A compression method based on non-uniform binary scalar quantization, designed for the memoryless Laplacian source with zero-mean and unit variance, is analyzed in this paper. Two quantizer design approaches are presented that investigate the effect of clipping with the aim of reducing the quantization noise, where the minimal mean-squared error distortion is used to determine the optimal clipping factor. A detailed comparison of both models is provided, and the performance evaluation in a wide dynamic range of input data variances is also performed. The observed binary scalar quantization models are applied in standard signal processing tasks, such as speech and image quantization, but also to quantization of neural network parameters. The motivation behind the binary quantization of neural network weights is the model compression by a factor of 32, which is crucial for implementation in mobile or embedded devices with limited memory and processing power. The experimental results follow well the theoretical models, confirming their applicability in real-world applications.

Achieving real-time inference is one of the major issues in contemporary neural network applications, as complex algorithms are frequently being deployed to mobile devices that have constrained storage and computing power. Moving from a full-precision neural network model to a lower representation by applying quantization techniques is a popular approach to facilitate this issue. Here, we analyze in detail and design a 2-bit uniform quantization model for Laplacian source due to its significance in terms of implementation simplicity, which further leads to a shorter processing time and faster inference. The results show that it is possible to achieve high classification accuracy (more than 96% in the case of MLP and more than 98% in the case of CNN) by implementing the proposed model, which is competitive to the performance of the other quantization solutions with almost optimal precision.

This paper considers the design of a binary scalar quantizer of Laplacian source and its application in compressed neural networks. The quantizer performance is investigated in a wide dynamic range of data variances, and for that purpose, we derive novel closed-form expressions. Moreover, we propose two selection criteria for the variance range of interest. Binary quantizers are further implemented for compressing neural network weights and its performance is analysed for a simple classification task. Good matching between theory and experiment is observed and a great possibility for implementation is indicated.

This paper introduces a novel approach that bridges the floating-point (FP) format, widely utilized in diverse fields for data representation, with the μ-law companding quantizer, proposing a method for designing and linearizing the μ-law companding quantizer to yield a piecewise uniform quantizer tailored to the FP format. A key outcome of the paper is a closed-form approximate expression for closely and efficiently evaluating the FP format’s performance for data with the Laplacian distribution. This expression offers generality across various bit rates and data variances, markedly reducing the computational complexity of FP performance evaluation compared to prior methods reliant on summation of a large number of terms. By facilitating the evaluation of FP format performance, this research substantially aids in the selection of the optimal bit rates, crucial for digital representation quality, dynamic range, computational overhead, and energy efficiency. The numerical calculations spanning a wide range of data variances provided for some commonly used FP versions with an 8-bit exponent have demonstrated that the proposed closed-form expression closely approximates FP format performance.

A novel 2‐bit adaptive delta modulation (ADM) algorithm is presented based on uniform scalar quantization and fractional linear prediction (FLP) for encoding the signals modelled by a Gaussian probability density function. The study focusses on two major areas: realization of a 2‐bit adaptive quantizer based on Q ‐function approximation that significantly facilitates quantizer design; and implementation of a recently introduced FLP approach with the memory of two samples, which replaces the first‐order linear prediction used in standard ADM algorithms and enables improved performance without increasing transmission costs. It furthermore represents the first implementation of FLP in signal encoding, therefore confirming its applicability in a real signal‐processing scenario. Based on the performance analysis conducted on a real speech signal, the proposed ADM algorithm with FLP is demonstrated to outperform other 2‐bit ADM baselines by a large margin for the gain in signal‐to‐noise ratio achieved over a wide dynamic range of input signals. The results of this research indicate that ADM with adaptive quantization based on Q‐function approximation and adaptive FLP represents a promising solution for encoding/compression of correlated time‐varying signals following the Gaussian distribution.