On the loss of single-letter characterization: The dirty multiple access channel

Tal Philosof*, Ram Zamir

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


For general memoryless systems, the existing information-theoretic solutions have a "single-letter" form. This reflects the fact that optimum performance can be approached by a random code (or a random binning scheme), generated using independent and identically distributed copies of some scalar distribution. Is that the form of the solution of any (information-theoretic) problem? In fact, some counter examples are known. The most famous one is the "two help one" problem: Körner and Marton showed that if we want to decode the modulo-two sum of two correlated binary sources from their independent encodings, then linear coding is better than random coding. In this paper we provide another counter example, the "doubly-dirty" multiple-access channel (MAC). Like the Körner-Marton problem, this is a multiterminal scenario where side information is distributed among several terminals; each transmitter knows part of the channel interference while the receiver only observes the channel output. We give an explicit solution for the capacity region of the binary doubly-dirty MAC, demonstrate how this region can be approached using a linear coding scheme, and prove that the "best known single-letter region" is strictly contained in it. We also state a conjecture regarding the capacity loss of single-letter characterization in the Gaussian case.

Original languageEnglish
Pages (from-to)2442-2454
Number of pages13
JournalIEEE Transactions on Information Theory
Issue number6
StatePublished - 2009


  • Dirty paper coding
  • Körner-Marton problem
  • Lattice strategies
  • Linear/lattice binning
  • Multiuser information theory
  • Random binning


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