A Deterministic Polynomial--Time Algorithm for Constructing a Multicast Coding Scheme for Linear Deterministic Relay Networks

TL;DR

This paper introduces a polynomial-time algorithm for constructing multicast coding schemes in linear deterministic relay networks, generalizing existing network coding methods to achieve capacity efficiently.

Contribution

It presents a new deterministic polynomial-time algorithm for multicast coding in linear deterministic relay networks, extending prior network coding schemes.

Findings

Deterministic algorithm achieves network capacity in logarithmic network uses.

Algorithm works for networks with multiple destinations.

Constructs multicast coding schemes efficiently in polynomial time.

Abstract

We propose a new way to construct a multicast coding scheme for linear deterministic relay networks. Our construction can be regarded as a generalization of the well-known multicast network coding scheme of Jaggi et al. to linear deterministic relay networks and is based on the notion of flow for a unicast session that was introduced by the authors in earlier work. We present randomized and deterministic polynomial--time versions of our algorithm and show that for a network with $g$ destinations, our deterministic algorithm can achieve the capacity in $\left\lceil \log(g+1)\right\rceil $ uses of the network.