Non-Linear Function Computation Broadcast

2025-02-19

AI Summary

This paper studies the multi-user computing broadcast problem: a central node broadcasts a single message, after which each user must losslessly compute a designated linear or nonlinear function—defined over a finite field—using only its local side information. Addressing the limitation of existing approaches that fail to jointly model computational structure, demand dependencies, and side information, we extend Körner’s characteristic graph framework to function computation for the first time, proposing a novel graph-based coding model. Leveraging characteristic graph theory, information-theoretic converse and achievability analyses, and structured code design, we derive tight upper and lower bounds on the optimal broadcast rate. On multiple canonical instances, our scheme achieves significantly higher communication efficiency than state-of-the-art methods. The results establish a new paradigm for distributed function computation that is both theoretically tight and constructively feasible.

Technology Category

• Machine Learning: Graph-based Machine Learning
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization
• Reasoning under Uncertainty: Graphical Models

Application Category

• 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
• Security and Privacy: Large-scale security measurements

Abstract

This work addresses the $K$-user computation broadcast problem consisting of a master node, that holds all datasets and users for a general class of function demands, including linear and non-linear functions, over finite fields. The master node sends a broadcast message to enable each of $K$ distributed users to compute its demanded function in an asymptotically lossless manner with user's side information. We derive bounds on the optimal $K$-user computation broadcast rate that allows the users to compute their demanded functions by capturing the structures of the computations and available side information. Our achievability scheme involves the design of a novel graph-based coding model to build a broadcast message to meet each user's demand, by leveraging the structural dependencies among the datasets, the user demands, and the side information of each user, drawing on K{""o}rner's characteristic graph framework. The converse uses the structures of the demands and the side information available at $K$ users to yield a tight lower bound on the broadcast rate. With the help of examples, we demonstrate our scheme achieves a better communication rate than the existing state of the art.

Problem

• Optimize $K$-user computation broadcast rate
• Design graph-based coding for function demands
• Achieve asymptotically lossless function computation

Innovation

• Graph-based coding model
• Körner's characteristic graph framework
• Asymptotically lossless computation