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The fundamental concepts of vector quantization (VQ) have been discussed, mainly concentrated on the high computational complexity and high storage complexity of vector quantization for image coding. A new multilevel codebook searching (MCS) algorithm is introduced to reduce VQ encoding complexity while preserving the quality of VQ. A VLSI implementation of vector quantization using distributed arithmetic has been proposed as well as a self-sustained chip design for image coding. The basic concepts of lattice vector quantization and its application in image coding have been introduced. A variable rate two-stage vector quantization-lattice vector quantization algorithm for vector sub-band image coding has been proposed. A Generalized labeling algorithm for various lattice with pyramid and sphere boundaries has been developed.