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The authors derive the log-likelihood ratio for iterative decoding of low-density parity-check codes transmitted using Binary Phase-Shift-Keying (BPSK) with pilot-symbol-assisted modulation. This is done with the aid of a reference phasor formed from the received pilot signals. They compare their metric with the existing Gaussian metric for differential BPSK transmission and also show that their metric converges to that for coherent BPSK transmission in the limit as the size of the pilot reference set becomes large. Simulation results verify their analysis and study the effects of carrier phase noise and signal-to-noise ratio mis-estimation on the performance of the metric.
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