New Bounds on the Rate-Distortion Function of a Binary Markov Source

S. Jalali, T. Weissman
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引用次数: 20

Abstract

This paper addresses the problem of bounding the rate-distortion function of a binary symmetric Markov source. We derive a sequence of upper and lower bounds on the rate- distortion function of such sources. The bounds are indexed by k, which corresponds to the dimension of the optimization problem involved. We obtain an explicit bound on the difference between the derived upper and lower bounds as a function of k. This allows to identify the value of k that suffices to compute the rate distortion function to a given desired accuracy. In addition to these bounds, a tighter lower bound which is also a function of k is derived. Our numerical results show that the new bounds improve on the Berger's upper and lower bounds even with small values of k.
二元马尔可夫源的率失真函数的新界
研究了二元对称马尔可夫源的率失真函数的边界问题。我们导出了这类源的率失真函数的上界和下界序列。边界以k为索引,k对应于所涉及的优化问题的维度。作为k的函数,我们获得了派生的上界和下界之间的差的显式界限。这允许识别k的值,该值足以计算速率失真函数到给定的所需精度。除了这些边界之外,我们还推导出了一个更严格的下界,它也是k的函数。我们的数值结果表明,即使k值很小,新的边界也比Berger的上界和下界更好。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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