Optimization-Based Linear Network Coding for General Connections of Continuous Flows

TL;DR

This paper introduces a new optimization-based method for constructing linear network codes for general continuous flow connections, minimizing edge costs with distributed algorithms and broad coding capabilities.

Contribution

It presents a novel formulation and distributed solutions for network coding that handle general flow connections and optimize resource use.

Findings

The proposed method guarantees no greater cost than non-coding solutions.

Distributed algorithms effectively solve the formulated optimization problems.

The approach supports fairly general coding across flows.

Abstract

For general connections, the problem of finding network codes and optimizing resources for those codes is intrinsically difficult and little is known about its complexity. Most of the existing solutions rely on very restricted classes of network codes in terms of the number of flows allowed to be coded together, and are not entirely distributed. In this paper, we consider a new method for constructing linear network codes for general connections of continuous flows to minimize the total cost of edge use based on mixing. We first formulate the minimumcost network coding design problem. To solve the optimization problem, we propose two equivalent alternative formulations with discrete mixing and continuous mixing, respectively, and develop distributed algorithms to solve them. Our approach allows fairly general coding across flows and guarantees no greater cost than any solution without network coding.