Symbol coding of Laplacian distributed prediction residuals

Abstract

Predictive coding schemes, proposed in the literature, essentially model the residuals with discrete distributions. However, real-valued residuals can arise in predictive coding, for example, from the usage of an r order linear predictor specified by r real-valued coefficients. In this paper, we propose a symbol-by-symbol coding scheme for the Laplace distribution, which closely models the distribution of real-valued residuals in practice. To efficiently exploit the real-valued predictions at a given precision, the proposed scheme essentially combines the process of residual computation and coding, in contrast to conventional schemes that separate these two processes. In the context of adaptive predictive coding framework, where the source statistics must be learnt from the data, the proposed scheme has the advantage of lower ‘model cost’ as it involves learning only one parameter. In this paper, we also analyze the proposed parametric coding scheme to establish the relationship between the optimal value of the coding parameter and the scale parameter of the Laplace distribution. Our experimental results demonstrated the compression efficiency and computational simplicity of the proposed scheme in adaptive coding of residuals against the widely used arithmetic coding, Rice–Golomb coding, and the Merhav–Seroussi–Weinberger scheme adopted in JPEG-LS.