Distributed Scalar Quantization for Computing: High-Resolution Analysis and Extensions

Abstract

Communication of quantized information is frequently followed by a computation. We consider situations of \emph{distributed functional scalar quantization}: distributed scalar quantization of (possibly correlated) sources followed by centralized computation of a function. Under smoothness conditions on the sources and function, companding scalar quantizer designs are developed to minimize mean-squared error (MSE) of the computed function as the quantizer resolution is allowed to grow. Striking improvements over quantizers designed without consideration of the function are possible and are larger in the entropy-constrained setting than in the fixed-rate setting. As extensions to the basic analysis, we characterize a large class of functions for which regular quantization suffices, consider certain functions for which asymptotic optimality is achieved without arbitrarily fine quantization, and allow limited collaboration between source encoders. In the entropy-constrained setting, a single bit per sample communicated between encoders can have an arbitrarily-large effect on functional distortion. In contrast, such communication has very little effect in the fixed-rate setting.

36 pages, 10 figures

References in corpus (1)

• Source Coding With Encoder Side Information

Cited by in corpus (16)

• Message-Passing Estimation from Quantized Samples
• Analysis-by-Synthesis Quantization for Compressed Sensing Measurements
• Optimal Quantization for Compressive Sensing under Message Passing Reconstruction
• Deterministic Annealing Based Optimization for Zero-Delay Source-Channel Coding in Networks
• Distributed Functional Scalar Quantization Simplified
• Distributed Quantization Networks
• High-Rate Vector Quantization for the Neyman-Pearson Detection of Correlated Processes
• Communication Cost of Transforming a Nearest Plane Partition to the Voronoi Partition
• Interactive Scalar Quantization for Distributed Resource Allocation
• Deep Learning for Distributed Channel Feedback and Multiuser Precoding in FDD Massive MIMO
• Interactive Nearest Lattice Point Search in a Distributed Setting: Two Dimensions
• Overhead Performance Tradeoffs - A Resource Allocation Perspective
• Towards a Converse for the Nearest Lattice Point Problem
• Very Low-Rate Variable-Length Channel Quantization for Minimum Outage Probability
• Entropy Density and Mismatch in High-Rate Scalar Quantization with Renyi Entropy Constraint
• On MMSE estimation from quantized observations in the nonasymptotic regime