On capacity regions of non-multicast networks

We study the network coding capacity of multi-source, multi-sink networks with colocated sources, but where each sink may demand a different subset of the sources. We show that in this scenario, the set of admissible (zero probability of decoding errors) and achievable (vanishing probability of decoding errors) rate capacity tuples are the same. We also simplify the capacity region by showing that the outer bound obtained in “A First Course in Information Theory” (Yeung, 2002) is in fact tight. We conjecture that this bound remains tight, even when the sources are not colocated.

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

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

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

[4]  Randall Dougherty,et al.  Insufficiency of linear coding in network information flow , 2005, IEEE Transactions on Information Theory.

[5]  Alex J. Grant,et al.  Dualities Between Entropy Functions and Network Codes , 2008, IEEE Transactions on Information Theory.

[6]  Raymond W. Yeung,et al.  On a relation between information inequalities and group theory , 2002, IEEE Trans. Inf. Theory.

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

[8]  Ho-Leung Chan,et al.  A combinatorial approach to information inequalities , 1999, 1999 Information Theory and Networking Workshop (Cat. No.99EX371).