This paper, first introduces the check matrix and the factor graph of LDPC, then describes the sum-product algorithm by using the factor graph, and finally presents the detailed steps of the sum-product algorithm and gives a proof of certain important expressions.

The generator matrix and check matrix of q-cyclic codes are discussed,and then the theory of rank distance codes can be studied expediently.

Although the check matrix of LDPC codes is sparse,the generator matrix is not.

Hence,this paper reduces the complexity of coding by using effective parity-check matrix,and realizes the encoding device for LDPC code by use of large-scale integrated circuits.

The matrix representation of convolution code and the relation between generation matrix and parity-check matrix are introduced briefly.

As the interleaver and parity-check matrix respectively play .

Although the importance of proper array calibration has been recognized widely and many array calibration algorithms have been reported extensively in the literature,the array calibration in the presence of multipath ha.

Multipath effect is rarely concerned in many existing array calibration algorithms.

By increasing weights of rows and columns of parity check matrix, the algorithm can achieve high rate codes and could optimize the girth distribution compared with Mackay Random construction and bit-filling algorithm.