Abstract

In this paper, we consider the problem of information multicast, namely transmitting common information from a sender s to a set of receivers T , in a communication network. Conventionally, in a communication network such as the Internet, this is done by distributing information over a multicast distribution tree. The nodes of such a tree are required only to replicate and forward, i.e., route, information received. Recently, Ahlswede et al. [1] demonstrated that it is in general suboptimal to restrict the network nodes to perform only routing. They show that the multicast capacity, which is defined as the maximum rate that a sender can communicate common information to a set of receivers, is given by the minimum C = min t#T C t of max-flows C t = maxflow(s, t) between the sender and each receiver. Moreover, they showed that while the multicast capacity cannot be achieved in general by routing, it can be achieved by network coding. Network coding refers to a scheme where coding is done at the interior nodes in the network, not only at the sender and receivers. Li, Yeung, and Cai [2] showed that it is su#cient for the encoding functions at the interior nodes to be linear. Koetter and Medard[3] gave an algebraic characterization of linear encoding schemes and proved existence of linear timeinvariant codes achieving the multicast capacity. Jaggi, Sanders, et al. [4][5][6] showed for acyclic networks how to find the encoding and decoding coe#cients in polynomial time. Chou, Wu, and Jain [7][8] proposed a distributed scheme for practical network coding in real packet networks achieving throughput close to capacity with low delay that is robust to random packet loss and delay as well as robust to any changes to network topology or capacity

Citations