English

On One-Bit Quantization

Information Theory 2022-02-14 v1 Machine Learning math.IT

Abstract

We consider the one-bit quantizer that minimizes the mean squared error for a source living in a real Hilbert space. The optimal quantizer is a projection followed by a thresholding operation, and we provide methods for identifying the optimal direction along which to project. As an application of our methods, we characterize the optimal one-bit quantizer for a continuous-time random process that exhibits low-dimensional structure. We numerically show that this optimal quantizer is found by a neural-network-based compressor trained via stochastic gradient descent.

Keywords

Cite

@article{arxiv.2202.05292,
  title  = {On One-Bit Quantization},
  author = {Sourbh Bhadane and Aaron B. Wagner},
  journal= {arXiv preprint arXiv:2202.05292},
  year   = {2022}
}