TY - JOUR

T1 - The uniform distribution as a universal prior

AU - Shulman, Nadav

AU - Feder, Meir

PY - 2004/6

Y1 - 2004/6

N2 - In this correspondence, we discuss the properties of the uniform prior as a universal prior, i.e., a prior that induces a mutual information that is simultaneously close to the capacity for all channels. We determine bounds on the amount of the mutual information loss in using the uniform prior instead of the capacity-achieving prior. Specifically, for the class of binary input channels with any output alphabet, we show that the Z-channel has the minimal mutual information with uniform prior, out of all channels with a given capacity. From this, we conclude that the degradation of the mutual information with respect to the capacity is at most 0.011 bit, and as was shown previously, at most 6%. A related result is that the capacity-achieving prior, for any channel, is not far from uniform. Some of these results are extended to channels with nonbinary input.

AB - In this correspondence, we discuss the properties of the uniform prior as a universal prior, i.e., a prior that induces a mutual information that is simultaneously close to the capacity for all channels. We determine bounds on the amount of the mutual information loss in using the uniform prior instead of the capacity-achieving prior. Specifically, for the class of binary input channels with any output alphabet, we show that the Z-channel has the minimal mutual information with uniform prior, out of all channels with a given capacity. From this, we conclude that the degradation of the mutual information with respect to the capacity is at most 0.011 bit, and as was shown previously, at most 6%. A related result is that the capacity-achieving prior, for any channel, is not far from uniform. Some of these results are extended to channels with nonbinary input.

KW - Uniform distribution

KW - Universal prior

KW - Z-channel

UR - http://www.scopus.com/inward/record.url?scp=2942655233&partnerID=8YFLogxK

U2 - 10.1109/TIT.2004.828152

DO - 10.1109/TIT.2004.828152

M3 - מזכר

AN - SCOPUS:2942655233

VL - 50

SP - 1356

EP - 1362

JO - IEEE Transactions on Information Theory

JF - IEEE Transactions on Information Theory

SN - 0018-9448

IS - 6

ER -