A lattice vector quantization using a geometric decomposition

An efficient lattice vector quantization design and the associated fast coding algorithm are proposed for high-bit-rate, high-quality data compression applications. The codewords are uniformly distributed and densely packed as 2ⁿ-dimensional lattice points, based on a geometric lattice decomposition technique. The maximum quantization error has been chosen as the design criterion. For high-rate applications, it has the following advantages: (1) simple vector codeword generation; (2) no codewords need to be stored and only predetermined rules are used at encoder and decoder ends; (3) highly regular code structure, so that encoding is done via an inverse tree-search suitable for fast parallel processing, and decoding is done similar to a scalar quantizer; (4) high coding quality capability, viz. the maximum quantization distortion can be prespecified to a desired value and the entire hyper-region is covered uniformly; and (5) dimensionality saving can be easily predicted and it can be achieved using fixed-length codes