Binary input reconstruction for linear systems: a performance analysis

TL;DR

This paper presents a simple, online binary input reconstruction algorithm for linear systems, analyzing its performance theoretically in terms of mean square error, with advantages of low complexity and real-time decoding.

Contribution

It introduces a low-complexity, online algorithm for binary input reconstruction in linear systems and provides a theoretical performance analysis of its long-term behavior.

Findings

Algorithm works online with current output measurement

Performance analyzed using convergence of probability measures

Long-term mean square error characterized theoretically

Abstract

Recovering the digital input of a time-discrete linear system from its (noisy) output is a significant challenge in the fields of data transmission, deconvolution, channel equalization, and inverse modeling. A variety of algorithms have been developed for this purpose in the last decades, addressed to different models and performance/complexity requirements. In this paper, we implement a straightforward algorithm to reconstruct the binary input of a one-dimensional linear system with known probabilistic properties. Although suboptimal, this algorithm presents two main advantages: it works online (given the current output measurement, it decodes the current input bit) and has very low complexity. Moreover, we can theoretically analyze its performance: using results on convergence of probability measures, Markov Processes, and Iterated Random Functions we evaluate its long-time behavior in terms of mean square error.