Source Coding
O.1.5
Lecture
Data Compression

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

Shashank Vatedka, Venkat Chandar, Aslan Tchamkerten

Date & Time

01:00 am – 01:00 am

Abstract

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 we can recover any bit of the raw file 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 decode and update algorithms, a converse result shows that the maximum of $ d_{wc} $ and $ u_{wc} $ must grow as $ \Omega(\log\log n) $.


Presenters

Shashank Vatedka

Indian Institute of Technology, Hyderabad

Aslan Tchamkerten

Telecom Paris
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Session Chair

Marcelo Weinberger

Center for Science of Information