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r The overlapping of 1 s per column and per row should be at most equal to one This is a necessary condition for avoiding the presence of cycles in the corresponding bipartite graph r The parameters s and v should be small numbers compared with the code length It is however very dif cult to satisfy the third condition if the intention is to construct good LDPC codes, because cycles are unavoidable in the bipartite graph of an ef cient LDPC code [18] The above construction does not normally lead to the design of a sparse parity check matrix H of systematic form, and so it is usually necessary to utilize Gaussian elimination to convert this resulting matrix into a systematic parity check matrix H = [I n k P T ], where I n k is the identity submatrix of dimension (n k) (n k).

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The initially designed sparse parity check matrix H is the parity check matrix of the LDPC code, whose generator matrix G is of the form G = [ P I k ] Summarizing the design method for an LDPC code, a sparse parity check matrix H = [A B] is constructed rst, obeying the corresponding construction conditions In general, this initial matrix is not in systematic form Submatrices A and B are sparse Submatrix A is a square matrix of dimension (n k) (n k) that is non-singular, and so it has an inverse matrix A 1 Submatrix B is of dimension (n k) k The Gaussian elimination method, operating over the binary eld, modi es the matrix H = [A B ] into the form H = [ I k A 1 B ] = [ I k P T ].

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This operation is equivalent to premultiplying H = [ A B ] by A 1 Once the equivalent parity check matrix H has been formed, the corresponding generator matrix G can be constructed by using the submatrices obtained, to give G = [ P I k ] In this way both the generator and the parity check matrices are de ned, and the LDPC code is nally designed Note that the matrices of interest are H and G LDPC codes can be classi ed, according to the construction method used for generating the corresponding sparse parity check matrix H, into [11] r random LDPC codes and r structured LDPC codes.

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(7) A == [aij], B = [bijl. C == [Cij] (m x m) lower triangular:

Millon, T. (2003). It s time to rework the blueprints: Building a science for clinical psychology. American Psychologist, 58, 949 961. Murray, H. A. (1938). Explorations in personality. New York: Oxford University Press. Reich, W. (1949). Character analysis (3rd ed.). New York: Farrar, Straus and Giroux. Rosenzweig, S. (1936). Some implicit common factors in diverse methods of psychotherapy. American Journal of Orthopsychiatry, 6, 412 415. Russell, B. (1945). A history of Western philosophy. New York: Simon & Schuster. Strack, S., & Lorr, M. (Eds.). (1994). Dif ferentiating normal and abnormal personality. New York: Springer.