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Stealing bits from a quantized source

机译：从量化来源窃取比特

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We consider "bit stealing" scenarios where the rate of a source code must be reduced without prior planning. We first investigate the efficiency of source requantization to reduce rate, which we term successive degradation. We focus on finite-alphabet sources with arbitrary distortion measures as well as the Gaussian-quadratic and high-resolution scenarios. We show an achievable rate-distortion tradeoff and prove that this is the best guaranteeable tradeoff for any good source code. This tradeoff is in general different from the rate-distortion tradeoff with successive refinement, where there is prior planning. But, we show that with quadratic distortion measures, for all sources with finite differential entropy and at least one finite moment, the gap is at most 1/2 bit or 3 dB in the high-resolution limit. In the Gaussian-quadratic case, the gap is at most 1/2 bit for all resolutions. We further consider bit stealing in the form of information embedding, whereby an embedder acts on a quantized source and produces an output at the same rate and in the original source codebook. We develop achievable distortion-rate tradeoffs. Two cases are considered, corresponding to whether or not the source decoder is informed of the embedding rate. In the Gaussian-quadratic case, we show the informed decoder need only augment the regular decoder with simple post-reconstruction distortion compensation in the form of linear scaling for the resulting system to be as efficient as bit stealing via successive degradation. Finally, we show that the penalty for uninformed versus informed decoders is at most 3 dB or 0.21-bit in the Gaussian-quadratic case and that their performance also lies within the 1/2-bit gap to that of successive refinement.
机译：我们考虑了“偷位”情况，其中未经事先计划就必须降低源代码的速率。我们首先研究源重新量化以降低速率的效率，我们将其称为连续降级。我们专注于具有任意失真度量的有限字母源以及高斯二次和高分辨率方案。我们展示了可以实现的速率失真折衷，并证明对于任何良好的源代码，这都是最佳的可保证折衷。通常，此折衷与先进行计划后进行连续优化的速率失真折衷不同。但是，我们表明，采用二次失真度量，对于所有具有有限差分熵和至少一个有限矩的信号源，在高分辨率极限中，间隙最大为1/2位或3 dB。在高斯二次方情况下，所有分辨率的间隙最大为1/2位。我们进一步考虑以信息嵌入的形式窃取比特，从而使嵌入器作用于量化的源并以相同的速率生成原始源代码本中的输出。我们开发出可以实现的失真率权衡。考虑两种情况，分别对应于是否通知源解码器嵌入率。在高斯二次方情况下，我们表明，明智的解码器仅需要使用简单的重构后失真补偿（以线性缩放的形式来扩展常规解码器），使所得系统与通过连续降级的比特窃取一样有效。最后，我们表明，在高斯二次方情况下，不知情的解码器与有信息的解码器的损失最多为3 dB或0.21位，并且它们的性能也与后续优化的性能相差1/2位。

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