Abstract
This is a literal copy of a manuscript from 1974. References have been updated. It contains a critical discussion of in those days recent concepts of “common information” and suggests also alternative definitions. (Compare pages 402–405 in the book by I. Csiszár, J. Körner “Information Theory: Coding Theorems for Discrete Memoryless Systems”, Akademiai Kiado, Budapest 1981.) One of our definitions gave rise to the now well–known source coding problem for two helpers (formulated in 2.) on page 7).
More importantly, an extension of one concept to “common information with list knowledge” has recently (R. Ahlswede and V. Balakirsky “Identification under Random Processes” invited paper in honor of Mark Pinsker, Sept. 1995) turned out to play a key role in analyzing the contribution of a correlated source to the identification capacity of a channel.
Thus the old ideas have led now to concepts of operational significance and therefore are made accessible here.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Gács, P., K”orner, J.: Common information is far less than mutual information. Problems of Contr. and Inf. Th. 2, 149–162 (1973)
Witsenhausen, H.S.: On sequences of pairs of dependent random variables. SIAM J. of Appl. Math. 28, 100–113 (1975)
Gray, R.M., Wyner, A.D.: Source coding for a simple network. Bell System. Techn. J. (December 1974)
Wyner, A.D.: The common information of two dependent random variables. IEEE Trans. Inform. Theory IT–21, 163–179 (1975)
Ahlswede, R., K”orner, J.: Source coding with side information and a converse for degraded broadcast channels. IEEE Trans. on Inf. Th. IT–21(6), 629–637 (1975)
Slepian, D., Wolf, J.K.: Noiseless coding for correlated information sources. IEEE Trans. on Inf. Th. IT–19, 471–480 (1973)
Ahlswede, R., K”orner, J.: On the connection between the entropies of input and output distributions of discrete memoryless channels. In: Proceedings of the 5th Conference on Probability Theory, Brasov (1974): Editura Academeiei Rep. Soc. Romania, Bucaresti, pp. 13–23 (1977)
Ahlswede, R.: Multi–way communication channels. In: Proc. 2nd Int. Symp. Inf. Th., Tsahkadsor, Armenian S.S.R, pp. 23–52 (1971); Publishing House of the Hungarian Academy of Sciences (1973)
Gallager, R.G.: Information Theory and Reliable Communication. Wiley and Sons, New York (1968)
Wyner, A.D.: On source coding sith side information at the decoder. IEEE Trans. on Inf. Th. IT–21(3) (May 1975)
Ahlswede, R., Gács, P., K”orner, J.: Bounds on conditional probabilities with applications in multi–user communication. Zeitschr. f”ur Wahrscheinlichkeitstheorie und verw. Gebiete 34, 157–177 (1976)
Ahlswede, R., Gács, P.: Spreading of sets in product spaces and hypercontraction of the Markov operator. Ann. of Probability 4(6), 925–939 (1976)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2006 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Ahlswede, R., Körner, J. (2006). Appendix: On Common Information and Related Characteristics of Correlated Information Sources. In: Ahlswede, R., et al. General Theory of Information Transfer and Combinatorics. Lecture Notes in Computer Science, vol 4123. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11889342_41
Download citation
DOI: https://doi.org/10.1007/11889342_41
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-46244-6
Online ISBN: 978-3-540-46245-3
eBook Packages: Computer ScienceComputer Science (R0)