Hardware-limited Non-uniform Task-based Quantizers

Hardware-limited task-based quantization is a new design paradigm for data acquisition systems equipped with scalar analog-to-digital converters using a small number of bits. By taking into account the system task, task-based quantizers can efficiently recover the desired parameters from the low-bit quantized observation. Current design and analysis frameworks for hardware-limited task-based quantization are only applicable to inputs with bounded support and uniform quantizers with non-subtractive dithering. In this paper, we propose a new framework based on generalized Bussgang decomposition that enables the design and analysis of hardware-limited task-based quantizers equipped with non-uniform scalar quantizers or have inputs with unbounded support. We consider the scenario in which the task is linear. Under this scenario, we derive new pre-quantization and post-quantization mappings for task-based quantizers with mean squared error (MSE) that closely matches the theoretical MSE.