A system, method and computer-readable medium for maximum a posteriori (MAP) estimation of a graphical model are disclosed. The MAP estimation process can include obtaining an encoded data message sent over a 4G cellular wireless network and generating a graphical model representation of the message. The graphical model can be converted into a nand Markov random field (NMRF). The MAP estimation process can also include determining whether the NMRF has a perfect graph structure, and solving for a MAP estimate configuration of the NMRF. The MAP estimation process can further include outputting the MAP estimate configuration, an indication of the MAP estimate configuration, and/or a result based on a combination of the MAP estimate configuration and the encoded data message (e.g., a decoded message).