Mean square error binary tree gain-shape vector quantization via hyperplane testing

Summary form only given, as follows. Tree-search vector quantization is an effective coding scheme at high bit rates to circumvent the high complexity of codevector search. The authors present a binary tree-search codebook design method suitable for gain/shape vector quantization. Conventional codebooks are often designed using the LBG (Linde-Buzo-Gray) algorithm when input signal distribution is unknown. In the LBG algorithm, codebook performance depends on the vectors used for the first iteration update. A splitting technique is usually used to determine the initial vectors if the input vectors have various norms or various average values. However, such a splitting technique is not available for gain/shape vector quantization, since input vectors have uniform norms and sometimes have average values of zero. When the codebook has binary tree structure, the training sequence, a set of input vectors, can be divided into two groups by using a hyperplane testing algorithm. This hyperplane is characterized by a first principal component vector. Validity of the proposed partition procedure is proved with the mean-square-error criterion.