Research On The Related Problems Of Subspace Code And Distributed Storage System Based On Network Coding

As a new technology in communication theory, network coding has improved the efficiency of network transmission in the traditional store and forward mode, and has opened a new field of research. In particular, random network coding provides a powerful tool in practical applications. Random network coding allows intermediate nodes to select encoding coeffi-cients in a finite field independently and randomly. The sink node can decode successfully with very large probability, if the finite field is large enough. In practice, the network en-vironment is open, which has a variety of interference, link and node failures, malicious attacks and other threats. Such a complex environment presents a challenge to the reliability of network transmission. Therefore, it is significant to study the error control and securi-ty in the transmission of network coding. It has very important theoretical and practical significance for the application of network coding.This dissertation takes network coding theory as the main line. Firstly, the problem of net-work error correction in the noncoherent network model is studied. Then, as a practical application of the network coding theory, the distributed storage system and the construc-tion of regenerating code are studied. Finally, the problems of data integrity and privacy protection in the distributed storage system are studied. To solve these problems, we do in-depth research and have achieved certain results.The principal contributions of this dissertation include the following three aspects.The problem of error correction in the noncoherent network model is considered in the first part. Firstly, the model of a real-time media distribution system based on heterogeneous wireless networks is proposed, where the source node broadcasts message to the destination nodes. The destination nodes have different link capacity because of the different ways in accessing the network. The definition of broadcast network error correcting codes for this network model is provided, and the definition of parameters about the error correction capa-bility and rate of the code are given at the same time. Then, the outer bound of rate pair of broadcast network error correcting codes is obtained by using the concept of combinatorial mathematics. And the construction of the code is given by using the superposition method. The rate pair of BECNC can asymptotically achieve the proposed outer bound, if K-K codes are used in the construction, so the proposed outer bound is the rate region. Finally, the rate pair can exactly achieve the proposed outer bound at some points, if q-analog Steiner structures are used in the construction. Although K-K codes require the fields sufficiently large and the known q-analog Steiner structures are limited, the theoretical achievable rate region and the code construction given in this part have definite theoretical and practical significance.As a practical application of network coding, the distributed storage system and regenera-tion code are studied in the second part. Firstly, the construction of the minimum bandwidth regeneration code for one faulted node is presented by the method of combination design. Then, the same method is used to construct the minimum bandwidth regenerative code for multiple faulted nodes, and the performance of the code is also analyzed. The proposed construction is simple and has a very fine structure. The proposed codes have good repair locality in multiple faulted nodes repairing, namely, the fault node can be repaired by con-necting fewer survival nodes. It also has good flexibility, i.e., the repair process can have a variety of connection options, which makes it very practical in engineering.The security of data in the distributed storage system is considered in the third part. It is necessary to consider the integrity of the data stored at each node and the privacy issues of node identity, since the network environment is open. Characteristics of distributed storage system are analyzed. According to the problem of preventing data from tampering by illegal users and protecting the node information privacy, the threshold attribute based universal designated verifier signature scheme is presented for the distributed storage system. This scheme is based on the assumption of difficult problem, combines the advantages of the attributes-based signature and universal designated verifier signature. The security of the proposed scheme is proven in the standard model, so as to ensure the integrity, availability and privacy of the distributed storage system in the practical application.