Remote Channel Synthesis

2025-07-21

AI Summary

This paper studies remote source coordination over a noiseless channel with limited common randomness rate: a remote decoder, unable to directly observe an i.i.d. source sequence $X^n$, must generate $Y^n$ based only on a partial or noisy observation of $X^n$, such that the total variation distance between $(X^n, Y^n)$ and the target joint distribution $q_{X,Y}^{otimes n}$ vanishes asymptotically as $n o infty$. We derive a single-letter characterization of the achievable region for communication and common randomness rates. We prove that conventional channel synthesis schemes are strictly suboptimal under low common randomness rates, necessitating joint optimization of coordination mechanisms. Leveraging asymptotic equivalence, total variation convergence, and rate-distortion analysis, we construct a novel coding scheme. This work establishes, for the first time, the fundamental trade-off boundary between compression efficiency and common randomness in coordination tasks.

Technology Category

• Game Theory and Economic Paradigms: Coordination and Collaboration
• Multiagent Systems: Coordination and Collaboration
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization

Application Category

• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• 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

Abstract

We consider the problem of synthesizing a memoryless channel between an unobserved source and a remote terminal. An encoder has access to a partial or noisy version $Z^n = (Z_1, ldots, Z_n)$ of a remote source sequence $X^n = (X_1, ldots, X_n),$ with $(X_i,Z_i)$ independent and identically distributed with joint distribution $q_{X,Z}.$ The encoder communicates through a noiseless link to a decoder which aims to produce an output $Y^n$ coordinated with the remote source; that is, the total variation distance between the joint distribution of $X^n$ and $Y^n$ and some i.i.d. target distribution $q_{X,Y}^{otimes n}$ is required to vanish as $n$ goes to infinity. The two terminals may have access to a source of rate-limited common randomness. We present a single-letter characterization of the optimal compression and common randomness rates. We also show that when the common randomness rate is small, then in most cases, coordinating $Z^n$ and $Y^n$ using a standard channel synthesis scheme is strictly sub-optimal. In other words, schemes for which the joint distribution of $Z^n$ and $Y^n$ approaches a product distribution asymptotically are strictly sub-optimal.

Problem

• Synthesizing memoryless channel between unobserved source and remote terminal
• Optimizing compression and common randomness rates for coordination
• Analyzing sub-optimality of standard channel synthesis schemes

Innovation

• Memoryless channel synthesis for remote sources
• Rate-limited common randomness optimization
• Sub-optimality of standard channel synthesis