My system can be represented by the following state-diagram.
where each arch represents Input/Output when a transition is made from one state to the other.
The inputs to this FSM are correlated. This implies that I can no longer make "independent input" assumption.
My question is: How will this impact on how we use the MARKOV-CHAIN/MARKOV-PROCESS properties in implementing Viterbi algorithm for computing Maximum Likelihood Sequence estimation. Also if someone can comment on the application of BCJR algorithm for MAP estimation of inputs.