On the Redundancy of Slepian–Wolf Coding
On the Redundancy of Slepian–Wolf Coding
复制标题
关于Slepian-Wolf编码的冗余
DOI：
10.1109/tit.2009.2032803
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发表时间：
2009
影响因子：
2.5
通讯作者：
Jun Chen
中科院分区：
文献类型：
--
作者：
Dake He;L. A. Lastras;E. Yang;A. Jagmohan;Jun Chen
本文考虑了可变码率和固定码率Slepian-Wolf编码的冗余性。给定任何具有有限字母表的联合无记忆源侧信息对{（Xi，Yi）} <sub>i=1</sub><sup>infin</sup>，具有仅解码器侧信息Y1 n的X1 n的可变速率Slepian-Wolf编码的冗余<sup>Rn</sup>（isin <sub>n</sub>）<sub></sub><sup></sup><sub></sub><sup></sup>取决于块长度n和解码块错误概率isin n两者<sub></sub>，并且被定义为具有小于或等于isin n的解码块错误概率的n阶可变速率Slepian-Wolf码的最小平均压缩率<sub></sub>与条件熵H（X| Y），其中H（X| Y）是给定边信息的源的条件熵率。类似地定义了具有仅解码器侧信息<sub>Y1</sub><sup>n</sup><sub>的X1</sub><sup>n的</sup>固定速率Slepian-Wolf编码的冗余，并表示为<sup>RFn</sup>（isin<sub>n</sub>）。<sub></sub>证明了在关于isin<sub>n的</sub>适当假设下，<sup>Rn</sup>（isin<sub>n</sub>）=<sub>dvradic-log</sub> isin<sub>n</sub>/n +（oradic-log isin<sub>n</sub>/n）和<sup>RFn</sup>（isin<sub>n</sub>）-<sub>dfradic-log</sub>isin<sub>n</sub>/n + o（radic-log isin<sub>n</sub>/n），其中df和dnu是两个完全由源端信息对的联合分布决定的常数.<sub></sub>由于<sub>DV</sub>一般小于<sub>DF</sub>，我们的结果表明，可变速率Slepian-Wolf编码确实比固定速率Slepian-Wolf编码更有效。
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)}<sub>i=1</sub> <sup>infin</sup> with finite alphabet, the redundancy R<sup>n</sup>(isin<sub>n</sub>) of variable rate Slepian-Wolf coding of X<sub>1</sub> <sup>n</sup> with decoder only side information Y<sub>1</sub> <sup>n</sup> depends on both the block length n and the decoding block error probability isin<sub>n</sub>, 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<sub>n</sub>, 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 X<sub>1</sub> <sup>n</sup> with decoder only side information Y<sub>1</sub> <sup>n</sup> is defined similarly and denoted by R<sub>F</sub> <sup>n</sup>(isin<sub>n</sub>). It is proved that under mild assumptions about isin<sub>n</sub>, R<sup>n</sup>(isin<sub>n</sub>) = d<sub>v</sub>radic-log isin<sub>n</sub>/n + (oradic-log isin<sub>n</sub>/n) and R<sub>F</sub> <sup>n</sup>(isin<sub>n</sub>) - d<sub>f</sub>radic-log isin<sub>n</sub>/n + o(radic-log isin<sub>n</sub>/n), where df and dnu are two constants completely determined by the joint distribution of the source-side information pair. Since d<sub>v</sub> is generally smaller than d<sub>f</sub>, our results show that variable rate Slepian-Wolf coding is indeed more efficient than fixed rate Slepian-Wolf coding.