TY - JOUR

T1 - On the loss of single-letter characterization

T2 - The dirty multiple access channel

AU - Philosof, Tal

AU - Zamir, Ram

N1 - Funding Information:
Manuscript received March 14, 2008; revised February 23, 2009. Current version published May 20, 2009. The work of R. Zamir was supported in part by BSF under Grant 2004398. The material in this paper was presented in part at Information Theory Workshop, Porto, Portugal, May 2008. The authors are with the Department of Electrical Engineering–Systems, Tel-Aviv University, Ramat-Aviv 699978, Tel-Aviv, Israel. Communicated by H. Yamamoto, Associate Editor for Shannon Theory. Digital Object Identifier 10.1109/TIT.2009.2018174

PY - 2009

Y1 - 2009

N2 - 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.

AB - 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.

KW - Dirty paper coding

KW - Körner-Marton problem

KW - Lattice strategies

KW - Linear/lattice binning

KW - Multiuser information theory

KW - Random binning

UR - http://www.scopus.com/inward/record.url?scp=66949135426&partnerID=8YFLogxK

U2 - 10.1109/TIT.2009.2018174

DO - 10.1109/TIT.2009.2018174

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AN - SCOPUS:66949135426

SN - 0018-9448

VL - 55

SP - 2442

EP - 2454

JO - IEEE Transactions on Information Theory

JF - IEEE Transactions on Information Theory

IS - 6

ER -