Bracher Annina, Lapidoth Amos, Pfister Christoph
P&C Solutions, Swiss Re, 8022 Zurich, Switzerland.
Signal and Information Processing Laboratory, ETH Zurich, 8092 Zurich, Switzerland.
Entropy (Basel). 2019 Mar 19;21(3):298. doi: 10.3390/e21030298.
Two correlated sources emit a pair of sequences, each of which is observed by a different encoder. Each encoder produces a rate-limited description of the sequence it observes, and the two descriptions are presented to a guessing device that repeatedly produces sequence pairs until correct. The number of guesses until correct is random, and it is required that it have a moment (of some prespecified order) that tends to one as the length of the sequences tends to infinity. The description rate pairs that allow this are characterized in terms of the Rényi entropy and the Arimoto-Rényi conditional entropy of the joint law of the sources. This solves the guessing analog of the Slepian-Wolf distributed source-coding problem. The achievability is based on random binning, which is analyzed using a technique by Rosenthal.
两个相关源发射一对序列，每个序列由不同的编码器进行观测。每个编码器对其观测到的序列生成一个速率受限的描述，并且这两个描述被呈现给一个猜测装置，该装置反复生成序列对直到正确为止。直到正确的猜测次数是随机的，并且要求当序列长度趋于无穷大时，它具有某个预定阶数的矩趋于1。允许这种情况的描述速率对是根据源的联合律的Rényi熵和Arimoto - Rényi条件熵来表征的。这解决了Slepian - Wolf分布式源编码问题的猜测类似问题。可达性基于随机分箱，使用Rosenthal的一种技术对其进行分析。
