The LLR Metric for q-ary LDPC Codes with MPSK Modulation over Rayleigh Channels with Imperfect CSI

We consider the iterative decoding of low-density parity-check codes with M-ary phase-shift keying transmission and pilot-symbol-assisted channel estimation over time correlated Rayleigh fading channels. We present the correct conceptual approach for deriving the log-likelihood ratio (LLR) expression for a general q-ary code. Its bit-error probability (BEP) performance is compared with that of the conventional metric which does not take into account the information concerning the channel estimation accuracy. Simulation results show that this LLR metric outperforms the conventional metric in both BEP performances and average number of decoding iterations required for convergence. The work here demonstrates the importance of incorporating the knowledge of the channel estimation accuracy in the iterative decoding process.