Deconvolution of linear systems with quantized input: an information theoretic viewpoint

TL;DR

This paper explores deconvolution of linear systems with quantized inputs using an information theoretic approach, proposing low complexity online algorithms for noisy sampled data.

Contribution

It introduces a novel information theoretic framework for deconvolution with quantized inputs and develops new low complexity online algorithms.

Findings

Algorithms achieve effective deconvolution in noisy, quantized settings

Theoretical analysis confirms algorithm optimality under certain conditions

Numerical results demonstrate practical applicability and performance

Abstract

In spite of the huge literature on deconvolution problems, very little is done for hybrid contexts where signals are quantized. In this paper we undertake an information theoretic approach to the deconvolution problem of a simple integrator with quantized binary input and sampled noisy output. We recast it into a decoding problem and we propose and analyze (theoretically and numerically) some low complexity on-line algorithms to achieve deconvolution.