LLR metrics for LDPC codes with quadrature differential PSK transmission, and their performances

Iterative decoding of low-density parity-check codes transmitted over noncoherent channels using quadrature differential phase-shift keying is investigated. The log-likelihood ratio for each of the two code bits sent over one transmission period, based on the joint probability of two consecutive received signal samples pertaining to these code bits, is derived. An approximation of this metric yields a less complex metric with negligible performance loss. Applications of these metrics to the decoding of binary and mixed alphabet LDPC codes are considered. In addition, performances of these metrics in the presence of signal-to-noise ratio estimation error are also studied.