Log-Likelihood Ratios for LDPC Codes with Pilot-Symbol-Assisted BPSK Transmission over the Noncoherent Channel

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.