Renyi's Entropy and the Probability of Error

The basic properties of Renyi's entropy are reviewed, and its concavity properties are characterized. New bounds (referred to as Iα bounds) on the probability of error are derived from Renyi's entropy and are compared with known bounds. It is proved that for the two-class case, the I2 bound is sharper than many of the previously known bounds. The difference between the I2 bound and the real value of the probability of error is at most 0.09. © 1978 IEEE