In this paper, we study a classical problem of source coding with side information available at the decoder. This problem is known as the Wyner-Ahlswede-Korner (WAK) problem. Nowadays, the interest in this problem is related to the concept of distributed source coding which implies coding of correlated sources under restriction that their encoders cannot cooperate. Most of the practical coding schemes consider a specific case of the binary symmetric source with uniform distribution and side information assumed to be perfectly known to the decoder. In this paper, we concentrate on a more complicated model of the binary source. Moreover, we consider a case when side information is lossy encoded. First we generalize the approach by Gu et al. [1] in order to obtain a lower bound on the achievable rates for a general binary source. Then, a new practical “multi-class” coding scheme for this binary source with uncoded binary side information is suggested. Simulation results for LDPC-based coding for both binary symmetric and general binary sources are presented for scenarios with trellis-coded and uncoded side information, respectively. Comparisons with the previously known numerical results are presented.