A system for decoding data includes a symbol based error correction code device. The error correction code device includes a channel detector configured to generate probability mass function (PMF) information. The error correction code device further includes a decoder coupled to the channel detector. The decoder is configured to use the PMF information from the channel detector to perform an error correction code operation. The decoder also is configured to generate PMF information. The channel detector is configured to receive extrinsic PMF information in a turbo equalization scheme.