Information-theoretic applications of the logarithmic probability comparison bound
Information-theoretic applications of the logarithmic probability comparison bound
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对数概率比较界的信息论应用
DOI：
10.1109/isit.2015.7282552
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发表时间：
2014
期刊：
影响因子：
--
通讯作者：
N. Merhav
中科院分区：
文献类型：
--
作者：
R. Atar;N. Merhav
评估稀有事件的概率(例如，在球体填充范围中使用)的众所周知的技术是找到感兴趣的事件具有一阶概率的参考测量，并使用Kullback-Leibler散度(KLD)估计所讨论的概率。最近提出了一种新的方法[2]，它可以看作是这一思想的扩展，其中参考测量下的概率本身可能是指数衰减的，而使用的是Rényi发散(RD)。我们在不同的信息论环境中展示了这种方法的有效性。对于信道编码，我们提供了一种方法来获得匹配、不匹配和稳健的误差指数界，以及在各种特定信道模型下的新结果。我们解决的其他应用包括率失真编码和猜测问题。
A well-known technique in assessing probabilities of rare events (used, e.g., in the sphere-packing bound), is that of finding a reference measure under which the event of interest has probability of order one and estimating the probability in question using the Kullback-Leibler divergence (KLD). A recent method has been proposed [2], that can be viewed as an extension of this idea in which the probability under the reference measure may itself be decaying exponentially, and the Rényi divergence (RD) is used instead. We demonstrate the usefulness of this approach in various information-theoretic settings. For channel coding, we provide a method for obtaining matched, mismatched and robust error exponent bounds, as well as new results in a variety of particular channel models. Other applications we address include rate-distortion coding and the problem of guessing.