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 with finite alphabet, the redundancy of variable rate Slepian–Wolf coding of  with decoder only side information depends on both the block length and the decoding block error probability , and is defined as the difference between the minimum average compression rate of order variable rate Slepian–Wolf codes having the decoding block error probability less than or equal to , and the conditional entropy , where is the conditional entropy rate of the source given the side information. The redundancy of fixed rate Slepian–Wolf coding of with decoder only side information  is defined similarly and denoted by  . It is proved that under mild assumptions about and , where and are two constants completely determined by the joint distribution of the source-side information pair. Since is generally smaller than , our results show that variable rate Slepian–Wolf coding is indeed more efficient than fixed rate Slepian–Wolf coding.