This paper considers the problem of distributed decoding of a coded message from a mobile access point (AP) sent to a sensor network. The distributed decoding problem is solved using a consensus algorithm on the log-likelihood ratio averages, which ensures that all sensors attain the same decision as if all received signals were available at a centralized location. Unlike existing distributed hypothesis testing problems, whose inter-sensor communication cost grows exponentially with the codeword size, the novel consensus-based distributed decoder exploits knowledge over the problem to reduce the cost to be linear. Link failures and inter-sensor communication noise are also accounted for. Analysis and simulations confirm that the resultant distributed decoder attains bit error rate performance approaching its centralized counterpart within a few iterations.