The Role of Eigenvalues of Parity Check Matrix in Low-Density Parity Check Codes

The new developments in coding theory research have revolutionized the application of coding to practical systems. Low-Density Parity Check (LDPC) codes form a class of Shannon limit approaching codes opted for digital communication systems that require high reliability. This thesis investigates the underlying relationship between the spectral properties of the parity check matrix and LDPC decoding convergence. The bit error rate of an LDPC code is plotted for the parity check matrix that has different Second Smallest Eigenvalue Modulus (SSEM) of its corresponding Laplacian matrix. It is found that for a given (n,k) LDPC code, large SSEM has better error floor performance than low SSEM. The value of SSEM decreases as the sparseness in a parity-check matrix is increased. It was also found from the simulation that long LDPC codes have better error floor performance than short codes. This thesis outlines an approach to analyze LDPC decoding based on the eigenvalue analysis of the corresponding parity check matrix.