On the Redundancy of Slepian–Wolf Coding

In this paper, the redundancy of both variable and fixed rate Slepian-Wolf coding is considered. Given any jointly memoryless source-side information pair {(Xi, Yi)}_i=1 ^infin with finite alphabet, the redundancy Rⁿ(isin_n) of variable rate Slepian-Wolf coding of X₁ ⁿ with decoder only side information Y₁ ⁿ depends on both the block length n and the decoding block error probability isin_n, and is defined as the difference between the minimum average compression rate of order n variable rate Slepian-Wolf codes having the decoding block error probability less than or equal to isin_n, and the conditional entropy H(X|Y), where H(X|Y) is the conditional entropy rate of the source given the side information. The redundancy of fixed rate Slepian-Wolf coding of X₁ ⁿ with decoder only side information Y₁ ⁿ is defined similarly and denoted by R_F ⁿ(isin_n). It is proved that under mild assumptions about isin_n, Rⁿ(isin_n) = d_vradic-log isin_n/n + (oradic-log isin_n/n) and R_F ⁿ(isin_n) - d_fradic-log isin_n/n + o(radic-log isin_n/n), where df and dnu are two constants completely determined by the joint distribution of the source-side information pair. Since d_v is generally smaller than d_f, our results show that variable rate Slepian-Wolf coding is indeed more efficient than fixed rate Slepian-Wolf coding.