Connecting Multiple-unicast and Network Error Correction: Reduction and Unachievability

TL;DR

This paper establishes a reduction from multiple-unicast network coding problems to single-unicast network error correction problems, demonstrating that capacity may not always be achievable, thus linking two key areas in network information theory.

Contribution

It introduces an efficient reduction from multiple-unicast to single-unicast network error correction, applicable to both zero-error and vanishing-error models, and provides an example of unachievable capacity.

Findings

Reduction preserves feasibility across models

Single-unicast error correction capacity may be unachievable

Links multiple-unicast problems to network error correction challenges

Abstract

We show that solving a multiple-unicast network coding problem can be reduced to solving a single-unicast network error correction problem, where an adversary may jam at most a single edge in the network. Specifically, we present an efficient reduction that maps a multiple-unicast network coding instance to a network error correction instance while preserving feasibility. The reduction holds for both the zero probability of error model and the vanishing probability of error model. Previous reductions are restricted to the zero-error case. As an application of the reduction, we present a constructive example showing that the single-unicast network error correction capacity may not be achievable, a result of separate interest.