Computer-aided Characterization of Fundamental Limits of Coded Caching with Linear Coding

2025-11-24

AI Summary

This work investigates the fundamental performance limits of coded caching systems under linear coding constraints. To address the looseness of conventional converse bounds, we introduce non-Shannon-type information inequalities—previously unexploited in this setting—and integrate them with the problem’s inherent symmetry and caching-specific structural constraints. We develop a computer-aided analytical framework grounded in representable polyhedra, leveraging symmetry reduction and minimal common information constructions to substantially lower the computational complexity of the associated linear programs. The proposed methodology yields significantly tighter converse bounds, enabling the first rigorous proof of optimality for several memory–load trade-off points under linear coding. Furthermore, it reveals that the global performance limit is fully characterized by structured request subsets of small cardinality—thereby surpassing the tightness and generality of existing analytical bounds.

Technology Category

• Constraint Satisfaction and Optimization: Other Foundations of Constraint Satisfaction
• Search and Optimization: Non-convex Optimization
• Cognitive Modeling & Cognitive Systems: Neural Spike Coding

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

Inspired by prior work by Tian and by Cao and Xu, this paper presents an efficient computer-aided framework to characterize the fundamental limits of coded caching systems under the constraint of linear coding. The proposed framework considers non-Shannon-type inequalities which are valid for representable polymatroids (and hence for linear codes), and leverages symmetric structure and problem-specific constraints of coded caching to reduce the complexity of the linear program. The derived converse bounds are tighter compared to previous known analytic methods, and prove the optimality of some achievable memory-load tradeoff points under the constraint of linear coding placement and delivery. These results seem to indicate that small, structured demand subsets combined with minimal common information constructions may be sufficient to characterize optimal tradeoffs under linear coding.

Problem

• Characterizing fundamental limits of coded caching with linear coding constraints
• Developing computer-aided framework using non-Shannon inequalities for polymatroids
• Establishing optimal memory-load tradeoffs under linear coding placement

Innovation

• Computer-aided framework for coded caching limits
• Uses non-Shannon inequalities for linear codes
• Leverages symmetric structure to reduce complexity