Design of linear Boolean network codes for combination networks
Shoupei Li · 2006
Network coding is a promising technique to improve the throughput of communication networks. In the thesis, we investigate linear Boolean network codes on a special class of multicast networks, called combination networks. Using companion matrices of primitive polynomials over finite fields, we design a class of symmetric linear Boolean network codes from Reed-Solomon codes for single-source combination networks. We also prove that, for some cases, the linear Boolean network codes are optimal in the sense of minimum network uses. In the thesis, we further consider two-source network coding problem for combination networks and other specific networks. We develop a method to evaluate an outer bound for these two-source networks. By designing linear Boolean network codes which achieve extreme points of rate regions, we show that the outer bound is actually tight for some of these networks.