Deconvolution of quantized-input linear systems: Analysis via Markov Processes of a low-complexity algorithm

This paper is concerned with the problem of the deconvolution, which consists in recovering the unknown input of a linear system from a noisy version of the output. The case of a system with quantized input is considered and a low-complexity algorithm, derived from decoding techniques, is introduced to tackle it. The performance of such algorithm is analytically evaluated through the Theory of Markov Processes. In this framework, results are shown which prove the uniqueness of an invariant probability measure of a Markov Process, even in case of non-standard state space. Finally, the theoretic issues are compared with simulations’ outcomes.