Analysis of Bit-Plane Probability for Generalized Gaussian Distribution and its Application in Audio Coding

Bit-plane probability of data is useful information for many applications such as entropy coding and rate estimation, particularly for scalable coding system. Typically, the value of bit-plane probability varies according to the distribution of the data represented, and due to inter-plane correlation, it is hard to get an analytic solution of bit-plane probability for the data with generalized Gaussian distribution. In this paper, bit-plane probability is analyzed when Generalized Gaussian distribution is used to model the input data. Based on the study of bit-plane probability for Laplace distribution and the relationship between different bit-planes, an approximated bit-plane probability for Generalized Gaussian distribution is presented. This closed-form expression is of low computational cost. Furthermore, a much practical format is derived with reduced complexity for implementation in the state-of-the-art MPEG-4 scalable to lossless audio coding system. With the same computational cost, the proposed algorithm presents higher compression efficiency than MPEG-4 scalable to lossless audio coding, which considers Laplace distribution only.