A Convergence Analysis of LDPC Decoding Based on Eigenvalues

Low-density parity check (LDPC) codes are very popular among error correction codes because of their high-performance capacity. Numerous investigations have been carried out to analyze the performance and simplify the implementation of LDPC codes. Relatively slow convergence of iterative decoding algorithm affects the performance of LDPC codes. Faster convergence can be achieved by reducing the number of iterations during the decoding process. In this thesis, a new approach for faster convergence is suggested by choosing a systematic parity check matrix that yields lowest Second Smallest Eigenvalue Modulus (SSEM) of its corresponding Laplacian matrix. MATLAB simulations are used to study the impact of eigenvalues on the number of iterations of the LDPC decoder. It is found that for a given (n, k) LDPC code, a parity check matrix with lowest SSEM converges quickly as compared to the parity check matrix with high SSEM. In other words, a densely connected graph that represents the parity check matrix takes more iterations to converge than a sparsely connected graph.