A Linear Network Code Construction for General Integer Connections Based on the Constraint Satisfaction Problem
Issue No. 06 - Dec. (2017 vol. 25)
Ying Cui , Department of Electronic Engineering, Shanghai Jiao Tong University, Shanghai, China
Muriel Medard , Massachusetts Institute of Technology, Cambridge, MA, USA
Edmund Yeh , Department of Electrical and Computer Engineering, Northeastern University, Boston, MA, USA
Douglas Leith , Trinity College Dublin, Dublin, Ireland
Fan Lai , Department of Electronic Engineering, Shanghai Jiao Tong University, Shanghai, China
Ken R. Duffy , Maynooth University, Maynooth, Ireland
The problem of finding network codes for general connections is inherently difficult in capacity constrained networks. Resource minimization for general connections with network coding is further complicated. Existing methods for identifying solutions mainly rely on highly restricted classes of network codes, and are almost all centralized. In this paper, we introduce linear network mixing coefficients for code constructions of general connections that generalize random linear network coding for multicast connections. For such code constructions, we pose the problem of cost minimization for the subgraph involved in the coding solution and relate this minimization to a path-based constraint satisfaction problem (CSP) and an edge-based CSP. While CSPs are NP-complete in general, we present a path-based probabilistic distributed algorithm and an edge-based probabilistic distributed algorithm with almost sure convergence in finite time by applying communication free learning. Our approach allows fairly general coding across flows, guarantees no greater cost than routing, and shows a possible distributed implementation. Numerical results illustrate the performance improvement of our approach over existing methods.
Network coding, Distributed algorithms, Minimization, Probabilistic logic, Linear codes, IEEE transactions
Y. Cui, M. Medard, E. Yeh, D. Leith, F. Lai and K. R. Duffy, "A Linear Network Code Construction for General Integer Connections Based on the Constraint Satisfaction Problem," in IEEE/ACM Transactions on Networking, vol. 25, no. 6, pp. 3441-3454, 2017.