ρ距离及随机场的失真率函数

ρDistance and Distortion-Rate Function of Random Fields

  • 摘要: 本文将ρ距离的概念推广到了随机场情形,证明了该推广定义的合理性,并导出了一些上界和下届估计,特别地,我们证明了有相变情况下2维Ising模型的两个极端测度μ+,μ-间的ρ距离大于1/3,我们着重研究了ρ距离和失真率函数之间的关系,得到了一些重要性质.这些性质可以用来证明编码定理。

     

    Abstract: We introduce the notation of ρ-distance of two random fields, and show the validness of the definition. Some lower and upper bounds are derived and applied to evaluate some examples. In particular, we show that the ρ-distance of the two extreme random fields μ+- of 2-D Ising model on Z2 is larger than 1/3 in the case of phase transition. We also introduce the notation of distortion-rate function of random fields. We pursue the relation betweenρ-distance and distortion-rate function, and obtain some interesting properties that are useful in the proof of coding theorem.

     

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