The prevalence of hidden Markov models (HMMs) in various applications of
statistical signal processing and communications is a testament to the power
and flexibility of the model. In this paper, we link the identifiability
problem with tensor decomposition, in particular, the Canonical Polyadic
decomposition. Using recent results in deriving uniqueness conditions for
tensor decomposition, we are able to provide a necessary and sufficient
condition for the identification of the parameters of discrete time finite
alphabet HMMs. This result resolves a long standing open problem regarding the
derivation of a necessary and sufficient condition for uniquely identifying an
HMM. We then further extend recent preliminary work on the identification of
HMMs with multiple observers by deriving necessary and sufficient conditions
for identifiability in this setting.Comment: Accepted to ISIT 2013. 5 pages, no figure
