Bounds on the Entropy Series

Upper bounds on the entropy of a countable integer-valued random variable are furnished in terms of the expectation of the logarithm function. In particular, an upper boundisderived that is sharper than that of Elias, H(P) ≤ EP(log) + 2(1 + √Ep(log)), for all values of Ep(log). Bounds that are better only for large values of Ep(log) than the previous known upper bounds are also provided. © 1988 IEEE