R. Ahlswede and J. Korner. On common information and related characteristics of correlated information sources. Preprint. Presented at the 7th Prague Conference on Information Theory, 1974. Home/Search Document Details and Download
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Logical operations and Kolmogorov complexity II - Muchnik, Vereshchagin (Correct)
....the string b n is obtained in the same way from another binary variable j. As ; eta on may choose any dependent random variables such that the outcome of does not determine the outcome of j and vice versa. This is an easy corollary of a theorem on Shannon entropy proven by Ahlswede and Korner in [1]. Another effective proof of the existence of strings having large mutual information but having no common information was given in [7] In the latter paper it was also pointed out that the words a; b have no common information may be understood in a stronger sense. Let us present the relevant ....
....n ) 3n whose profile is equal to M min (all equalities are valid up to an additive O(log n) term) The proof of this theorem presented in the paper [7] is non effective and its authors wonder whether there is a quasi effective one. Note that the profile of neither of constructive examples from [1] and [7] is known. Quasi effective proof of theorem 4. The profile of a; b is equal to M min if the following holds. Any triple u; v; w such that u v 2, or u w 2, or u v w 3, or simultaneously u v 3; u w 3; u v w 4 does not belong to the profile of a; b. If at least one ....
R. Ahlswede and J. Korner. On common information and related characteristics of correlated information sources. Preprint. Presented at the 7th Prague Conference on Information Theory, 1974.
Identification under Random Processes - Ahlswede, Balakirsky (1996) Self-citation (Ahlswede) (Correct)
....(7.1) and (7.2) correspond to theorems 1 and 2. By the method of [2] the expressions give achievable second order identi cation rates. There is another remarkable connection. In case C = 0 formula (7. 2) gives for correlated sources the common information in the sense of [8] This was shown in [9]. Common randomness extends in this situation the notion of common information to the case where a channel of capacity C helps to extract a common part. By standard techniques it can actually be shown that (7.2) gives the optimal value (see [7] Detailed de nitions and proofs can be found in a ....
....of capacity C helps to extract a common part. By standard techniques it can actually be shown that (7.2) gives the optimal value (see [7] Detailed de nitions and proofs can be found in a subsequent paper [11] where also several other new models are introduced and analyzed. It has been argued in [9] that the concept of common information of [8] is likely the most meaningful among such notions. Now it is naturally incorporated in the theory of common randomness and thus has for instance operational signi cance in the theory of identi cation and cryptography. Notice also that it ranges between ....
R. Ahlswede and J. Korner, "On common information and related characteristics of correlated information sources", SFB Diskrete Strukturen in der Mathematik, Erganzungsreihe 95-003, Bielefeld 1995.
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