Construction Of Coding Caching Schemes Based On Hamming Distance

Coding cache technology is widely used in wireless networks because it can effectively reduce the transmission load during peak hours.In 2014,Maddah-Ali and Niesen creatively proposed an coded caching scheme.However,in order to implement this coded caching scheme,each file must be divided into packets,and the number of these file packets usually increases exponentially with the increase of user number ,which limits the practical application of this scheme.Yan et al.proposed the concept of placement and delivery array(PDA)which transform the construction of centralized coded caching scheme into a PDA with appropriate parameters,it effectively reducing the file packets in the coded caching scheme.Therefore,it is of practical significance to study how to construct PDA with appropriate parameter.Zhong et al.in [16] put forward a framework of constructing PDA by using the Hamming distance,and transform the constructing PDA into a problem of partitioning sets,and propose two different partitions are for the cases of q=2 and q=3,then two kinds of coding caching schemes with lower number of blocks can be obtained.Compared with some previously known schemes with linear subpacketizations,the authors showed that their schemes have significant advantages on number of users,subpacketizations,memory fractions and transmission loads.The authors point out it is significant to give the appropriate partition for constructing coded caching scheme.But also point out that the complexity of partition increases with the increase of q,only two cases of q=2 and q=3 are studied in their paper.In this paper,we focus on constructing PDAs by modifying the rule of defining vector entries of P in [16] for any positive integer ? 2 such that the realized schemes by these PDAs have linear subpacketizations and small transmission loads.And according to the new construction,we directly obtain a coded caching scheme with low subpacketization,and then prove that constructing the PDA is equivalent to design a appropriate partition for the new construction.Thus we Put forward a corresponding partition to obtain a new coded caching scheme.we find that not all file packets cached by users can be used to produce multicast gain,the useless file packets not only make no contribution to reducing the transmission rate,but also result in a high subpacketization and a large memory ratio.In order to solve this problem,we use MDS code to encode the above scheme.By deleting the useless file packets,a new coded caching scheme with lower subpacketization is obtained.Finally,we use point coloring in graph theory to divide the new construction again,and obtain another kind of coded caching scheme with different parameters.Through analysis and comparison,it is shown that the proposed coded caching schemes have full advantages on subpacketization and transmission load than the existing schemes.