Multishot Capacity of Networks with Restricted Adversaries

TL;DR

This paper studies the limits of network communication under restricted adversarial errors in multishot scenarios, providing bounds and capacity-achieving schemes for specific network topologies.

Contribution

It introduces bounds and capacity-achieving schemes for multishot adversarial network coding in certain network structures, and initiates capacity analysis for 3-level networks.

Findings

Derived capacity bounds for the Diamond and Mirrored Diamond networks.

Proposed capacity-achieving coding schemes for these networks.

Computed the multishot capacity of the Butterfly Network.

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.