We present a novel blind source separation (BSS) method using a hierarchical structure of sample space that is incorporated with a log-linear model. Our approach is formulated as a convex optimization with theoretical guarantees to uniquely recover a set of source signals by minimizing the KL divergence from a set of mixed signals. Source signals, received signals, and mixing matrices are realized as different layers in our hierarchical sample space. Our empirical results have demonstrated superiority compared to well established techniques.