1. A communication system, comprising: an encoder configured to encode first data words to generate code words; a modulator configured to modulate the code words into a first signal that is transmitted on a communication channel; a demodulator configured to demodulate a second signal, received from the communication channel, into estimates of the code words, wherein the second signal is based on the first signal; and a decoding module configured to i) group the estimates of the code words into a plurality of groups of correlated data bits, wherein the correlated data bits include statistical relationships between different data bits, ii) generate a plurality of group estimate signals each corresponding to a respective one of the plurality of groups of correlated data bits, and iii) generate, by combining the plurality of group estimate signals, an estimate signal corresponding to the first data words.