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Iterative decoding of low-density parity-check codes transmitted over non-coherent 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. The authors establish the relationship of their metric with that derived for differential BPSK transmission and also prove that their 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.
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