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.
DepartmentLincoln 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
2015 IEEE International Symposium on Information Theory (ISIT)
Institute of Electrical and Electronics Engineers (IEEE)
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.
Author's final manuscript