The lossless compression of a single source $X^n$ was recently shown to be achievable with a notion of strong locality; any $X_i$ can be decoded from a {\emph{constant}} number of compressed bits, with a vanishing in $n$ probability of error. In contrast with the single source setup, we show that for two separately encoded sources $(X^n,Y^n)$, lossless compression and strong locality is generally not possible. More precisely, we show that for the class of "confusable" sources strong locality cannot be achieved whenever one of the sources is compressed below its entropy. In this case, irrespectively of $n$, the probability of error of decoding any $(X_i,Y_i)$ is lower bounded by $2^{-O(d_{\mathrm{loc}})}$, where $d_{\mathrm{loc}}$ 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 any number of sources.

翻译：最近,一个源的无损压缩 $X $n 最近显示,一个源的无损压缩 $X $n 是一个强点的概念可以实现; 任何X_ i 美元都可以从一个 emph{ constant}} 块块块解码, 以美元差错概率消失 。 与单一源的设置相比, 我们显示, 对于两个单独编码源 $( Xn, Y ⁇ n) 、 无损压缩和强点通常是不可能的 。 更确切地说, 我们显示, 对于“ 不可变” 源类的强点, 当一个源被压缩到其酶下面时, 无法实现。 在这种情况下, 无论$0, 任何( X_ i, Y_ i) 块块块块的错误概率都较低, $%- O (dämathrm{loc}}} 美元, 其中, $ d ⁇ mathrm{ {loc} 表示本地解码器访问到的压缩点数 。 相反, 如果源不是可变的, 强点点是可能的, 即使一个源的, 即使其磁号也有可能扩展。