On The Stopping Sets Of LDPC Codes Based On Geometry Of Classical Groups

The development of decoding is one of the factors to promote the research of LDPC codes.All kinds of good iterative decoding enrich the study of LDPC codes.The concepts of stopping sets arise from the study of iterative decoding performance of LDPC codes over BEC?binary erasure channel?.The study of stopping sets and stopping distances plays an important role to understand the decoding performance of LDPC codes.There are many ways to evaluate the qualities of a code in coding theory,and many parameters are needed to characterize the nature of a code.A code has better performance of maximum likelihood decoding over BSC?binary symmetric channel?,when it has a larger minimum Hamming distance.Stopping distance is similar to the minimum Hamming distance,which can explain the good decoding performance of codes over BEC.Geometry of classical groups over finite fields have characteristics of combinatorial structure and anzahl theorems.Combination schemes,combinatorial designs,pooling designs,authentication codes,compressed sensing matrices can be constructed based on these spaces.Two classes of LDPC codes construct based on these spaces and the main study is the stopping distances.In the first part,a class of LDPC codes is constructed based on the subspaces of type?m,k?and type?m₁,k₁?of the singular linear space over finite field.And another class of LDPC codes is constructed based on the subspaces of type?m,s?and type?m ₁,s?of the symplectic space over finite field.The stopping distances of the two classes of codes are studied,and the lower bounds of the stopping distance of the codes are calculated.In the second part,a stopping set of the LDPC codes constructed based on the?-flat and??+1?-flat of affine space and projective space over binary field has be found.The size of the stopping set reached the lower bound of the stopping distance of finite geometry LDPC codes.Then the stopping distance of this classes of the LDPC codes is obtained.