Deep Task-Based Quantization

Quantizers play a critical role in digital signal processing systems. Recent works have shown that the performance of quantization systems acquiring multiple analog signals using scalar analog-to-digital converters (ADCs) can be significantly improved by properly processing the analog signals prior to quantization. However, the design of such hybrid quantizers is quite complex, and their implementation requires complete knowledge of the statistical model of the analog signal, which may not be available in practice. In this work we design data-driven task-oriented quantization systems with scalar ADCs, which determine how to map an analog signal into its digital representation using deep learning tools. These representations are designed to facilitate the task of recovering underlying information from the quantized signals, which can be a set of parameters to estimate, or alternatively, a classification task. By utilizing deep learning, we circumvent the need to explicitly recover the system model and to find the proper quantization rule for it. Our main target application is multiple-input multiple-output (MIMO) communication receivers, which simultaneously acquire a set of analog signals, and are commonly subject to constraints on the number of bits. Our results indicate that, in a MIMO channel estimation setup, the proposed deep task-bask quantizer is capable of approaching the optimal performance limits dictated by indirect rate-distortion theory, achievable using vector quantizers and requiring complete knowledge of the underlying statistical model. Furthermore, for a symbol detection scenario, it is demonstrated that the proposed approach can realize reliable bit-efficient hybrid MIMO receivers capable of setting their quantization rule in light of the task, e.g., to minimize the bit error rate.