On The Temporal Parallelisation of The Viterbi Algorithm

This paper presents an algorithm to parallelise the Viterbi algorithm along the temporal dimension to compute the maximum a posteriori (MAP) trajectory estimate of a hidden Markov model. We reformulate the MAP estimation problem as an optimal control problem. The proposed algorithm uses a parallelisation algorithm developed for optimal control problems that first performs a backward value function pass and then a forward trajectory recovery pass. The parallel Viterbi algorithm then corresponds to a specialised backward optimal control problem with a forward value function pass and backward MAP-trajectory recovery pass. The algorithm is empirically tested by running numerical simulations on a multi-core central processing unit (CPU) and a graphics processing unit (GPU).