IHMM for system combination, HMM in GIZA++ software for statistical machine translation (SMT) (Och and Ney, 2000;Koehn et al., 2003), are designed for one-to-many alignment, and running GIZA++ from two directions to gain better performance turns into a standard operation in SMT, therefore we are seeking a way to empower IHMM by introducing bi-directional information.
it appears to be intractable in an IHMM model to search the optimal solution by simply defining a new goal as a product of probabilities from two directions.