论文标题
$ O（\ log \ log n）$最差的本地解码和更新数据压缩效率
$O(\log \log n)$ Worst-Case Local Decoding and Update Efficiency for Data Compression
论文作者
论文摘要
本文通过本地解码和本地更新解决了数据压缩问题。压缩方案具有最差的本地解码$ d_ {wc} $，如果可以通过最多探测压缩顺序的$ d_ {wc} $位来恢复任何原始文件，并且如果可以通过在最多的$ u_ u__} $上进行修改，则可以通过修改单个原始文件来更新一个原始文件的更新效率。本文为无内存来源提供了一个熵调整的压缩方案，该方案同时实现了$ O（\ log \ log n）$本地解码和更新效率。这种可实现结果的关键是稀疏序列的新型简洁数据结构，该数据结构允许有效的本地解码和本地更新。在本地解码器和更新算法上的一般假设下，相反的结果表明$ d_ {wc} $和$ u_ {wc} $必须成长为$ω（\ log log \ log \ log n）$。
This paper addresses the problem of data compression with local decoding and local update. A compression scheme has worst-case local decoding $d_{wc}$ if any bit of the raw file can be recovered by probing at most $d_{wc}$ bits of the compressed sequence, and has update efficiency of $u_{wc}$ if a single bit of the raw file can be updated by modifying at most $u_{wc}$ bits of the compressed sequence. This article provides an entropy-achieving compression scheme for memoryless sources that simultaneously achieves $ O(\log\log n) $ local decoding and update efficiency. Key to this achievability result is a novel succinct data structure for sparse sequences which allows efficient local decoding and local update. Under general assumptions on the local decoder and update algorithms, a converse result shows that $d_{wc}$ and $u_{wc}$ must grow as $ Ω(\log\log n) $.
