Research On Security And Error Correction Mechanisms Of Network Coding

Network coding theory breaks through the concept of store-and-forward,and it uses network nodes to deal with mathematical coding of data organically to get transmission gain.Therefore,it is an important break through in information processing and transmission theory research.But in network coding,the intermediate nodes make mixture operation on upstream nodes so that the errors in networks have the characteristic of propagation.As a result,a small part of contaminated information results in a large area of propagation so that host nodes cannot decode data correctly.Due to the characteristic of the mixture operation of network coding on upstreamnodes,the traditional correction and security solutions cannot be applied in network coding environment.In view of correction,the construction algorithm of traditional network correction code based on Hamming distance has high complexity and the network error-correcting code based on subspace distance or rank distance require too power of coding field.At the same time,network error-correcting code can only correct the original errors when error number is lower than half of Maximum flow minimum cut.Although network coding error-correcting based on cryptology can correct any number of original errors,but it requires too high operation load.In view of security,the approaches based on information theory can not confront lots of eavesdroppers,but the approaches based on cryptology require very high operation loads.Secure error-correcting(SEC)schemes for network coding which provides security and correcting-errorneeds to provide information redundancy to resist error and intercept in order to guarantee security and correcting-error,so it is lower in information rate.In view of above issues,the thesis makes the following research works.(1)The quick construction algorithms of network correcting-error code and secure network coding.In view of the issues that the construction algorithm of network correcting-error code based on Hamming distance in determined network has too high time complexity and constructing network correcting-error code in random network requires too large coding field,the maximum distance separable(MDS)property can easily and approximately maintain such feature,this paper proposed simplified network correcting-error code construction method,and this paper realizes the separation of designing the channel code and designing network coding.Compared with the error-correcting characteristic of the construction method with traditional network correcting-error code while considering error propagation characteristic,the distance of correcting-error does not alter in common or decrease with 1.The proposed method obviously decreases the time complexity of network correcting-error code construction algorithm.Based on the difficulty of solving the multi-parameters higher order system,we propose a security scheme based on the nonlinear network coding.This scheme reduces the size of coding field.When the number of eavesdroppers is big,this scheme has certain advantage in the time complexity of constructing algorithm.(2)Network security correcting-errorcode based on McEliece.In view of the issues that the current network security correcting-errorcode has too low information rate,network security correcting-error scheme based on McEliece cryptosystem is proposed in this thesis on the basis of McEliece cryptosystem and network correcting-error.In view of random networks,network security correcting-error code of McEliece cryptosystem based on rank distance code is proposed.In view of determined networks,network security correcting-errorcode of McEliece cryptosystem based on quasi-cyclic ldpc codes is presented.In two schemes,the correcting-error code of McEliece cryptosystem provides the functions of both security and correcting-error.The added redundancy information for correcting-error function and redundancy information for security function can reuse each other in order to improve the information rate of system.Because the security of this type is provided by cryptosystem,its security strength is higher than traditional network security correcting-error code based on information theorem.At the same time,because cryptographic operations are done in source node and destination node,its operation loads are much less than cryptography method and contamination detection method which requires that all the nodes in the whole network participate in check operation.(3)Network coding correcting-error method based on sparse learning.In view of issues that the number of original errors corrected by network coding correcting-error scheme based on information theory is too low and network correcting-error scheme based on cryptography has too high operation loads and so on,cross-and-bouquet model based on sparse learning,which uses dense errors to correct errors,correct propagation errors in network coding.The method can correct errors for nearly completely polluted received message with not less than decoding efficiency of linear group code,thus resisting any number of original errorsand solving the rough propagation of network coding errorseffectively.The method scheme is implemented around cross-and-bouquet model based on sparse learning.This paper proposed three detailed network coding correcting-error scheme: network coding correcting-error scheme with error transfer matrix sparseness,network coding correcting-error scheme based on secret channel and sparse learning,network coding correcting-error scheme combining sub-space code based on list decoding and sparse learning.Because cross-and-bouquet can not correct errors of 100% polluted message.Under Hamming distance metric,propagation errorsare 100% polluted.Therefore,the proposed three schemes all reduce error propagation rate using corresponding methods from 100%,and then corrects errors with cross-and-bouquetmodel,thus completing error-correction of network coding.