On a relation between information inequalities and group theory
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2002
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Chan, T.H.L.
Yeung, R.
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IEEE Transactions on Information Theory, 2002; 48(7):1992-1995
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In this paper, 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 recently dis. covered by Zhang and Yeung, we obtain a new inequality in group theory whose meaning is yet to be understood.
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Copyright IEEE 2002