Nonbinary LDPC Code for Noncoherent Underwater Acoustic Communication under Non-Gaussian Noise

Concatenated code based on nonbinary LDPC code and Hadamard code is used for noncoherent underwater acoustic communication system. 32-ary (620, 320) regular LDPC code and irregular LDPC code is constructed by quasi-cyclic extension method and Progressive edge-growth (PEG) algorithm, respectively. Under non-Gaussian noise model, Gaussian mixture model (GMM) is used to fit the noise, and the parameters in GMM is estimated by Expectation Maximization (EM) algorithm, the probability density of noise is further estimated. In Rayleigh fading channel, posterior probabilities of Hadamard code-words are calculated based on GMM, and nonbinary LDPC code is further decoded by Belief Propagation (BP) algorithm based on Tanner graph. It is verified by simulation that concatenated irregular LDPC code and Hadamard code has a 0.4 dB benefit than concatenated regular LDPC code and Hadamard code under white Gaussian noise; under Gaussian mixture noise, the EM algorithm based on GMM can exactly estimate the probability density of noise and improve the error correcting performance of concatenated code, the performance gap is 0.1 dB compared to results in known probability density condition. Noise samples were acquired by experiments carried out in deep sea and shallow lake. Under actual noise, the advantages of concatenated code based on GMM in practical application is verified.