An Implicit Characterization of the Achievable Rate Region for Acyclic Multisource Multisink Network Coding

The achievable information rate region problem of multisource multisink network coding for general acyclic networks with arbitrary transmission requirements has previously been studied, where inner and outer bounds on the region were derived in terms of <formula formulatype="inline"><tex Notation="TeX">$\Gamma^{\ast}$</tex> </formula>, the fundamental region of entropy functions. In this paper, we derive the exact characterization of the achievable rate region in terms of entropic functions, thus closing the gap between the existing inner and outer bounds.

[1]  Zhen Zhang,et al.  The Capacity Region for Multi-source Multi-sink Network Coding , 2007, 2007 IEEE International Symposium on Information Theory.

[2]  Rudolf Ahlswede,et al.  Network information flow , 2000, IEEE Trans. Inf. Theory.

[3]  Frantisek Matús,et al.  Infinitely Many Information Inequalities , 2007, 2007 IEEE International Symposium on Information Theory.

[4]  Milan Studený,et al.  Conditional Independences among Four Random Variables I , 1995, Combinatorics, Probability and Computing.

[5]  Zhen Zhang,et al.  Distributed Source Coding for Satellite Communications , 1999, IEEE Trans. Inf. Theory.

[6]  Randall Dougherty,et al.  Six New Non-Shannon Information Inequalities , 2006, 2006 IEEE International Symposium on Information Theory.

[7]  Frantisek Matús,et al.  Conditional Independences among Four Random Variables II , 1995, Combinatorics, Probability and Computing.

[8]  Raymond W. Yeung,et al.  A First Course in Information Theory , 2002 .

[9]  Raymond W. Yeung,et al.  On Information Divergence Measures and a Unified Typicality , 2006, IEEE Transactions on Information Theory.

[10]  Zhen Zhang,et al.  On Characterization of Entropy Function via Information Inequalities , 1998, IEEE Trans. Inf. Theory.

[11]  Raymond W. Yeung,et al.  Symmetrical multilevel diversity coding , 1997, IEEE Trans. Inf. Theory.

[12]  Raymond W. Yeung,et al.  Information Theory and Network Coding , 2008 .

[13]  Raymond W. Yeung,et al.  A framework for linear information inequalities , 1997, IEEE Trans. Inf. Theory.

[14]  Alex J. Grant,et al.  Entropy Vectors and Network Codes , 2007, 2007 IEEE International Symposium on Information Theory.

[15]  Zhen Zhang,et al.  A non-Shannon-type conditional inequality of information quantities , 1997, IEEE Trans. Inf. Theory.

[16]  Randall Dougherty,et al.  Networks, Matroids, and Non-Shannon Information Inequalities , 2007, IEEE Transactions on Information Theory.

[17]  Raymond W. Yeung,et al.  Multilevel diversity coding with distortion , 1995, IEEE Trans. Inf. Theory.

[18]  F. Matús,et al.  Two Constructions on Limits of Entropy Functions , 2007, IEEE Transactions on Information Theory.

[19]  Lihua Song,et al.  Zero-error network coding for acyclic network , 2003, IEEE Trans. Inf. Theory.