In this paper, we propose an efficient coding scheme for the binary Chief Executive Officer (CEO) problem under logarithmic loss criterion. Courtade and Weissman obtained the exact ratedistortion bound for a two-link binary CEO problem under this criterion. We find the optimal test-channel model and its parameters for the encoder of each link by using the given bound.Furthermore, an efficient encoding scheme based on compound LDGM-LDPC codes is presented to achieve the theoretical rates. In the proposed encoding scheme, a binary quantizer using LDGM codes and a syndrome-decoding employing LDPC codes are applied. An iterative decoding is also presented as a fusion center to reconstruct the observation bits. The proposed decoder consists of a sum-product algorithm with a side information from other decoder and a soft estimator.The output of the CEO decoder is the probability of source bits conditional to the received sequences of both links. This method outperforms the majority-based estimation of the source bits utilized in the prior studies of the binary CEO problem. Our numerical examples verify a close performance of the proposed coding scheme to the theoretical bound in several cases.M. Nangir and M. Ahmadian-Attari are with the ⋆ CEO if |Q| ≤ 4 and |U i | ≤ |Y i | = 2, for i = 1, 2, are satisfied. To find a complete characterization of the sumrate-distortion function for the two-link binary CEO problem, we should solve the following DRAFT