On One-Bit Quantization
This provides theoretical foundations for efficient one-bit quantization in signal processing and communications applications.
The paper tackles the problem of designing optimal one-bit quantizers that minimize mean squared error for sources in real Hilbert spaces, showing the optimal solution is a projection followed by thresholding and providing methods to find the optimal projection direction. As a result, they characterize the optimal quantizer for continuous-time random processes with low-dimensional structure and demonstrate numerically that a neural-network-based compressor trained via SGD finds this optimal quantizer.
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.