An Optimization-Based Approach to One-Bit Quantization

An Optimization-Based Approach to One-Bit Quantization — Code and Test Data

Reference implementation and reproducible test framework accompanying the publication An Optimization-Based Approach to One-Bit Quantization (F. Mayer, C. Vogel, ISCAS 2024).

One-bit quantization converts real-valued signals into binary sequences. This work introduces a mapping function that formulates the conversion as an optimization problem: an error measure between the real-valued signal and its two-level representation is minimized, weighted by a filter matrix W. The structure of W determines the character of the quantization, so the behaviour of the quantizer can be modelled without changing the algorithm itself. The well-known first-order Sigma-Delta modulator turns out to be a special case, obtained by choosing W as a lower-triangular matrix of ones. Replacing the global error by the instantaneous error yields a sequential optimization with complexity O(N), which is fast enough for practical signal lengths and provides a good initial vector for a subsequent global optimization.

The archive contains the quantization algorithms, the generator for the band-limited multitone test signals, the evaluation and plotting tools, and the parameter sets used in the paper.

Getting started: unpack the archive and open README.md for an overview of the repository structure and the individual modules. HOWTO.md is the step-by-step guide: required Python packages, the Gurobi academic license needed for the solver, and the three-stage pipeline from signal generation through quantization to evaluation, including how to define your own test scenarios.

Requires Python 3 with NumPy, SciPy, Matplotlib and PyQt5, plus a Gurobi license (free for academic use).

Funded by the Austrian Science Fund (FWF) [10.55776/DFH 5] and the province of Styria.