Predictive Coding of Integers with Real-valued Predictions

In this paper, we have extended the Rice-Golomb code so that it can operate at fractional precision to efficiently exploit the real-valued predictions. Coding at infinitesimal precision allows the residuals to be modeled with the Laplace distribution. Unlike the Rice-Golomb code, which maps equally probable opposite-signed residuals to different integers, the proposed coding scheme is symmetric in the sense that, at infinitesimal precision, it assigns codewords of equal length to equally probable residual intervals. The symmetry of both the Laplace distribution and the coding scheme facilitates the analysis of the proposed coding scheme to determine the average code-length and the optimal value of the associated coding parameter.