Belief propagation for nonlinear block codes

Special cases of the belief propagation algorithm are commonly used to decode various linear error correcting codes. We show that the belief propagation algorithm can also be applied to the decoding problem for nonlinear error correcting codes by considering a modified set of update rules. We demonstrate the modified belief propagation algorithm by applying it to the well-known Nordstrom-Robinson (15, 256, 5) nonlinear code. The Nordstrom-Robinson code contains many cycles, which means that belief propagation is suboptimal. Nevertheless, we observe a coding gain of about 1.2 dB with this method.