Applications of Projective Geometry in Computing and Communications

摘要: Projective geometry (PG) based graphs have found many applications in the areas of computing and error-control coding. Firstly, we look at the use of PG in the design of processor-memory interconnection architectures. We have used projective subspaces to create novel schemes to solve the problem of LU decomposition. We have simulated these architectures and compared them with conventional schemes. In this report, we present our findings. Then, we study a new family of networks based on PG. We understand how the regularity and symmetry in their structure is used to develop communication primitives for them. Finally, we look at expander codes, which are based on expander graphs, and present our construction of such codes based on graphs obtained using PG. Through simulations, we have found that these codes perform better than the theoretical bounds suggested in literature. We present the results of these simulations in this report.