Constructions Of The Placement Delivery Array In Coded Caching Scheme

As an effective technique to reduce network congestion during peak traffic times,coded caching is being widely studied in wireless network.The coded caching scheme was first proposed by Maddah-Ali and Niesen in 2014.In the placement phase of offpeak times,each file is divided into equal packets,and each user caches some packets of each file elaborately from the server.In the delivery phase of peak times,each user first requires a file from the server.And then according to each user's cache,the server sends a coded signal with size at most to users so that various user demands are satisfied.In order to study this problem better,the placement delivery array was defined by Yan Q et al.in 2016.And they found that the problem of designing a coded caching scheme can be converted into the problem of constructing an appropriate PDA.In this thesis,we give several new constructions which have obvious advantages in packet number.Firstly,we construct three kinds of new PDAs based on -design of6)= + 1,the incidence matrix of a resolvable transversal design and the partitioning of the incidence matrix.Secondly,by establishing the relationship between graph and PDA,we construct a new PDA with small packet number by using the incidence relation of vertex and edge in the direct product graph.Finally,based on the kronecker product of matrix,we obtain a class of strong practicability PDA by defining the product of two PDAs.