Universal lossy compression under logarithmic loss
Universal lossy compression under logarithmic loss
复制标题
对数损失下的通用有损压缩
DOI：
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发表时间：
2017
期刊：
影响因子：
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通讯作者：
S. Verdú
中科院分区：
文献类型：
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作者：
Yanina Y. Shkel;M. Raginsky;S. Verdú
研究了基于对数损失失真准则的通用有损信源编码。推导了关于分布族的固定长度通用编码的非渐近基本极限的界限。这些界限概括了众所周知的通用无损源编码的极小极大界限。研究了一系列 i.i.d. 所产生的优化问题的渐近行为。源具有有限的字母大小，并且被表征为常数。无记忆源的冗余行为类似于 k/2 log n，其中 n 是块长度，k 是参数空间中的自由度数。编码率的影响在于常数项：较高的压缩率有效地减少了参数不确定性集的体积。
Universal lossy source coding with the logarithmic loss distortion criterion is studied. Bounds on the non-asymptotic fundamental limit of fixed-length universal coding with respect to a family of distributions are derived. These bounds generalize the well-known minimax bounds for universal lossless source coding. The asymptotic behavior of the resulting optimization problem is studied for a family of i.i.d. sources with a finite alphabet size, and is characterized up to a constant. The redundancy of memoryless sources behaves like k/2 log n, where n is the blocklength and k is the number of degrees of freedom in the parameter space. The impact of the coding rate is on the constant term: higher compression rate effectively reduces the volume of the parameter uncertainty set.