A Ziv-Zakai-Rényi lower bound on distortion at high resolution

We follow a method introduced by Ziv and Zakai for finding ´informational´ lower bounds on delay constrained joint source-channel coding. Their method uses the data processing theorem for generalized measures of information. We introduce the use of Renyi´s information of order alpha in their framework, and use high-resolution approximations to find its rate distortion function for a source that possesses a smooth distribution with rth-power distortion. This allows us to present two new lower bounds, one on the distortion in fixed rate vector quantization, and the other on the transmission through low-dimensional modulo-lattice additive noise channels.