Alternative structure for computing APPs of the Markov source

We introduce an alternative structure for computing the a posteriori probabilities (APPs) for state and transition sequences of a Markov source observed through a noisy output sequence. Compared to the well-established forward-backward recursion algorithm of Bahl et al. (1974), the proposed structure allows a reduction in computational complexity at the expense of increased memory requirements. Alternatively, for a similar complexity level, the proposed structure needs smaller memory when the input alphabet size is small.