Bit-error rate analysis of low-density parity-check codes with generalised selection combining over a rayleigh-fading channel using gaussian approximation

Bit-error rate (BER) expressions of generalised selection combining with low-density parity-check (LDPC) codes, using binary phase-shift keying signals, over an independent and identically distributed Rayleigh-fading channel are derived using the Gaussian approximation (GA) approach. BER results for both selection combining and maximum-ratio combining can be computed from this BER expression as special cases. The symmetry and stability conditions of both density evolution (DE) and GA analysis are also studied. The degree distribution for irregular LDPC codes is optimised using differential evolution. The theoretical results are compared with both simulation results and DE thresholds. These BER expressions allow us to achieve a significant reduction in computational complexity for analysing the system performance as compared to simulation and DE.