Abstract: Noncoherent underwater acoustic communication channel in adverse condition is modeled as phase-random Rayleigh fading channel, and its capacity curve is derived. To approach channel capacity curve, concatenated code of nonbinary LDPC code and constant weight code is proposed for noncoherent communication and iteratively decoded in probability domain. Without information of channel amplitude or phase in the receiver, statistic parameters of signal and noise bins were estimated based on moment estimation method, posterior probabilities of constant weight code words were further calculated, and nonbinary LDPC code was decoded with nonbinary factor graph algorithm. It is verified by simulation that by utilizing the proposed concatenated code and its processing algorithm, gap to channel capacity curve is reduced from previous 4.5 dB to 1.5 dB. Underwater communication experiments were carried out in both deep ocean (vertical communication, 5 kin) and shallow lake (horizontal communication, near 3 km, delay spread larger than 50 ms), signal frequency band was 6 to 10 kHz, and data transmission rate was 357 bps. The proposed scheme can correctly transmit in both experiments with a signal noise ratio threshold of 2 dB. The performance of proposed algorithm was well verified by experiments.