Theory Research And Encoding Optimization Of LDPC Codes

Low density parity check codes have attracted considerable attention in the coding community because they can achieve near-capacity performance, and many of the applications being explored for LDPC codes, including application to deep space and satellite communications, wireless communications, magnetic storage, and internet packet transmission. In this paper, we mainly do the research on the encoding optimization of LDPC codes.The main works of this paper are as follow:First, by analyzing the shapes of the cycles of TG in parity check matrix, this paper presents two kinds of algorithms for counting the number of short cycles. 1. In the parity check matrix, we search the nodes of a cycle one by one. When finding all the nodes of a cycle, we find a cycle in the check matrix. By checking all the possible nodes-combinations in the check matrix, we can find the number of cycles in it. 2. The algorithm based on the combinations. Taking out a certain number of rows for different cycles, counting the number of cycles contained in these rows, then adding up all the number of cycles that contained in all possible combinations of the rows in the matrix, and we can get the number of cycles in the matrix. Using the check algorithms we can calculate the number of short cycles in the check matrix. We can also use the check algorithms for finding the good Quasi-Cyclic (QC) Code with large girth.Second, this paper also present an approach for constructing LDPC codes with girth 8. First, we design 3 submatrices with different shifting functions given by our schemes, then combine them into a matrix according to our approach, finally, expand the matrix into a desired parity-check matrix using identity matrices and cyclic shift matrices of the identity matrices. The simulation results in AWGN channels show that these codes which can be obtained by the generator matrix derived from this check matrix for encoding the random information bits are as good as random LDPC codes.