The main aim of the paper is to provide effective and accurate solutions for the calculation of the support region of the μ-law logarithmic companding quantizers. A new solution for the starting point of iterative methods will be proposed, that provides very accurate value of the support region (being the main parameter needed for the design of the quantizer) only after one iteration of the iterative method. Based on this new starting point, an accurate closed-form approximate expression for the calculation of the support region will be derived, as one of the main contributions of the paper. To significantly simplify implementation of the μ-law companding quantizer, piecewise linearization is performed. A new linearization method is presented, based on the optimization of the last segments. Derivation of an accurate closed-form formula for the support region of the linearized quantizer is done, as an important contribution. The obtained linearized μ-law companding quantizer is very simple to design (due to closed-form formulas) and to implement (due to linearization), providing at the same time very high performance (due to optimization of the last segments). Due to these and other advantages (robustness, adjustability to the statistical distribution of the input signal), the proposed quantizer can be used in many topical applications, such as in receivers of 5G wireless systems or in neural networks for quantization of weights and activations. The paper provides an application of the designed quantizers for quantization of weights of a neural network, showing significant decreasing of the bit-rate compared to the standard full-precision representation (from 32 bits to just 5 bits), with the same prediction accuracy of the network.

本文的主要目的是为μ律对数压扩量化器的支持区域的计算提供有效和准确的解决方案。将提出一种新的迭代方法起点的解决方案，它仅在迭代方法的一次迭代后提供非常准确的支持区域值（这是设计量化器所需的主要参数）。基于这个新的起点，将推导出用于计算支撑区域的精确闭式近似表达式，这是本文的主要贡献之一。为了显着简化 μ 律压扩量化器的实现，执行分段线性化。提出了一种新的线性化方法，基于对最后段的优化。推导了线性化量化器的支持区域的精确闭式公式，这是一个重要的贡献。所获得的线性化 μ 律压扩量化器的设计（由于封闭式公式）和实现（由于线性化）非常简单，同时提供了非常高的性能（由于对最后一段的优化）。由于这些和其他优点（鲁棒性、输入信号统计分布的可调整性），所提出的量化器可用于许多主题应用，例如 5G 无线系统的接收器或用于量化权重和激活的神经网络。该论文提供了设计的量化器在神经网络权重量化中的应用，