Binary input reconstruction for linear systems: a performance analysis
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.
Cite
@article{arxiv.2012.01339,
title = {Binary input reconstruction for linear systems: a performance analysis},
author = {Sophie M. Fosson},
journal= {arXiv preprint arXiv:2012.01339},
year = {2020}
}