相关信源流压缩的可压缩中偏差渐近性
Achievable Moderate Deviations Asymptotics for Streaming Compression of Correlated Sources
摘要：
受流多视点视频编码和无线传感器网络的启发，我们考虑了一对相关源的分块流压缩问题，我们称之为流Slepian-Wolf编码。我们研究了中等偏差制度，在该制度中，一个序列的代码的速率对收敛，沿着一条直线，在Slepian-Wolf区域的边界上的各个点的速度慢于块长度的平方根倒数$n$，而错误概率衰减亚指数快速$n$。我们的主要结果集中在Slepian-Wolf区域的角点的方法的方向。它指出，对于每个相关的源和所有角点，存在接近方向的非空子集，使得适度偏差常数（错误概率的次指数衰减的比例常数）被增强（在非流传输情况下）至少$T$的因子，$T$是解码源块对的块延迟。我们专门我们的主要结果流无损信源编码的设置，并概括这一结果的设置，我们有不同的延迟要求的两个源块。我们的主要结果的证明涉及到各种分析工具的使用，并融合了最近的信息理论流文献的几个想法。我们采用了Draper和Khisti（2011）以及Lee，Tan和Khisti（2016）的所谓截断内存编码思想，以确保在大块长度的限制下，错误累积的影响是无效的。我们还调整了所谓的最小加权经验后缀熵解码器的使用，Draper，Chang和Sahai（2014）使用该解码器来推导符号流Slepian-Wolf编码的可实现误差指数。
英文摘要：
Motivated by streaming multi-view video coding and wireless sensor networks, we consider the problem of blockwise streaming compression of a pair of correlated sources, which we term streaming Slepian-Wolf coding. We study the moderate deviations regime in which the rate pairs of a sequence of codes converge, along a straight line, to various points on the boundary of the Slepian-Wolf region at a speed slower than the inverse square root of the blocklength $n$, while the error probability decays subexponentially fast in $n$. Our main result focuses on directions of approaches to corner points of the Slepian-Wolf region. It states that for each correlated source and all corner points, there exists a non-empty subset of directions of approaches such that the moderate deviations constant (the constant of proportionality for the subexponential decay of the error probability) is enhanced (over the non-streaming case) by at least a factor of $T$, the block delay of decoding source block pairs. We specialize our main result to the setting of streaming lossless source coding and generalize this result to the setting where we have different delay requirements for each of the two source blocks. The proof of our main result involves the use of various analytical tools and amalgamates several ideas from the recent information-theoretic streaming literature. We adapt the so-called truncated memory encoding idea from Draper and Khisti (2011) and Lee, Tan, and Khisti (2016) to ensure that the effect of error accumulation is nullified in the limit of large blocklengths. We also adapt the use of the so-called minimum weighted empirical suffix entropy decoder which was used by Draper, Chang, and Sahai (2014) to derive achievable error exponents for symbolwise streaming Slepian-Wolf coding.
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