  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.
