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We propose an iterative decoding scheme for low density parity check codes concatenated with binary differential phase shift keying (BDPSK) in additive white Gaussian channels with unknown phase offset by viewing the BDPSK modulator as the encoder of a rate-one convolutional code. To assist this iterative scheme, a new log-likelihood ratio (LLR) metric based on three consecutive received symbols is derived. This metric takes a priori information of other coded bits into account and therefore applicable to the proposed iterative scheme. We show that the proposed iterative scheme has better performance than systems using other LLR metrics for noncoherent detections. The performance of the proposed scheme under signal-to-noise ratio estimation error is also investigated.