Simple proof of the concavity of the entropy power with respect to added Gaussian noise

A very simple proof of M.H. Costa´s result (see ibid., vol.IT-31, p.751-60, 1985) that the entropy power of X_t=X +N(O,tI) is concave in t, is derived as an immediate consequence of an inequality concerning Fisher information. This relationship between Fisher information and entropy is found to be useful for proving the central limit theorem. Thus, one who seeks new entropy inequalities should try first to find new equalities about Fisher information, or at least to exploit the existing ones in new ways