Design and analysis of root-protograph LDPC codes for non-ergodic block-fading channels

We investigate the performance of the protograph low-density parity-check (LDPC) codes over Nakagami block-fading (BF) channels with multiple receive antennas. Using the modified protograph extrinsic information transfer (PEXIT) algorithm, we observe that the existing protograph LDPC codes, which have been shown to possess excellent error performance over additive white Gaussian noise channels, cannot perform well over non-ergodic BF channels. To address this problem, a simple design scheme is proposed to construct three new root-protograph (RP) LDPC codes, i.e., the regular RP code, the improved RP1 (IRP1) code, and the IRP2 code. The convergence analysis, error-performance analysis, and simulated results show that the three proposed RP codes outperform the existing protograph LDPC codes and regular quasi-cyclic LDPC code. Furthermore, the IRP1 code and the IRP2 code are superior to the regular RP code and the regular root-LDPC code and exhibit outage-limit-approaching error performance. Consequently, these two proposed IRP codes appear to be better alternatives as compared to other error-correction codes for slowly-varying wireless communication systems.