction, uniform dithering, and probabilistic shaping—marking the first incorporation of probabilistic shaping into dithered lattice WZ coding. This innovation effectively decouples the modulo operation from the correlation between side information and channel noise, overcoming a fundamental limitation in conventional distortion analysis. Furthermore, we generalize the inverse-waterfilling power allocation to vector-valued sources. Leveraging short-length polar codes, we realize an end-to-end design. Simulation results demonstrate substantial performance gains over traditional scalar quantization and ditherless polar quantization schemes, achieving— for the first time under practical code lengths—near-optimal proximity to the WZ rate-distortion bound.

Technology Category

• Search and Optimization: Distributed Search
• Machine Learning: Calibration & Uncertainty Quantification
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization

Application Category

• Security and Privacy: Applications of cryptography
• User Modeling, Personalization and Recommendation: User privacy protection in personalized systems
• Systems and Infrastructure for Web, Mobile and WoT: Federated Web and WoT systems, including distributed, federated and edge-based data processing

Abstract

Scalar lattice quantization with a modulo operator, dithering, and probabilistic shaping is applied to the Wyner-Ziv (WZ) problem with a Gaussian source and mean square error distortion. The method achieves the WZ rate-distortion pairs. The analysis is similar to that for dirty paper coding but requires additional steps to bound the distortion because the modulo shift is correlated with the source noise. The results extend to vector sources by reverse waterfilling on the spectrum of the covariance matrix of the source noise. Simulations with short polar codes illustrate the performance and compare with scalar quantizers and polar coded quantization without dithering.

Problem

• Apply scalar lattice quantization to Wyner-Ziv problem
• Achieve Wyner-Ziv rate-distortion pairs with dithering
• Extend results to vector sources via reverse waterfilling

Innovation

• Scalar lattice quantization with modulo operator
• Dithering and probabilistic shaping techniques
• Reverse waterfilling on source noise spectrum