Linearization of Non-Uniform Quantizers via Adaptive Non-Subtractive Dithering

Morriel Kasher, P. Spasojevic, M. Tinston
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Abstract

Non-subtractive dithering is an effective method to improve quantizer performance by injecting input noise that reduces statistical correlations between input signals and quantization error. Existing non-subtractive dither theory has primarily designed dither signal distributions for linear, uniform quantizers, neglecting real-world non-idealities including non-uniformity and finite-level saturation. We develop a generalized analytical condition to guarantee independence of the quantization error moments from the input signal for an arbitrary finite-level non-linear quantizer characteristic. We use this to propose a novel asymmetric, adaptive dither technique for effective linearization of non-uniform quantizers via reduction of the first conditional quantization error moment. These adaptive dither distributions are shown to completely eliminate the first error moment in Lloyd-Max quantizers and significantly reduce it in non-linear quantizers. This allows the use of time-averaging to converge to an arbitrarily precise signal estimate in non-uniform quantizers.
基于自适应非减法抖动的非均匀量化器线性化
非减法抖动是一种提高量化器性能的有效方法,它通过注入输入噪声来降低输入信号之间的统计相关性和量化误差。现有的非减法抖动理论主要是为线性均匀量化器设计抖动信号分布,忽略了现实世界的非理想性,包括非均匀性和有限级饱和。对于任意有限级非线性量化器特性,给出了保证量化误差矩与输入信号无关的广义解析条件。我们利用这一点提出了一种新的非对称、自适应抖动技术,通过减少第一条件量化误差矩来有效地对非均匀量化器进行线性化。这些自适应抖动分布被证明可以完全消除Lloyd-Max量化器中的第一误差矩,并显着降低非线性量化器中的第一误差矩。这允许在非均匀量化器中使用时间平均收敛到任意精确的信号估计。
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