In this paper, we present a novel class of simple soft-input soft-output (SISO) detection algorithms for transmission over phase-uncertain channels. In order to limit the complexity, the set of possible phase values (i.e., the interval [0,2pi)) is properly quantized. We then use a forward-backward (FB) algorithm in correspondence to each quantized phase value. The forward and backward metrics computed by the different FB algorithms are properly combined to make the receiver robust against the time-varying phase. We apply the proposed SISO algorithms to perform joint detection and decoding of serially concatenated low-density parity-check (LDPC) codes and differentially encoded (DE) quaternary phase shift keying (QPSK), transmitted over a phase-uncertain channel. As a validation of the effectiveness of the proposed algorithms, we show that the performance loss with respect to that of the corresponding ideal (i.e., perfectly coherent) system is limited. Besides having a limited complexity, the proposed SISO algorithms are blind, i.e., no knowledge of the channel phase statistics is required, and highly parallelizable, as desirable in high-throughput future wireless communication systems