Abstract
This chapter provides a brief introduction to the Fundamental Problem of Communication, as formulated by Shannon, and evolved over the years into various generalities, including the authors’ views on Duality of a Source to a Channel. Suggestions for further research are described, with emphasis on the importance of this duality in nonanticipative or real-time information transmission in both communication and communication for control, of delay-sensitive applications.
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Shannon CE (1948) A mathematical theory of communication. Bell Sys Tech J 27:379–423, 1948.
Berger T (1971) Rate Distortion Theory: a mathematical basis for data compression. Prentice-Hall, Englewood Cliffs
Shannon CE (1959) Coding theorems for a discrete source with a fidelity criterion. IRE Nat Conv Rec 4:142–163
Richardson T, Urbanke R (2008) Modern coding theory. Cambridge University Press, Cambridge
Marko H (1973) The bidirectional communication theory-A generalization of information theory. IEEE Trans Commun 21(12):1345–1351
Csiszár I, Körner J (1981) Information theory: coding theorems for discrete memoryless systems. Academic Press, Waltham
Gallager RG (1968) Information theory and reliable communication. Wiley, New York
Cover TM, Thomas JA (1991) Elements of information theory. Wiley-Interscience, New York
Gray RM (1990) Entropy and information theory. Springer, Berlin
Han TS (2003) Information-spectrum methods in information theory. Springer, Berlin
Gamal AE, Kim YH (2011) Network information theory. Cambridge University Press, Cambridge
Ihara S (1993) Information theory for continuous systems. World-Scientific, Singapore
Massey JL (1990) Causality, feedback and directed information. In: International symposium on information theory and its applications (ISITA). Nov 27–30:303–305
Kramer G (1998) Directed information for channels with feedback. Ph.D thesis, Swiss Federal Institute of Technology, Zurich, Switzerland
Tatikonda S (2000) Control under communication constraints. Ph.D thesis, Massachusetts Institute of Technology (MIT), MA, USA
Chen J, Berger T (2005) The capacity of finite-state channels with feedback. IEEE Trans Inf Theory 51(3):780–798
Tatikonda S, Mitter S (2009) The capacity of channels with feedback. IEEE Trans Inf Theory 55(1):323–349
Permuter HH, Weissman T, Goldsmith A (2009) Finite state channels with time-invariant deterministic feedback. IEEE Trans Inf Theory 55(2):644–662
Kramer G (2008) Topics in multi-user information theory. Found Trends Inf Theory 4(4–5):265–444
Cover TM, Pombra S (1989) Gaussian feedback capacity. IEEE Trans Inf Theory 35(1):37–43
Neuhoff DL, Gilbert R (1982) Causal source codes. IEEE Trans Inf Theory 28(5):701–713
Berger T (2003) Shannon lecture: living information theory. IEEE Inf Theory Soc Newslett 53(1)
Gastpar M, Rimoldi B, Vetterli M (2003) To code or not to code: lossy source-channel communication revisited. IEEE Trans Inf Theory 49(5):1147–1158
Wong W, Brockett R (1997) Systems with finite communication bandwidth constraints I: state estimation problems. IEEE Trans Autom Control 42(9):1294–1299
Nair GN, Evans RJ, Mareels IMY, Moran W (2004) Topological feedback entropy and nonlinear stabilization. IEEE Trans Autom Control 49(9):1585–1597
Gorbunov AK, Pinsker MS (1973) Nonanticipatory and prognostic epsilon entropies and message generation rates. Probl Inf Transm 9(3):184–191
Acknowledgments
The authors are grateful to Jan H. van Schuppen for stimulating discussions and technical suggestions, during the preparation of this manuscript and throughout the years.
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Charalambous, C.D., Kourtellaris, C.K., Stavrou, P.A. (2015). On Shannon’s Duality of a Source and a Channel and Nonanticipative Communication and Communication for Control. In: van Schuppen, J., Villa, T. (eds) Coordination Control of Distributed Systems. Lecture Notes in Control and Information Sciences, vol 456. Springer, Cham. https://doi.org/10.1007/978-3-319-10407-2_35
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DOI: https://doi.org/10.1007/978-3-319-10407-2_35
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