TY - GEN

T1 - Universal a posteriori metrics game

AU - Abbe, Emmanuel

AU - Pulikkoonattu, Rethnakaran

PY - 2010

Y1 - 2010

N2 - Over binary input channels, the uniform distribution is a universal prior, in the sense that it maximizes the worst case mutual information of all binary input channels and achieves at least 94.2% of the capacity. In this paper, we address a similar question. We look for the best collection of finitely many a posteriori metrics, to maximize the worst case mismatched mutual information achieved by decoding with these metrics (instead of an optimal decoder such as the Maximum Likelihood (ML) tuned to the true channel). It is shown that for binary input and output channels, two metrics suffice to actually achieve the same performance as an optimal decoder. In particular, this implies that there exist a decoder which is generalized linear and achieves at least 94.2% of the compound capacity on any compound set, without knowledge of the underlying set.

AB - Over binary input channels, the uniform distribution is a universal prior, in the sense that it maximizes the worst case mutual information of all binary input channels and achieves at least 94.2% of the capacity. In this paper, we address a similar question. We look for the best collection of finitely many a posteriori metrics, to maximize the worst case mismatched mutual information achieved by decoding with these metrics (instead of an optimal decoder such as the Maximum Likelihood (ML) tuned to the true channel). It is shown that for binary input and output channels, two metrics suffice to actually achieve the same performance as an optimal decoder. In particular, this implies that there exist a decoder which is generalized linear and achieves at least 94.2% of the compound capacity on any compound set, without knowledge of the underlying set.

UR - http://www.scopus.com/inward/record.url?scp=80051949903&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=80051949903&partnerID=8YFLogxK

U2 - 10.1109/CIG.2010.5592854

DO - 10.1109/CIG.2010.5592854

M3 - Conference contribution

AN - SCOPUS:80051949903

SN - 9781424482641

T3 - 2010 IEEE Information Theory Workshop, ITW 2010 - Proceedings

BT - 2010 IEEE Information Theory Workshop, ITW 2010 - Proceedings

T2 - 2010 IEEE Information Theory Workshop, ITW 2010

Y2 - 30 August 2010 through 3 September 2010

ER -