Note that the CTC formulation uses L-length letter sequence C = {c l ∈ U|l = 1, • • • , L} with a set of distinct letters U.
similarly to section 2.1, by introducing framewise letter sequence with an additional "blank" and by using the probabilistic chain rule and conditional independence assumption, the posterior distribution p(C|X) is factorized as follows: CTC has three distribution components similar to the DNN/HMM case, i.e., framewise posterior distribution p(z t |X), transition probability p(z t |z t−1 , C) 1 , and prior distributions of letter and hidden-state sequences, p(C) and p(Z), respectively.