Joint bit allocation and dimensions optimization for vector transform quantization

In vector transform quantization (VTQ), vectors consisting of M consecutive samples of a waveform are transformed into a set of M coefficients that are quantized by m≪M vector quantizers. The bit allocation problem in the transform domain is considered for a memoryless stationary vector source encoded by a VTQ system. It is assumed that the vector quantizer parameters (dimension, codebook size) are subject to a complexity constraint. The vector quantization lower bound on the attainable distortion at a given (high) rate is used for deriving the bit allocation algorithm for given vector dimensions. Then, the joint optimization of vector dimensions and bit allocations is considered. Given a complexity constraint, the optimal dimensions depend on the bit allocation, which, in turn, depends on the dimensions. An iterative algorithm is proposed for solving this problem