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 non-coherent 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.