On Optimal Coding of Hidden Markov Sources
The hidden Markov model (HMM) is widely used to model processes in several real world applications, including speech processing and recognition, image understanding and sensor networks. A problem of concern is that of quantization of the sequence of observations generated by an HMM, which is referred as a hidden Markov source (HMS). Despite the importance of the problem, and the well-defined structure of the process, there has been very limited work addressing the optimal quantization of HMS, and conventional approaches focus on optimization of parameters of known quantization schemes. This paper proposes a method that directly tracks the state probability distribution of the underlying source and optimizes the encoder structure according to the estimated HMS status. Unlike existing approaches, no stationarity assumption is needed, and code parameters are updated on they: with each observation, both the encoder and the decoder refine the estimated probability distribution over the states. The main approach is then specialized to a practical variant involving switched quantizers, and an algorithm that iteratively optimizes the quantize codebooks is derived. Numerical results show superiority of the proposed approach over prior methods.