Construction of nonbinary LDPC codes using λ-FRC for circle elimination

In this paper, an improved full rank condition (named as λ-FRC) is proposed for the construction of nonbinary LDPC codes. Compared with the conventional FRC, the λ-FRC introduces a metric λ to evaluate the reliability of the messages passing through the circle. Codes with better performance can be obtained by selecting elements of the parity matrix according to the metric. Based on the λ-FRC, a greedy search algorithm is proposed to design the codes efficiently. In order to further improve the performance of the codes constructed, an iterative search algorithm is applied in the construction. Simulation results show that the performance of codes constructed by the λ-FRC methods outperforms those by the FRC methods, and the iterative search algorithm improves the performance of the codes as the iteration number increases¹.