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

• Published in: IEEE/ACM transactions on networking Vol. 26; no. 5; pp. 2033 - 2047
• Main Authors: Cui, Ying, Medard, Muriel, Yeh, Edmund, Leith, Douglas, Duffy, Ken R.
• Format: Journal Article
• Language: English
• Published: New York IEEE 01.10.2018; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Coding; Complexity theory; Cost engineering; Design optimization; distributed algorithm; Distributed algorithms; Formulations; general connection; Identification methods; IEEE transactions; Linear codes; Manufacturing cells; Network coding; network mixing; Optimization; resource optimization
• ISSN: 1063-6692; 1558-2566
• DOI: 10.1109/TNET.2018.2865534

For general connections, the problem of finding network codes and optimizing resources for those codes is intrinsically difficult and a little is known about its complexity. Most of the existing methods for identifying 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 the edge use based on mixing. We first formulate the minimum-cost 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 fairly allows general coding across flows and guarantees no greater cost than existing solutions. Numerical results illustrate the performance of our approach.