Combinatorial Reasoning in Information Theory

Combinatorial techniques play a crucial role in the investigation of problems in Information Theory. We describe a few representative examples, focusing on the tools applied, and mentioning several open problems.

[1]  László Lovász,et al.  Kneser's Conjecture, Chromatic Number, and Homotopy , 1978, J. Comb. Theory A.

[2]  E. Capone Hide and Seek , 1991 .

[3]  Yitzhak Birk,et al.  Coding on demand by an informed source (ISCOD) for efficient broadcast of different supplemental data to caching clients , 2006, IEEE Transactions on Information Theory.

[4]  Claude E. Shannon,et al.  The zero error capacity of a noisy channel , 1956, IRE Trans. Inf. Theory.

[5]  Ziv Bar-Yossef,et al.  Index Coding With Side Information , 2011, IEEE Trans. Inf. Theory.

[6]  Ferenc Juhász,et al.  The asymptotic behaviour of lovász’ ϑ function for random graphs , 1982, Comb..

[7]  László Lovász,et al.  On the Shannon capacity of a graph , 1979, IEEE Trans. Inf. Theory.

[8]  Tom Bohman A limit theorem for the Shannon capacities of odd cycles. II , 2003 .

[9]  N. Alon,et al.  Repeated communication and Ramsey graphs , 1994, Proceedings of 1994 IEEE International Symposium on Information Theory.

[10]  H. S. WITSENHAUSEN,et al.  The zero-error side information problem and chromatic numbers (Corresp.) , 1976, IEEE Trans. Inf. Theory.

[11]  Femke Bekius,et al.  The Shannon Capacity of a Graph , 2011 .

[12]  Noga Alon,et al.  Multilinear polynomials and Frankl-Ray-Chaudhuri-Wilson type intersection theorems , 1991, J. Comb. Theory, Ser. A.

[13]  Noga Alon,et al.  The Probabilistic Method, Third Edition , 2008, Wiley-Interscience series in discrete mathematics and optimization.

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

[15]  Noga Alon,et al.  The Shannon Capacity of a Union , 1998, Comb..

[16]  Noga Alon,et al.  The Probabilistic Method , 2015, Fundamentals of Ramsey Theory.

[17]  Noga Alon,et al.  The Shannon capacity of a graph and the independence numbers of its powers , 2006, IEEE Transactions on Information Theory.

[18]  Uri Stav,et al.  Non-Linear Index Coding Outperforming the Linear Optimum , 2007, FOCS.

[19]  R. McEliece,et al.  Hide and Seek, Data Storage, and Entropy , 1971 .

[20]  Imre Csiszár,et al.  Information Theory - Coding Theorems for Discrete Memoryless Systems, Second Edition , 2011 .

[21]  Peter Frankl,et al.  Intersection theorems with geometric consequences , 1981, Comb..

[22]  Alon Orlitsky,et al.  Scalar versus vector quantization: Worst case analysis , 2002, IEEE Trans. Inf. Theory.

[23]  Robert J. McEliece,et al.  Ramsey bounds for graph products , 1971 .

[24]  Noga Alon,et al.  Broadcasting with Side Information , 2008, 2008 49th Annual IEEE Symposium on Foundations of Computer Science.

[25]  Joshua Evan Greene,et al.  A New Short Proof of Kneser's Conjecture , 2002, Am. Math. Mon..

[26]  Noga Alon,et al.  Privileged users in zero-error transmission over a noisy channel , 2007, Comb..

[27]  Miklós Simonovits,et al.  The coloring numbers of the direct product of two hypergraphs , 1974 .