Log-likelihood Metrics based on Two-Symbol-Interval Observations for LDPC Codes with BDPSK Transmission

Iterative decoding of low-density parity-check codes transmitted over noncoherent channels using binary differential phase-shift keying modulation is examined. Using the joint estimation approach and the averaged likelihood function approach, the log-likelihood ratios of the two values of each bit, based on two contiguous received signal samples that convey the bit, are derived. In addition, a simplified approximate metric is introduced and shown to yield similar performance to the two metrics. Simulation results also show that these metrics derived here outperform the existing Gaussian metric. The performances of these metrics in the presence of phase noise and signal-to-noise ratio estimation error are also studied.