It is well known that independent (separate) encoding of KK correlated sources may incur some rate loss compared to joint encoding, even if the decoding is done jointly. This loss is particularly evident in the multiple descriptions problem, where it is the same source that is encoded in each description. We observe that under mild conditions about the source and distortion measure, the sum-rate of KK separately encoded individually good descriptions tends to the rate-distortion function of the joint decoder in the limit of vanishing small coding rates of the descriptions. Moreover, we then propose to successively encode the source into KK independent descriptions in each round in order to achieve a final distortion DD after MM rounds. We provide two examples – a Gaussian source with mean-squared error and an exponential source with one-sided error – for which the excess rate vanishes in the limit as the number of rounds MM goes to infinity, for any fixed DD and KK . This result has an interesting interpretation for a multi-round variant of the multiple descriptions problem, where after each round the encoder gets a (block) feedback regarding which of the descriptions arrived: In the limit as the number of rounds MM goes to infinity (i.e., many incremental rounds), the total rate of received descriptions approaches the rate-distortion function. We provide theoretical and experimental evidence showing that this phenomenon is in fact more general than in the two examples above.

中文翻译：

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渐进式改进和带有反馈的多重描述


众所周知，与联合编码相比，KK 相关源的独立（单独）编码可能会导致一些速率损失，即使解码是联合完成的。这种损失在多重描述问题中尤其明显，其中每个描述中都编码相同的源。我们观察到，在源和失真测量的温和条件下，在描述的小编码率消失的限制下，KK单独编码的单独良好描述的总速率趋向于联合解码器的速率失真函数。此外，我们建议在每一轮中将源连续编码为KK独立描述，以便在MM轮之后实现最终的失真DD。我们提供了两个例子——具有均方误差的高斯源和具有单边误差的指数源——对于任何固定的 DD 和 KK ，当 MM 轮数趋于无穷大时，超额率在极限内消失。这个结果对多描述问题的多轮变体有一个有趣的解释，其中在每一轮之后，编码器都会获得一个关于哪个描述到达的（块）反馈：在极限中，当轮数 MM 趋于无穷大时（即，许多增量轮），接收到的描述的总速率接近速率失真函数。我们提供的理论和实验证据表明，这种现象实际上比上面两个例子更普遍。