PAE cannot be made a basis for either a generalized statistical mechanics or a generalized information theory. Either statistical independence must be waived, or the expression of the averaged conditional probability as the difference between the marginal and joint entropies must be relinquished. The same inequality, relating the PAE to the Renyi entropy, when applied to the mean code length produces an expression that is without bound as the order of the code length approaches infinity. Since the mean code length associated with the Renyi entropy is finite and can be made to come as close to the Hartley entropy as desired in the same limit, the PAE have a more limited range of validity than the Renyi entropy which they approximate.
Information and coding discrimination of pseudo-additive entropies (PAE)
LAVENDA, Bernard Howard
2004-01-01
Abstract
PAE cannot be made a basis for either a generalized statistical mechanics or a generalized information theory. Either statistical independence must be waived, or the expression of the averaged conditional probability as the difference between the marginal and joint entropies must be relinquished. The same inequality, relating the PAE to the Renyi entropy, when applied to the mean code length produces an expression that is without bound as the order of the code length approaches infinity. Since the mean code length associated with the Renyi entropy is finite and can be made to come as close to the Hartley entropy as desired in the same limit, the PAE have a more limited range of validity than the Renyi entropy which they approximate.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
