Modified Rice-Golomb Code for Predictive Coding of Integers with Real-valued Predictions

TL;DR

This paper introduces a modified Rice-Golomb coding scheme that operates at fractional precision to better encode real-valued prediction residuals, improving compression efficiency in lossless audio, image, and video coding.

Contribution

The paper extends Rice-Golomb codes to fractional precision, enabling symmetric coding of residuals modeled by the Laplace distribution, which enhances compression performance.

Findings

Achieves better compression than conventional schemes.

Facilitates analysis of code-length and optimal parameters.

Utilizes real-valued predictions for improved efficiency.

Abstract

Rice-Golomb codes are widely used in practice to encode integer-valued prediction residuals. However, in lossless coding of audio, image, and video, specially those involving linear predictors, the predictions are from the real domain. In this paper, we have modified and extended the Rice-Golomb code so that it can operate at fractional precision to efficiently exploit the real-valued predictions. Coding at arbitrarily small precision allows the residuals to be modeled with the Laplace distribution instead of its discrete counterpart, namely the two-sided geometric distribution (TSGD). 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 arbitrarily small precision, it assigns codewords of equal length to equally probable residual intervals. The symmetry of both the Laplace distribution and the code facilitates the analysis of the proposed coding scheme to determine the average code-length and the optimal value of the associated coding parameter. Experimental results demonstrate that the proposed scheme, by making efficient use of real-valued predictions, achieves better compression as compared to the conventional scheme.