An Entropy Bound for Random Number Generation Sung-il Pae,

Many computer applications use random numbers as an important computational resource, and they often require random numbers of particular probability distributions. We consider a very general model of random number generation that converts a source that produces symbols according to a probability distribution into a random numbers of another probability distribution. In such a procedure, we are particularly interested in the average amount of source symbols to produce an output, which we call efficiency of the procedure. We discuss the entropy bound for the efficiency of random number generation, and as a main contribution, we give a new elementary proof for the entropy bound. Key words: Random number generation, Shannon entropy, information