TY - GEN

T1 - The rate loss of single letter characterization for the "dirty" multiple access channel

AU - Philosof, Tal

AU - Zamir, Ram

PY - 2008

Y1 - 2008

N2 - For general memoryless systems, the typical information theoretic solution, when exists, has 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 single-letter distribution. Is that the form of the solution of any (information theoretic) problem? In fact, some counter examples are known, perhaps the most famous being the Korner-Marton "two help one" problem, where the modulo-two sum of two binary sources is to be decoded from their independent encodings. In this paper we provide another counter example, the "doubly-dirty" multiple access channel (MAC). Like the Korner-Marton problem, this example is associated with a multiterminal scenario where side information is distributed among several terminals; each transmitter knows part of the channel interference but the receiver is not aware of any part of it. We give an explicit solution for the capacity region of a binary version of the doubly-dirty MAC, demonstrate how this capacity 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 a similar rate loss of single letter characterization in the Gaussian case.

AB - For general memoryless systems, the typical information theoretic solution, when exists, has 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 single-letter distribution. Is that the form of the solution of any (information theoretic) problem? In fact, some counter examples are known, perhaps the most famous being the Korner-Marton "two help one" problem, where the modulo-two sum of two binary sources is to be decoded from their independent encodings. In this paper we provide another counter example, the "doubly-dirty" multiple access channel (MAC). Like the Korner-Marton problem, this example is associated with a multiterminal scenario where side information is distributed among several terminals; each transmitter knows part of the channel interference but the receiver is not aware of any part of it. We give an explicit solution for the capacity region of a binary version of the doubly-dirty MAC, demonstrate how this capacity 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 a similar rate loss of single letter characterization in the Gaussian case.

UR - http://www.scopus.com/inward/record.url?scp=51849128316&partnerID=8YFLogxK

U2 - 10.1109/ITW.2008.4578616

DO - 10.1109/ITW.2008.4578616

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AN - SCOPUS:51849128316

SN - 9781424422708

T3 - 2008 IEEE Information Theory Workshop, ITW

SP - 31

EP - 35

BT - 2008 IEEE Information Theory Workshop, ITW

T2 - 2008 IEEE Information Theory Workshop, ITW

Y2 - 5 May 2008 through 9 May 2008

ER -