论文标题
分布式压缩中的本地解码
Local Decoding in Distributed Compression
论文作者
论文摘要
最近显示，单个来源的无损压缩$ x^n $是可以实现的，具有强大的区域概念。任何$ x_i $都可以从恒定数量的压缩位中解码，并消失在$ n $错误的概率中。相比之下，我们表明，对于两个单独编码的来源$（x^n，y^n）$，通常不可能进行无损压缩和强大的位置。具体而言，我们表明，对于``混乱''来源的类别，每当一个来源之一被压缩到其熵以下时，就无法实现强的地方。不论$ n $，对于某些索引$ i $，解码$（x_i，y_i）$的错误可能性都是由$ 2^{ - o（d）} $降低的，其中$ d $表示本地解码器访问的压缩位数。相反，如果源不混淆，即使其中一个来源被压缩到其熵下方，也可能存在强大的位置。结果扩展到任意数量的来源。
It was recently shown that the lossless compression of a single source $X^n$ is achievable with a notion of strong locality; any $X_i$ can be decoded from a constant number of compressed bits, with a vanishing in $n$ probability of error. By contrast, we show that for two separately encoded sources $(X^n,Y^n)$, lossless compression and strong locality is generally not possible. Specifically, we show that for the class of ``confusable'' sources, strong locality cannot be achieved whenever one of the sources is compressed below its entropy. Irrespective of $n$, for some index $i$ the probability of error of decoding $(X_i,Y_i)$ is lower bounded by $2^{-O(d)}$, where $d$ denotes the number of compressed bits accessed by the local decoder. Conversely, if the source is not confusable, strong locality is possible even if one of the sources is compressed below its entropy. Results extend to an arbitrary number of sources.
