Network Coding for Linear Finite-Field Deterministic Network

A novel network coding model for linear finite-field deterministic network is considered. In our model, each channel between 2 connected nodes is represented by a channel gain matrix, while each mapping from input signals to output signals in a node is represented by an encoder mapping matrix. We apply our model to algebraic network coding framework introduced by Ralf Koetter and Muriel Médard. Those matrices are regarded as elements to generate the adjacency matrix F, from which the system matrix M can be derived. Based on our model, we propose an algorithm to trace all the feasible routes in a network for given source and destination. We also give the capacity of the network based on the routes enumerated by the algorithm.