Analysis of a Deconvolution Algorithm for quantized-input linear systems through Iterated Random Functions

Deconvolution consists in recovering the unknown input of a system given noisy measurements of the output. If the input is quantized, the problem can be faced via Information and Decoding techniques, which provide the suitable tools to work in hybrid contexts, namely when discrete signals are transmitted through analog communication systems. Derived from BCJR, a low-complexity, recursive decoding algorithm has been developed by Fagnani and Fosson (2009) and is here applied to tackle deconvolution of one-dimensional linear systemswith binary input. The aim of the paper is to provide a rigorous mathematical analysis of the performance of such algorithm, in terms of a mean square error and for long time transmissions. This task is accomplished by means of Iterated Random Functions.