Capacity of Non-Separable Networks with Restricted Adversaries

TL;DR

This paper studies the capacity of non-separable networks under restricted adversaries, providing exact capacity results for certain network families and exploring the impact of network separability on capacity.

Contribution

It introduces a new framework for analyzing capacity in restricted-adversary networks, including exact results and new network families with partial capacity bounds.

Findings

Exact one-shot capacity for a fundamental network family.

Improved lower bounds for another network family.

Illustration of phenomena specific to restricted-adversary networks.

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.