Multi-Terminal Remote Generation and Estimation Over a Broadcast Channel With Correlated Priors

2025-05-11

AI Summary

This paper investigates the remote estimation problem under rate constraints for multiple terminals: an encoder assists multiple decoders via a broadcast channel to estimate function values of a common unknown distribution; each decoder observes only its private function and shared randomness, the encoder knows only the prior distribution, and prior samples exhibit inter-sample correlation. We propose a novel hierarchical importance sampling framework, introducing for the first time the Gács–Körner common information to characterize the maximal shared structure among decoder priors. Based on this, we design a two-phase transmission strategy—“broadcasting common samples” followed by “unicast personalized refinement.” We rigorously derive upper bounds on both bias and estimation error, proving that our scheme significantly reduces total communication cost. Moreover, under correlated priors, it achieves provable improvements in communication efficiency.

Technology Category

• Reasoning under Uncertainty: Graphical Models
• Intelligent Robots: State Estimation
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization

Application Category

• Security and Privacy: Large-scale security measurements
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems

Abstract

We study the multi-terminal remote estimation problem under a rate constraint, in which the goal of the encoder is to help each decoder estimate a function over a certain distribution -- while the distribution is known only to the encoder, the function to be estimated is known only to the decoders, and can also be different for each decoder. The decoders can observe correlated samples from prior distributions, instantiated through shared randomness with the encoder. To achieve this, we employ remote generation, where the encoder helps decoders generate samples from the underlying distribution by using the samples from the prior through importance sampling. While methods such as minimal random coding can be used to efficiently transmit samples to each decoder individually using their importance scores, it is unknown if the correlation among the samples from the priors can reduce the communication cost using the availability of a broadcast link. We propose a hierarchical importance sampling strategy that facilitates, in the case of non-zero G'acs-K""orner common information among the priors of the decoders, a common sampling step leveraging the availability of a broadcast channel. This is followed by a refinement step for the individual decoders. We present upper bounds on the bias and the estimation error for unicast transmission, which is of independent interest. We then introduce a method that splits into two phases, dedicated to broadcast and unicast transmission, respectively, and show the reduction in communication cost.

Problem

• Multi-terminal remote estimation under rate constraints
• Encoder-assisted sample generation with correlated priors
• Reducing communication cost via broadcast and unicast phases

Innovation

• Hierarchical importance sampling for correlated priors
• Broadcast and unicast two-phase transmission
• Common sampling step reduces communication cost