A simple technique for bounding the redundancy of source coding with side information

Abstract

A simple technique for bounding the redundancy of Slepian-Wolf coding is given. We demonstrate that our simple technique gives the tight bound established by He et al. Our proof is so simple that it can be easily extended to the case where the source (X <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n</sup> , Y <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n</sup> ) has an n-fold product distribution (i.e., (X <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> , Y <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> ), ..., (X <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n</sub> , Y <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n</sub> ) are independent but not necessarily identically distributed). It can be also applied to Wyner-Ahlswede-Körner coding and gives novel bounds of the redundancies of the coding rates of the encoder and the helper.