arXiv 2001.086792020-01-23cs.ITcs.DSmath.IT

数据压缩的$O(\log \log n)$最坏情况局部解码和更新效率

$O(\log \log n)$ Worst-Case Local Decoding and Update Efficiency for Data Compression

Shashank Vatedka, Venkat Chandar, Aslan Tchamkerten

摘要：

本文讨论了局部译码和局部更新的数据压缩问题。如果通过探测压缩序列的至多$d_{wc}$位可以恢复原始文件的任何位，则压缩方案具有最坏情况的局部解码$d_{wc}$，并且如果通过修改压缩序列的至多$u_{wc}$位可以更新原始文件的单个位，则压缩方案具有$u_{wc}$的更新效率。本文提供了一种用于无记忆源的熵实现压缩方案，其同时实现$ O(\log\log n) $本地解码和更新效率。该可扩展性结果的关键是用于稀疏序列的新颖简洁的数据结构，其允许有效的局部解码和局部更新。在对局部解码器和更新算法的一般假设下，相反的结果表明$d_{wc}$和$u_{wc}$必须按$ Ω(\log\log n) $增长。

英文摘要：

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) $.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

摘要：

英文摘要：

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