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首页> 外文期刊>Information Theory, IEEE Transactions on >Output Constrained Lossy Source Coding With Limited Common Randomness
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Output Constrained Lossy Source Coding With Limited Common Randomness

机译：具有受限公共随机性的输出受限有损源编码

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摘要

This paper studies a Shannon-theoretic version of the generalized distribution preserving quantization problem where a stationary and memoryless source is encoded subject to a distortion constraint and the additional requirement that the reproduction also be stationary and memoryless with a given distribution. The encoder and decoder are stochastic and assumed to have access to independent common randomness. Recent work has characterized the minimum achievable coding rate at a given distortion level when unlimited common randomness is available. Here, we consider the general case where the available common randomness may be rate limited. Our main result completely characterizes the set of achievable coding and common randomness rate pairs at any distortion level, thereby providing the optimal tradeoff between these two rate quantities. We also consider two variations of this problem where we investigate the effect of relaxing the strict output distribution constraint and the role of private randomness used by the decoder on the rate region. Our results have strong connections with Cuff’s recent work on distributed channel synthesis. In particular, our achievability proof combines a coupling argument with the approach developed by Cuff, where instead of explicitly constructing the encoder–decoder pair, a joint distribution is constructed from which a desired encoder–decoder pair is established. We show, however, that for our problem, the separated solution of first finding an optimal channel and then synthesizing this channel results in a suboptimal rate region.
机译：本文研究了广义分配保留量化问题的香农理论版本，其中编码静态和无记忆源受到失真约束，并且还要求在给定的分布下，复制也必须是静态和无记忆。编码器和解码器是随机的，并且假定可以访问独立的公共随机性。当无限制的公共随机性可用时，最近的工作已经表征了在给定失真水平下最小可实现的编码率。在这里，我们考虑可用公共随机性可能受到速率限制的一般情况。我们的主要结果完全表征了在任何失真水平下可实现的编码和常见随机率对的集合，从而在这两个速率量之间提供了最佳折衷。我们还考虑了此问题的两个变体，其中我们研究了放宽严格的输出分布约束的效果以及解码器在速率区域上使用的私有随机性的作用。我们的结果与Cuff最近在分布式渠道综合方面的工作紧密相关。尤其是，我们的可实现性证明将耦合参数与Cuff开发的方法结合在一起，在这种方法中，不是显式构造编码器-解码器对，而是构造了一个联合分布，从中建立了所需的编码器-解码器对。但是，我们表明，对于我们的问题，首先找到最佳信道，然后合成该信道的分离解决方案将导致次优速率区域。

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