An Optimized Algorithm for Constructing Effective LDPC Code

Wang Li

In order to improve the performance of LDPC code,an optimized LDPC code was constructed by calculating extrinsic message degree of the cycle.This algorithm can remove the short cycle,which is produced unavoidably in constructing LDPC codes,to improve a bipartite graph local connectivity.Experimental results show that the algorithm is better to improve LDPC codes' performance in the same code length,code rate and the degree distribution.

W.E. Ryan, Shu Lin

Lingjun Kong, Yang Xiao

The existing construction of Quasi-Cyclic low-density parity-check (short for QC-LDPC) codes has not considered the problems of small stopping sets and small girth and small minimum code weight together, while their existences will lead to the BER performance of QC-LDPC codes to be much poorer than that of randomly constructed LDPC codes even decoding failure. To solve the problem, some theorems of the QC-LDPC codes without small stopping sets and small girth were proposed first. Then good QC-LDPC codes without small stopping sets and small girth were designed based on the row vectors of generator matrix. The small minimum code weight also can be prevented due to the new algorithm based on the row vectors of generator matrix, which is the new way to choose the shifted factors to construct the good QC-LDPC codes for the given prime. The effectiveness and the practicability of the algorithm are demonstrated by the simulation results. It is significant for us to analyze and optimize the design of LDPC codes.

B. N. Sindhu Tejaswini, Rajendra Prasad Lal, Vadlamudi Ch. Venkaiah

Hengzhou Xu, Baoming Bai

In this letter, we consider the construction of q-ary low-density parity-check (LDPC) codes by jointly optimizing the girth and number of shortest cycles in the frame of superposition. We begin with constructing binary quasi-cyclic LDPC codes by superposition. By replacing the nonzero entries of the parity-check matrices of the resulting binary codes with the nonzero elements of GF(q), a class of q-ary LDPC codes is obtained. Furthermore, we analyze the cycle structure of the constructed codes for a given degree distribution and code length, and present a search algorithm for finding q-ary LDPC codes with few cycles of length g, where g is the optimized girth value. Simulation results show that the proposed codes perform well under the iterative decoding algorithms.

Emmanuel Boutillon