O(loglog n) Worst-Case Local Decoding and Update Efficiency for Data Compression
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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(loglog 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(loglog n).
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