Distributed Quantization for Sparse Time Sequences

Analog signals processed in digital hardware are quantized into a discrete bit-constrained representation. Quantization is typically carried out using analog-to-digital converters (ADCs), operating in a serial scalar manner. In some applications, a set of analog signals are acquired individually and processed jointly. Such setups are referred to as distributed quantization. In this work, we propose a distributed quantization scheme for representing a set of sparse time sequences acquired using conventional scalar ADCs. Our approach utilizes tools from secure group testing theory to exploit the sparse nature of the acquired analog signals, obtaining a compact and accurate representation while operating in a distributed fashion. We then show how our technique can be implemented when the quantized signals are transmitted over a multi-hop communication network providing a low-complexity network policy for routing and signal recovery. Our numerical evaluations demonstrate that the proposed scheme notably outperforms conventional methods based on the combination of quantization and compressed sensing tools

A Distributed Computationally Aware Quantizer Design via Hyper Binning

We design a distributed function aware quantization scheme for distributed functional compression. We consider $2$ correlated sources $X_1$ and $X_2$ and a destination that seeks the outcome of a continuous function $f(X_1,\,X_2)$. We develop a compression scheme called hyper binning in order to quantize $f$ via minimizing entropy of joint source partitioning. Hyper binning is a natural generalization of Cover's random code construction for the asymptotically optimal Slepian-Wolf encoding scheme that makes use of orthogonal binning. The key idea behind this approach is to use linear discriminant analysis in order to characterize different source feature combinations. This scheme captures the correlation between the sources and function's structure as a means of dimensionality reduction. We investigate the performance of hyper binning for different source distributions, and identify which classes of sources entail more partitioning to achieve better function approximation. Our approach brings an information theory perspective to the traditional vector quantization technique from signal processing