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

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 the maximum of d wc and u wc must grow as Ω(log log n).