General description
The point to point communication problem, through a noisy channel using error correcting codes, can be formulated as the study of a random spin system (or spin glass). An approach known as the replica method then allows to analyze the performance of the code ensemble. Although these calculations are far from rigorous they are very useful because they allow to guess solutions. Moreover in some special cases these solutions have been proven to be indeed the correct ones.

Goals
Very little work has been done along the above lines in multiuser settings. One goal would be to formulate the spin glass problems obtained for a few settings with a small number of users and apply the replica method (multi-access, broadcast, relay). One may then investigate if various rigorous methods at hand may help to prove the replica formulas. Another possibility is to extend recent rigorous results obtained for the capacity of the CDMA channel with binary inputs, in the limit of a large number of users.

References
H. Nishimori, Statistical Physics of Spin Glasses and Information Processing Oxford University Press (2001)

Prerequisites
One among these is sufficient: basic information theory or basic statistical mechanics.

Supervisor
Dr. Nicolas Macris, LTHC, office inr134, tel 693 8114, nicolas.macris@epfl.ch


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