INFORMATIONTHEORETICAL RESULTS FOR THE DISCRETE MEMORYLESS MULTIPLE ACCESS CHANNEL
Ph.D. thesis, Frans M.J. Willems

Katholieke Universiteit Leuven, Faculteit der Wetenschappen, Departement Wiskunde

Proefschrift tot het verkrijgen van de graad van doctor in de wetenschappen door Frans M.J. Willems

Promotor: Prof.dr. E.C. van der Meulen

October 1982

SUMMARY - In this thesis we defined the MAC with cribbing encoders and the MAC with partially cooperating encoders. For these and other MAC configurations we determined the capacity region(s) or new achievable rate regions.
We introduced the use of non-random partitions, restricted decoding and backward decoding in achievability proofs which involve block Markov superposition encoding. Also the importance of Shannon strategies for multi-user achievability proofs is demonstrated.
We gave our achievability proofs in terms of epsilon-typical N-sequences. The first rigorous multi-user channel achievability proof based on epsilon-typicality was given by Cover [1975] for the broadcast channel. Our proofs involve similar methods. In fact Lemma 2 in Cover [1975] is implicitly used in all these proofs.
With the converse of paragraph 4 we obtained for a well known feedback configuration the capacity region. The new techniques in this converse are also used in other converses in this thesis.
Using lemma's based on Caratheodory's theorem we found cardinality bounds for the auxiliary random variables.
The methods in this thesis can be useful in proving coding theorems for multi-user communication situations. However for the as yet unsolved problem of determining the capacity region of the general d.m. MAC with feedback new techniques seem to be necessary. It is possible that instead of the codes in this thesis, coding strategies as in Shannon [1961], Ozarow [1979] or Schalkwijk [1982] should be used. Also it is not obvious at all that a single-letter characterization for this capacity region can be given.

SCANNED VERSION OF THE THESIS:

• Table of Contents
• General Preliminaries and Definitions
• The Slepian-Wolf Theorem for the Discrete Memoryless Multiple Access Channel with Correlated Sources Revisited
• The Feedback Capacity for a Class of Discrete Memoryless Multiple Access Channels. Also published in IEEE Trans. Inform. Theory, vol. IT-28, pp. 93-95, January 1982.
•  Partial Feedback for the Discrete Memoryless Multiple Access Channel. Also published in IEEE Trans. Inform. Theory, vol. IT-29, pp. 287-290, March 1983. Co-author E.C. van der Meulen.
• The Discrete Memoryless Multiple Access Channel with Cribbing Encoders. Also published in IEEE Trans. Inform. Theory, vol. IT-31, pp. 313-327, May 1985. Co-author E.C. van der Meulen. Transparencies of presentation at ISIT-1992 (6MB), Les Arcs, France. Lecture at MSRI's Workshop Mathematics of Relaying and Cooperation in Communication Networks, April 10-12, 2006, Berkeley, CA.
• Generalized Feedback for the Discrete Memoryless Multiple Access Channel. Also published in Proceedings 21st Annual Allerton Conference on Communication, Control, and Computing, Allerton House, Monticello, Illinois, pp. 284-292, October 5-7, 1983. Co-authors E.C. van der Meulen and J.P.M. Schalkwijk.
• The Discrete Memoryless Multiple Access Channel with Partially Cooperating Encoders. Also published in IEEE Trans. Inform. Theory, vol. IT-29, pp. 441-445, May 1983.
• General Remarks and Acknowledgement
• Appendices
• List of Symbols, Subject Index
• References

"The Multiple-Access Channel with Cribbing Encoders Revisited," Tutorial Lecture at MSRI's Workshop: Mathematics of Relaying and Cooperation in Communication Networks, April 10-12, 2006, Berkeley, CA.

ABSTRACT: We first discuss the capacity regions for various communication situations in which one or both encoders for a multiple-access channel crib from the other encoder and learn the channel input(s) (to be) emitted by this encoder. Most of the achievability proofs for cribbing encoders hinge upon the concept of backward decoding. Also the notion of Shannon strategies seems to be of crucial importance. After having reviewed these concepts we discuss a recent development related to cribbing encoders that corresponds to the relay-channel without delay.

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