## Local recovery in data compression for general sources

##### Author(s)

Wornell, Gregory W; Mazumdar, Arya; Chandar, Venkat B
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Source coding is concerned with optimally compressing data, so that it can be reconstructed up to a specified distortion from its compressed representation. Usually, in fixed-length compression, a sequence of n symbols (from some alphabet) is encoded to a sequence of k symbols (bits). The decoder produces an estimate of the original sequence of n symbols from the encoded bits. The rate-distortion function characterizes the optimal possible rate of compression allowing a given distortion in reconstruction as n grows. This function depends on the source probability distribution. In a locally recoverable decoding, to reconstruct a single symbol, only a few compressed bits are accessed. In this paper we find the limits of local recovery for rates near the rate-distortion function. For a wide set of source distributions, we show that, it is possible to compress within ε of the rate-distortion function such the local recoverability grows as Ω(log(1/ε)); that is, in order to recover one source symbol, at least Ω(log(1/ε)) bits of the compressed symbols are queried. We also show order optimal impossibility results. Similar results are provided for lossless source coding as well.

##### Date issued

2015-10##### Department

Lincoln Laboratory; Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science; Massachusetts Institute of Technology. Department of Mathematics; Massachusetts Institute of Technology. Research Laboratory of Electronics##### Journal

2015 IEEE International Symposium on Information Theory (ISIT)

##### Publisher

Institute of Electrical and Electronics Engineers (IEEE)

##### Citation

Mazumdar, Arya, et al. "Local Recovery in Data Compression for General Sources." 2015 IEEE International Symposium on Information Theory (ISIT), 14-19 June 2015, Hong Kong, China, IEEE, 2015, pp. 2984–88.

Version: Author's final manuscript

##### ISBN

978-1-4673-7704-1