We consider the problem of recovering n i.i.d. samples from a zero mean multivariate Gaussian distribution with an unknown covariance matrix, from their modulo wrapped measurements, i.e., measurements where each coordinate is reduced modulo Δ, for some Δ >0. For this setup, which is motivated by quantization and analog-to-digital conversion, we develop a low-complexity iterative decoding algorithm. We show that if a benchmark informed decoder that knows the covariance matrix can recover each sample with small error probability, and n is large enough, the performance of the proposed blind recovery algorithm closely follows that of the informed one. We complement the analysis with numerical results that show that the algorithm performs well even in non-asymptotic conditions.
Bibliographical noteFunding Information:
Manuscript received January 29, 2019; revised January 8, 2021; accepted January 17, 2021. Date of publication January 21, 2021; date of current version February 17, 2021. This work was supported in part by ISF under Grant 1791/17 and Grant 1523/16 and in part by the GENESIS Consortium via the Israel Ministry of Economy and Industry. The work of Elad Romanov was supported in part by the HUJI Leibniz Center and an Einstein-Kaye fellowship. The article was presented in part at the 2019 International Symposium on Information Theory. (Corresponding author: Or Ordentlich.) This authors are with the School of Computer Science and Engineering, Hebrew University of Jerusalem, Jerusalem 919050, Israel (e-mail: firstname.lastname@example.org; email@example.com).
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- Modulo-analog-to-digital converter (ADC)
- blind estimation