An algebraic approach to network coding

We consider the problem of information flow in networks. In particular, we relate the question whether a set of desired connections can be accommodated in a network to the problem of finding a point on a variety defined over a suitable field. This approach lends itself to the derivation of a number of theorems concerning the feasibility of a communication scenario involving failures.

[1]  David A. Cox,et al.  Ideals, Varieties, and Algorithms: An Introduction to Computational Algebraic Geometry and Commutative Algebra, 3/e (Undergraduate Texts in Mathematics) , 2007 .

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

[3]  Abbas El Gamal,et al.  Capacity theorems for the relay channel , 1979, IEEE Trans. Inf. Theory.

[4]  Richard D. Gitlin,et al.  Diversity coding: using error control for self-healing in communication networks , 1990, Proceedings. IEEE INFOCOM '90: Ninth Annual Joint Conference of the IEEE Computer and Communications Societies@m_The Multiple Facets of Integration.

[5]  W. Fulton.  Algebraic curves , 1969 .

[6]  Dimitri P. Bertsekas,et al.  Network optimization : continuous and discrete models , 1998 .

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

[8]  E. Meulen,et al.  Three-terminal communication channels , 1971, Advances in Applied Probability.

[9]  R. Gallager,et al.  The Gaussian parallel relay network , 2000, 2000 IEEE International Symposium on Information Theory (Cat. No.00CH37060).

[10]  Thomas M. Cover,et al.  Comments on Broadcast Channels , 1998, IEEE Trans. Inf. Theory.

[11]  Rudolf Ahlswede,et al.  Multi-way communication channels , 1973 .

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

[13]  R. Yeung,et al.  Network information flow-multiple sources , 2001, Proceedings. 2001 IEEE International Symposium on Information Theory (IEEE Cat. No.01CH37252).

[14]  Shuo-Yen Robert Li,et al.  Linear network coding , 2003, IEEE Trans. Inf. Theory.

[15]  Peter Elias,et al.  A note on the maximum flow through a network , 1956, IRE Trans. Inf. Theory.

[16]  Jacob Wolfowitz,et al.  Multiple Access Channels , 1978 .