1. A method for estimating channel data bit probabilities of a multi-channel signal received through a communication channel, comprising: summing a conditional bit probability conditioned on an observation of the multi-channel signal and a hypothetical channel data pattern by summing over a subset of hypothetical channel data patterns to obtain a channel data bit probability summation; generating the subset of hypothetical channel data patterns using a plurality of Markov chain Monte Carlo simulations to stochastically select the subset of hypothetical channel data patterns corresponding to dominant conditional bit probability terms in the channel data bit probability summation; and initializing the plurality of Markov chain Monte Carlo simulations with a plurality of different starting states, wherein the starting state of at least a first one of the plurality of Markov chain Monte Carlo simulations is selected using a first selection approach and the starting state of at least a second one of the plurality of Markov chain Monte Carlo simulations is selected using a second selection approach which is different than the first selection approach.