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For general memoryless systems, the typical information theoretic solution -when exists - has a "single-letter" form. This reflects the fact that optimumperformance can be approached by a random code (or a random binning scheme),generated using independent and identically distributed copies of somesingle-letter distribution. Is that the form of the solution of any(information theoretic) problem? In fact, some counter examples are known. Themost famous is the "two help one" problem: Korner and Marton showed that if wewant to decode the modulo-two sum of two binary sources from their independentencodings, then linear coding is better than random coding. In this paper weprovide another counter example, the "doubly-dirty" multiple access channel(MAC). Like the Korner-Marton problem, this is a multi-terminal scenario whereside information is distributed among several terminals; each transmitter knowspart of the channel interference but the receiver is not aware of any part ofit. We give an explicit solution for the capacity region of a binary version ofthe doubly-dirty MAC, demonstrate how the capacity region can be approachedusing a linear coding scheme, and prove that the "best known single-letterregion" is strictly contained in it. We also state a conjecture regarding asimilar rate loss of single letter characterization in the Gaussian case.

The Rate Loss of Single-Letter Characterization: The "Dirty" Multiple Access Channel