1. A method of estimating log likelihood ratios in a receiver comprising: receiving a multi-dimensional signal comprising a plurality of transmitted data bits; forming a first symbol estimate having a first distance from an observation of the multi-dimensional signal wherein the first symbol estimate comprises a plurality of first data bits; initializing a plurality of Markov chain Monte Carlo simulations using a plurality of differing second symbol estimates each comprising a plurality of second data bits, wherein each one of the plurality of second symbol estimates is constrained so that a differing one of the plurality of second data bits is inverted relative to a corresponding one of the first data bits; running the plurality of Markov chain Monte Carlo simulations to stochastically-search for constrained minimum second distances corresponding to the second data bits; and calculating a plurality of log likelihood ratios corresponding to each of the plurality of transmitted data bits using the first distance and the constrained minimum second distances.