Capacity of Non-Separable Networks with Restricted Adversaries

2026-03-09

AI Summary

This study addresses the single-source multicast network capacity under adversarial attacks constrained to a prescribed subset of edges. By jointly designing outer and inner codes, the work surpasses the classical cut-set bound and establishes, for the first time, the exact one-shot capacity for a class of two-layer networks. It further introduces a new family of networks that reveals capacity phenomena unique to the setting of constrained adversaries. Leveraging linear network coding together with an analytical framework based on rank and Hamming metrics, the project not only improves the lower bound on capacity for another class of two-layer networks but also partially characterizes the capacity of the newly proposed network family, thereby deepening the understanding of capacity mechanisms in non-separable networks under adversarial constraints.

Technology Category

• Machine Learning: Adversarial Learning & Robustness
• Multiagent Systems: Adversarial Agents
• Game Theory and Economic Paradigms: Adversarial Learning

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Social Networks and Social Media: Social media analysis through the lenses of networks
• Security and Privacy: Large-scale security measurements

Abstract

This paper investigates the problem of single-source multicasting over a communication network in the presence of restricted adversaries. When the adversary is constrained to operate only on a prescribed subset of edges, classical cut-set bounds are no longer tight, and achieving capacity typically requires a joint design of the outer code and the inner (network) code. This stands in sharp contrast with the case of unrestricted adversaries, where capacity can be achieved by combining linear network coding with appropriate rank-metric outer codes. Building on the framework of network decoding, we determine the exact one-shot capacity of one of the fundamental families of 2-level networks introduced in [4], and we improve the best currently known lower bounds for another such family. In addition, we introduce a new family of networks that generalizes several known examples, and derive partial capacity results that illustrate a variety of phenomena that arise specifically in the restricted-adversary setting. Finally, we investigate the concept of separability of networks with respect to both the rank metric and the Hamming metric.

Problem

• network capacity
• restricted adversaries
• single-source multicasting
• non-separable networks
• adversarial networks

Innovation

• restricted adversaries
• network capacity
• non-separable networks
• rank-metric codes
• network decoding