New communication standards need to deal with machine-to-machine communications, in which users may start or stop transmitting at any time in an asynchronous manner. Thus, the number of users is an unknown and time-varying parameter that needs to be accurately estimated in order to properly recover the symbols transmitted by all users in the system. In this paper, we address the problem of joint channel parameter and data estimation in a multiuser communication channel in which the number of transmitters is not known. For that purpose, we develop the infinite factorial finite state machine model, a Bayesian nonparametric model based on the Markov Indian buffet that allows for an unbounded number of transmitters with arbitrary channel length. We propose an inference algorithm that makes use of slice sampling and particle Gibbs with ancestor sampling. Our approach is fully blind as it does not require a prior channel estimation step, prior knowledge of the number of transmitters, or any signaling information. Our experimental results, loosely based on the LTE random access channel, show that the proposed approach can effectively recover the data-generating process for a wide range of scenarios, with varying number of transmitters, number of receivers, constellation order, channel length, and signal-to-noise ratio.