Single-Source/Sink Network Error Correction Is as Hard as Multiple-Unicast

TL;DR

This paper demonstrates that determining the capacity of networks with certain unjammable edges under adversarial jamming is as computationally hard as solving the longstanding open problem of multiple-unicast network coding.

Contribution

It establishes a complexity equivalence between a class of error correction problems in networks and the multiple-unicast network coding problem.

Findings

Capacity determination is as hard as multiple-unicast problem.

Networks with some unjammable edges pose complex capacity challenges.

The problem remains open and computationally difficult.

Abstract

We study the problem of communicating over a single-source single-terminal network in the presence of an adversary that may jam a single link of the network. If any one of the edges can be jammed, the capacity of such networks is well understood and follows directly from the connection between the minimum cut and maximum flow in single-source single- terminal networks. In this work we consider networks in which some edges cannot be jammed, and show that determining the network communication capacity is at least as hard as solving the multiple-unicast network coding problem for the error-free case. The latter problem is a long standing open problem.