Approximation Algorithms for Probabilistic Decoding

It was recently shown that the problem of decoding messages transmitted through a noisy channel can be formulated as a belief updating task over a probabilistic network [13]. Moreover, it was observed that iterative application of the (linear time) belief propagation algorithm designed for polytrees [14] outperformed state of the art decoding algorithms, even though the corresponding networks may have many cycles. Much of recent research in coding focuses on explaining this phenomenon. This paper demonstrates empirically that an approximation algorithm approx-mpe for solving the most probable explanation (MPE) problem, developed within the recently proposed mini-bucket elimination framework [3], outperforms iterative belief propagation on classes of coding networks that have bounded induced width. Our experiments suggest that decoders based on nding an MPE assignment (block-wise decoding) can be superior to the commonly used belief updating decoders (bit-wise decoders).