Alignment based Network Coding for Two-Unicast-Z Networks

TL;DR

This paper introduces a new linear network coding algorithm for two-unicast-Z networks that uses interference alignment, achieving optimal rates efficiently and providing a new proof of the max-flow min-cut theorem for directed acyclic graphs.

Contribution

It presents a novel interference alignment-based linear coding algorithm for two-unicast-Z networks with proven optimal rate achievement and a new proof of the max-flow min-cut theorem.

Findings

Algorithm achieves rate-pair (1, 1) when feasible.

Algorithm has linear complexity for bounded degree graphs.

Provides a new proof of the max-flow min-cut theorem.

Abstract

In this paper, we study the wireline two-unicast-Z communication network over directed acyclic graphs. The two-unicast-Z network is a two-unicast network where the destination intending to decode the second message has apriori side information of the first message. We make three contributions in this paper: 1. We describe a new linear network coding algorithm for two-unicast-Z networks over directed acyclic graphs. Our approach includes the idea of interference alignment as one of its key ingredients. For graphs of a bounded degree, our algorithm has linear complexity in terms of the number of vertices, and polynomial complexity in terms of the number of edges. 2. We prove that our algorithm achieves the rate-pair (1, 1) whenever it is feasible in the network. Our proof serves as an alternative, albeit restricted to two-unicast-Z networks over directed acyclic graphs, to an earlier result of Wang et al. which studied necessary and sufficient conditions for feasibility of the rate pair (1, 1) in two-unicast networks. 3. We provide a new proof of the classical max-flow min-cut theorem for directed acyclic graphs.