# Blind Unwrapping of Modulo Reduced Gaussian Vectors: Recovering MSBs from LSBs

arXiv: https://arxiv.org/abs/1901.10396 · HTML: https://mlsanity.com/paper/1901.10396/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 29 Jan 2019.

## Built on by (most cited first, 3 of 3)

- [Spiked Covariance Estimation from Modulo-Reduced Measurements](https://mlsanity.com/paper/2110.01150/) (2021)
- [Blind-Adaptive Quantizers](https://mlsanity.com/paper/2409.04077/) (2024)
- [One-Bit-Aided Modulo Sampling for DOA Estimation](https://mlsanity.com/paper/2309.04901/) (2023)

## Abstract (arXiv)

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., measurement where each coordinate is reduced modulo Delta, for some Delta>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 numeric results that show that the algorithm performs well even in non-asymptotic conditions.