Secret Sharing and Non-Shannon Information Inequalities
TCC '09 Proceedings of the 6th Theory of Cryptography Conference on Theory of Cryptography
Violating the Ingleton inequality with finite groups
Allerton'09 Proceedings of the 47th annual Allerton conference on Communication, control, and computing
Kolmogorov complexity as a language
CSR'11 Proceedings of the 6th international conference on Computer science: theory and applications
| Hi-index | 754.84 |
We establish a one-to-one correspondence between information inequalities and group inequalities. The major implication of our result is that we can prove information inequalities by proving the corresponding group inequalities, and vice versa. By giving a group-theoretic proof for all Shannon-type inequalities, we suggest that new inequalities could be discovered by making use of the rich set of tools in group theory. On the other hand, via a non-Shannon-type information inequality discovered by Zhang and Yeung (1997), we obtain a new inequality in group theory whose meaning is yet to be understood