Efficient backward decoding of high-order hidden Markov models

The forward–backward search (FBS) algorithm [S. Austin, R. Schwartz, P. Placeway, The forward–backward search algorithm, in: Proceedings of the IEEE International Conference on Acoustics, Speech and Signal Processing, 1991, pp. 697–700] has resulted in increases in speed of up to 40 in expensive time-synchronous beam searches in hidden Markov model (HMM) based speech recognition [R. Schwartz, S. Austin, Efficient, high-performance algorithms for N-best search, in: Proceedings of the Workshop on Speech and Natural Language, 1990, pp. 6–11; L. Nguyen, R. Schwartz, F. Kubala, P. Placeway, Search algorithms for software-only real-time recognition with very large vocabularies, in: Proceedings of the Workshop on Human Language Technology, 1993, pp. 91–95; A. Sixtus, S. Ortmanns, High-quality word graphs using forward–backward pruning, in: Proceedings of the IEEE International Conference on Acoustics, Speech and Signal Processing, 1999, pp. 593–596]. This is typically achieved by using a simplified forward search to decrease computation in the following detailed backward search. FBS implicitly assumes that forward and backward searches of HMMs are computationally equivalent. In this paper we present experimental results, obtained on the CallFriend database, that show that this assumption is incorrect for conventional high-order HMMs. Therefore, any improvement in computational efficiency that is gained by using conventional low-order HMMs in the simplified backward search of FBS is lost.This problem is solved by presenting a new definition of HMMs termed a right-context HMM, which is equivalent to conventional HMMs. We show that the computational expense of backward Viterbi-beam decoding right-context HMMs is similar to that of forward decoding conventional HMMs. Though not the subject of this paper, this allows us to more efficiently decode high-order HMMs, by capitalising on the improvements in computational efficiency that is obtained by using the FBS algorithm.