The Extension And Application Of Polynomial Remainder Codes

Cloud computing and Internet of Things technologies are rapidly developing,the continuous development of social information technology and information services have been gradually promoted,a large amount of data emerges from various information services at all times,which makes the scale of data storage rapid increase.Massive data presents severe challenges to the reliability of modern storage systems.Due to the dramatic increase in the magnitude of stored data,erasure coding technology has become a fault-tolerant technology widely used in storage systems to improve the reliability and availability of storage systems.RS(Reed-Solomon)code and MDS(Maximum Distance Separable)array code are commonly used in erasure correction code technology,which have better fault tolerance and storage characteristics.In recent years,a generalized code based on RS codes,namely Polynomial Remainder Codes(Polynomial Remainder Codes),has been proposed.A polynomial remainder code,derived from the Chinese remainder theorem,is a class of linear block codes,where the Reed-Solomon code is a special case.For MDS array codes,a generalized code based on MDS array codes,Irregular MDS Array Codes(Irregular MDS Array Codes)has been proposed,the code is used to solve the problem of different storage requirements of different data nodes.This article takes the above two generalized codes as the research goal,and focuses on the key content of the extension of polynomial remainder codes and optimization of irregular MDS array codes.The main work of this thesis are:1.An extended version of polynomial remainder code is proposed,and it is deduced that the extended RS code is a special case of extended polynomial remainder code.Based on the original decoding method of polynomial remainder code,an erasure decoding method of extended polynomial remainder code is proposed,and the mathematical derivation of related decoding principles is given.An extended version of the Chinese remainder code is proposed,in which the Chinese remainder code is an extension of the polynomial remainder code on the set of integers,and at the same time,an erasure decoding method for the extended Chinese remainder code is proposed.2.The optimized design scheme of irregular MDS array code with two parameter cases is proposed,which solves the problem of data redundancy existing in the original design method.Then,some examples are given to illustrate that the proposed optimized scheme successfully improves the storage space utilization of irregular MDS array codes and reduces the number of parity check symbols.