A Construction Algorithm of Universal Global Encoding Kernels for Variable-rate Linear Broadcast Network Coding

To solve the problem that global encoding kernels for the edges have great changes for variable-rate linear broadcast network coding, the concept of universal global encoding kernel is put forward in this paper. And the construction algorithm of such universal global encoding kernel is proposed based on the algorithm of variable-rate linear broadcast network coding. In this algorithm, the same local encoding kernel at every non-source node can be used for different transmission rates, and the global encoding kernel can be acquired easily by removing the corresponding rows of the universal global encoding kernel for each edge when the source-rate decreases. The polynomial-time complexity and memory complexity of the algorithm are given explicitly based on linear information flow.