Approximate inference in hidden Markov models using iterative active state selection

The inferential task of computing the marginal posterior probability mass functions of state variables and pairs of consecutive state variables of a hidden Markov model is considered. This can be exactly and efficiently performed using a message passing scheme such as the Bahl-Cocke-Jelinek-Raviv (BCJR) algorithm. We present a novel iterative reduced complexity variation of the BCJR algorithm that uses reduced support approximations for the forward and backward messages, as in the M-BCJR algorithm. Forward/backward message computation is based on the concept of expectation propagation, which results in an algorithm similar to the M-BCJR algorithm with the active state selection criterion being changed from the filtered distribution of state variables to beliefs of state variables. By allowing possibly different supports for the forward and backward messages, we derive identical forward and backward recursions that can be iterated. Simulation results of application for trellis-based equalization of a wireless communication system confirm the improved performance over the M-BCJR algorithm.