On One-Bit Quantization

Sourbh Bhadane; Aaron B. Wagner

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arXiv · 2202.05292

On One-Bit Quantization

Sourbh Bhadane·Aaron B. Wagner

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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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Sourbh Bhadane, Aaron B. Wagner. 2022-02-10. On One-Bit Quantization. https://arxiv.org/abs/2202.05292

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