Application of Mean-Square Approximation for Piecewise Linear Optimal Compander Design for Gaussian Source and Gaussian Mixture Model
Keywords:linearization, mean-square approximation, spline approximation, Gaussian PDF, Gaussian mixture model, SQNR
AbstractThis paper proposes a novel piecewise linear optimal compander design method based on the mean-square approximation of the first derivative of the optimal compressor function. Designing of the piecewise linear optimal compander is conducted for signals modeled with the Gaussian probability density function (PDF) and signals modeled with the Gaussian mixture model (GMM). The slopes of the piecewise linear optimal compressor function are optimized for each quantization segment from the support region. The optimization is performed with a goal of obtaining minimal mean-squared error introduced with the proposed approximation, in this manner affecting the number of the uniform cells within each segment. The obtained numerical results show that signal-to-quantization-noise ratio (SQNR) of so obtained piecewise linear optimal compander overreaches SQNR of the uniform quantizer, whereas approaches to the SQNR of the nonlinear optimal compander for higher number of quantization segments. Features of the proposed quantizer indicate great possibilities for its widespread application in quantization of signals modeled by Gaussian PDF and GMM.
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