For any memoryless source-side information pair (X, Y) with finite alphabet, it is well known that the smallest compression rate in bits per letter achievable in Slepian-Wolf coding, I.e., coding X with Y being available only to the decoder, is the conditional entropy H(X|Y). Though this rate is the same as the best rate achievable in traditional lossless source coding of X with Y being available to both the encoder and the decoder, it has been found recently that the redundancy R_n(ε_n) of Slepian-Wolf coding, which is defined as the minimum of the difference between the compression rate of any Slepian-Wolf code resulting from coding X_1~n with decoding error ε_n, and H(X|Y), is significantly worse than that of traditional source coding. In this paper, we investigate whether feedback from the decoder to the encoder can improve the compression efficiency of Slepian-Wolf coding. It turns out that the answer is affirmative. More specifically, it is shown that feedback reduces the redundancy of Slepian-Wolf coding significantly.
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