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Additive successive refinement

机译：连续相加精炼

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摘要

Rate-distortion bounds for scalable coding, and conditions under which they coincide with nonscalable bounds, have been extensively studied. These bounds have been derived for the general tree-structured refinement scheme, where reproduction at each layer is an arbitrarily complex function of all encoding indexes up to that layer. However, in most practical applications (e.g., speech coding) "additive" refinement structures such as the multistage vector quantizer are preferred due to memory limitations. We derive an achievable region for the additive successive refinement problem, and show via a converse result that the rate-distortion bound of additive refinement is above that of tree-structured refinement. Necessary and sufficient conditions for the two bounds to coincide are derived. These results easily extend to abstract alphabet sources under the condition E{d(X,a)}>/spl infin/ for some letter a. For the special cases of square-error and absolute-error distortion measures, and subcritical distortion (where the Shannon lower bound (SLB) is tight), we show that successive refinement without rate loss is possible not only in the tree-structured sense, but also in the additive-coding sense. We also provide examples which are successively refinable without rate loss for all distortion values, but the optimal refinement is not additive.
机译：已经对可伸缩编码的速率失真范围及其与不可伸缩范围一致的条件进行了广泛的研究。这些界限是针对一般的树状结构细化方案得出的，其中，每一层的重现是直至该层的所有编码索引的任意复杂函数。但是，在大多数实际应用中（例如，语音编码），由于存储器的限制，优选“累加”的细化结构，例如多级矢量量化器。我们推导了加法连续精细化问题的可实现区域，并通过相反的结果表明，加法精细化的速率失真范围高于树结构化精细化的速率失真范围。得出两个边界重合的充要条件。这些结果可以很容易地扩展到条件E {d（X，a）}> / spl infin /的某些字母a的抽象字母来源。对于特殊的平方误差和绝对误差失真测度以及次临界失真（香农下限（SLB）严格的情况），我们证明了在不降低速率的情况下进行连续细化不仅可以在树状结构上进行，而且在加性编码意义上。我们还提供了可以对所有失真值连续进行精炼而不会降低速率的示例，但最佳精炼不是累加的。

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