Construction and Performance Evaluation of QC-LDPC Codes over Finite Fields

Abstract: Low Density Parity Check (LDPC) codes are one of the block coding techniques that can approach the Shannon’s limit within a fraction of a decibel for high block lengths. In many digital communication systems these codes have strong competitors of turbo codes for error control. LDPC codes performance depends on the excellent design of parity check matrix and many diverse research methods have been used by different study groups to evaluate the performance. In this research work finite fields construction method is used and diverse techniques like masking, dispersion and array dispersion for the construction of parity check matrix H. These constructed codes are then simulated to make the performance evaluation. The key interest of this research work was to inspect the performance of LDPC codes based on finite fields. A comprehensive masking technique was also an objective of this research work. Simulation was done for different rates using additive white Gaussian noise (AWGN) channel. In MATLAB a library of different functions was created to perform the task for base matrix construction, dispersion, masking, generator matrix construction etc. Results give an idea that even at BER of 10-6 these short length LDPC codes performed much better and have no error floor. BER curves are also with 2-3dB from Shannon’s limit at BER of 10-6 for different rates.