Locally Decodable Slepian-Wolf Compression

This paper investigates the Slepian-Wolf distributed compression of two sources Xn and Yn with the additional property that any pair (Xi, Yi) should reliably be decoded by probing a small number d of compressed bits. We show that for certain source distributions, the error probability of any such local decoder is lower bounded by 2–O(d), in the worst case over index i, whenever one of the sources is compressed below its entropy. Unlike the single-source setup, it is thus impossible to simultaneously achieve constant local decodability d and vanishing local decoding error probability as n increases. We also provide a compression scheme with a local decoder that almost achieves the above lower bound.