The memory center.

Abstract: As we know, the length of binary code of a point (with accuracy h >0) is approximately . We will consider the problem where we should translate the origin a of the coordinate system so that the mean amount of bits needed to code a randomly chosen element from a realization of a random variable X is minimal. In other words, we want to find such that attains minimum. We show that under reasonable assumptions the choice of a does not depend on h asymptotically. Consequently, we reduce the problem to finding the minimum of function where f is the density distribution of the random variable X. Moreover, we provide constructive approach for determining a. [Copyright &y& Elsevier]