AI RESEARCH
PrismQuant: Rate-Distortion-Optimal Vector Quantization for Gaussian-Mixture Sources
arXiv CS.AI
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ArXi:2605.15507v1 Announce Type: cross For a Gaussian source under mean-squared error (MSE), classical transform coding is rate--distortion (RD) optimal: the Karhunen--Loeve transform (KLT) diagonalizes the covariance, reverse waterfilling allocates the bits, and scalar quantization closes the loop. This elegant story breaks down for multimodal sources, where no single covariance can capture heterogeneous local geometries, and the RD function loses its closed form. We revisit this problem through Gaussian-mixture sources and develop a constructive RD theory for them.