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arXiv 1306.6288cs.ITmath.IT
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信源信道分离定理的信息谱方法

Information Spectrum Approach to the Source Channel Separation Theorem

Nir Elkayam, Meir Feder

摘要:

Aggrawal等人最近给出了一般信道的源-信道分离定理。该定理指出,如果存在在一般信道W上实现最大失真水平d_{max}的编码方案,则可以在该信道上以小于R(d_{max})的速率完成可靠的通信,其中R(.)是信源的率失真函数。然而,源本质上被限制为离散和无记忆(DMS)的。在这项工作中,我们证明了一个更强的要求,源是一般的,只满足一个“球包装最优”的功能,和通道是完全一般的。此外,我们表明,如果信道满足强逆属性定义的汉和verdu,那么同样的声明可以与d_{avg},平均失真水平,取代d_{max}。与那里的证明不同,我们使用信息谱方法来证明陈述,并且结果可以很容易地扩展到其他情况。

英文摘要:

A source-channel separation theorem for a general channel has recently been shown by Aggrawal et. al. This theorem states that if there exist a coding scheme that achieves a maximum distortion level d_{max} over a general channel W, then reliable communication can be accomplished over this channel at rates less then R(d_{max}), where R(.) is the rate distortion function of the source. The source, however, is essentially constrained to be discrete and memoryless (DMS). In this work we prove a stronger claim where the source is general, satisfying only a "sphere packing optimality" feature, and the channel is completely general. Furthermore, we show that if the channel satisfies the strong converse property as define by Han & verdu, then the same statement can be made with d_{avg}, the average distortion level, replacing d_{max}. Unlike the proofs there, we use information spectrum methods to prove the statements and the results can be quite easily extended to other situations.

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