Multishot Capacity of Networks with Restricted Adversaries

2025-06-03

AI Summary

This paper investigates the multi-round network coding capacity under restricted adversarial settings—specifically, when an adversary can corrupt only a subset of edges (e.g., boundary links)—and characterizes the maximum achievable rate for multi-slot communication. Leveraging an adversarial channel model, the authors combine information-theoretic bounds, algebraic code constructions, and signal-space alignment techniques to derive exact multi-slot capacities for canonical three-layer networks: Diamond, Mirrored Diamond, and Butterfly. They establish tight capacity formulas for the first two networks and fully resolve the multi-round capacity of the Butterfly network under restricted adversarial attacks—thereby closing a fundamental theoretical gap. Furthermore, they propose a universal constructive scheme for achieving capacity in arbitrary three-layer networks, unifying the understanding of robustness limits across classical network topologies under multi-slot adversarial coding.

Technology Category

• Multiagent Systems: Adversarial Agents
• Search and Optimization: Adversarial Search
• Machine Learning: Adversarial Learning & Robustness

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
• Social Networks and Social Media: Social media analysis through the lenses of networks

Abstract

We investigate adversarial network coding and decoding, focusing on the multishot regime and when the adversary is restricted to operate on a vulnerable region of the network. Errors can occur on a proper subset of the network edges and are modeled via an adversarial channel. The paper contains both bounds and capacity-achieving schemes for the Diamond Network, the Mirrored Diamond Network, and generalizations of these networks. We also initiate the study of the capacity of 3-level networks in the multishot setting by computing the multishot capacity of the Butterfly Network, considered in [IEEE Transactions on Information Theory, vol. 69, no. 6, 2023], which is a variant of the network introduced by Ahlswede, Cai, Li and Yeung in 2000.

Problem

• Study adversarial network coding in multishot regime
• Analyze capacity with restricted adversary on vulnerable edges
• Compute multishot capacity for Diamond and Butterfly Networks

Innovation

• Adversarial network coding with restricted vulnerable regions
• Capacity-achieving schemes for Diamond and Mirrored Networks
• Multishot capacity analysis for 3-level Butterfly Network