On One-Bit Quantization

• URL: http://arxiv.org/abs/2202.05292v1
• Date: Thu, 10 Feb 2022 19:07:06 GMT
• Title: On One-Bit Quantization
• Authors: Sourbh Bhadane and Aaron B. Wagner
• Abstract summary: 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 gradient descent.
• Score: 27.057313611640918
• License: http://creativecommons.org/licenses/by/4.0/
• 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.

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