Distributed Algorithms for Minimum Cost Multicast With Network Coding

Abstract

Network coding techniques are used to find the minimum-cost transmission scheme for multicast sessions with or without elastic rate demand. It is shown that in wireline networks, solving for the optimal coding subgraphs in network coding is equivalent to finding the optimal routing scheme in a multicommodity flow problem. A set of node-based distributed gradient projection algorithms are designed to jointly implement congestion control/routing at the source node and virtual routing at intermediate nodes. The analytical framework and distributed algorithms are further extended to interference-limited wireless networks where link capacities are functions of the signal-to-interference-plus-noise ratio (SINR). To achieve minimum-cost multicast in this setting, the transmission powers of links must be jointly optimized with coding subgraphs and multicast input rates. Node-based power allocation and power control algorithms are developed for the power optimization. The power algorithms, when iterated in conjunction with the congestion control and routing algorithms, converge to the jointly optimal multicast configuration. The scaling matrices required in the gradient projection algorithms are explicitly derived and are shown to guarantee fast convergence to the optimum from any initial condition.