Abstract: A decoder is operable to decode data transmitted on a noisy communication channel. The decoder includes a memory storing bits of encoded data received over the communication channel. The decoder also includes a processor estimating a transmitted codeword from the received bits. The processor is operable to determine a linear program (LP) for decoding the received data, wherein the linear program includes a cost function. A solution to the LP is calculated using a coordinate-ascent method that varies multiple variables associated with the cost function in one iteration. A transmitted codeword is estimated from the received encoded data using the solution to the LP.