We delve into the impact of memoryless scalar quantization on matrix
completion. We broaden our theoretical discussion to encompass the coarse
quantization scenario with a dithering scheme, where the only available
information for low-rank matrix recovery is few-bit low-resolution data. Our
primary motivation for this research is to evaluate the recovery performance of
nuclear norm minimization in handling quantized matrix problems without the use
of any regularization terms such as those stemming from maximum likelihood
estimation. We furnish theoretical guarantees for both scenarios: when access
to dithers is available during the reconstruction process, and when we have
access solely to the statistical properties of the dithers. Additionally, we
conduct a comprehensive analysis of the effects of sign flips and
prequantization noise on the recovery performance, particularly when the impact
of sign flips is quantified using the well-known Hamming distance in the upper
bound of recovery error.Comment: arXiv admin note: substantial text overlap with arXiv:2310.0322