Markov Chain Monte Carlo Detectors for Channels With Intersymbol Interference

In this paper, we propose novel low-complexity soft-in soft-out (SISO) equalizers using the Markov chain Monte Carlo (MCMC) technique. We develop a bitwise MCMC equalizer (b-MCMC) that adopts a Gibbs sampler to update one bit at a time, as well as a group-wise MCMC (g-MCMC) equalizer where multiple symbols are updated simultaneously. The g-MCMC equalizer is shown to outperform both the b-MCMC and the linear minimum mean square error (MMSE) equalizer significantly for channels with severe amplitude distortion. Direct application of MCMC to channel equalization requires sequential processing which leads to long processing delay. We develop a parallel processing algorithm that reduces the processing delay by orders of magnitude. Numerical results show that both the sequential and parallel processing MCMC equalizers perform similarly well and achieve a performance that is only slightly worse than the optimum maximum
a posteriori
(MAP) equalizer. The MAP equalizer, on the other hand, has a complexity that grows exponentially with the size of the memory of the channel, while the complexity of the proposed MCMC equalizers grows linearly.