This Letter considers the finite-length analysis of iterative decoding of low-density parity-check codes under differential binary-phase-shift-keying (DBPSK) and differential quadrature-phase-shift-keying (DQPSK) over the noncoherent additive-white-Gaussian-noise channel. Specifically, we derive the weight of the pseudocodewords of a Tanner graph under these signaling schemes and use them to explain the difference in error performance between coded DBPSK and coded DQPSK.

We 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. We compare our metric with the existing Gaussian metric for differential BPSK transmission and also show that our metric converges to that for coherent BPSK transmission in the limit as the size of the pilot reference set becomes large. Simulation results verify our analysis and study the effects of carrier phase noise and signal-to-noise ratio mis-estimation on the performance of the metric.

Iterative decoding of low-density parity-check codes transmitted over noncoherent channels using pilot-symbol- assisted binary phase-shift keying (BPSK) is studied. The log- likelihood ratio of the two values of each transmitted code bit is derived using the joint probability density function of the received signal that carries that bit and a set of reference pilot signals. We establish the relationship of our metric with that derived for differential BPSK transmission and also prove that our metric converges to that for coherent BPSK transmission. The theoretical analysis is further verified through simulation studies. In addition, two approximations of the metric that yield lower computational cost with negligible performance losses are introduced. Finally, we study the effects of signal-to-noise ratio estimation error on the performance of these metrics.

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.