Analysis and Code Design for the Binary CEO Problem Under Logarithmic Loss

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 rate-distortion bound for a two-link binary CEO problem under this criterion. We find optimal parameters of the binary symmetric test-channel model for the encoder of each link by using the given bound. Furthermore, an efficient coding scheme based on compound low-density generator matrix (LDGM)-low-density parity-check (LDPC) codes is presented to achieve the theoretical rates. In the proposed encoding scheme, a binary quantizer using LDGM codes and a syndrome generator using LDPC codes are applied. The proposed decoder employs a sum-product algorithm and a soft estimator to produce an approximate a posteriori distribution of the source bits given the data received through both links. Our numerical examples verify a close performance of the proposed coding scheme to the theoretical bound in several cases.