实值预测整数预测编码的改进Rice-Golomb码
Modified Rice-Golomb Code for Predictive Coding of Integers with Real-valued Predictions
摘要：
莱斯-哥伦布码在实践中被广泛用于对整数值预测残差进行编码。然而，在音频、图像和视频的无损编码中，特别是那些涉及线性预测器的无损编码中，预测来自实域。在本文中，我们已经修改和扩展了赖斯-哥伦布码，使其可以在小数精度下有效地利用实值预测。以任意小的精度编码允许用拉普拉斯分布而不是其离散对应物（即双侧几何分布（TSGD））对残差进行建模。与莱斯-哥伦布码不同，该码将相等概率的相反符号残差映射到不同的整数，所提出的编码方案在任意小的精度下将相等长度的码字分配到相等概率的残差区间的意义上是对称的。拉普拉斯分布和编码的对称性有利于分析所提出的编码方案，以确定平均码长和相关编码参数的最佳值。实验结果表明，该方案，通过有效地利用实值预测，实现更好的压缩相比，传统的计划。
英文摘要：
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.
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