Analog circuit implementations of Hidden Markov Models (HMM) use currentmode or voltage-mode circuits which limit their scalability for implementing large networks. In this paper, asynchronous analog HMM circuit is proposed that performs log-likelihood decoding directly in time-domain using binary pulses. The core of the implementation is an integrate-and-fire margin propagation circuit that can approximate a soft-max function and can be cascaded together to build large, complex HMMs. This paper verifies the concept by implementing experiments for sequence decoding HMM using the proposed pulse modules in both software simulation and circuit simulation.