New bounds on the expected length of one-to-one codes

摘要

We provide new bounds on the expected length L of a binary one-to-one code for a discrete random variable X with entropy H. We prove that L/spl ges/H-log(H+1)-Hlog(1+1/H). This bound improves on previous results. Furthermore, we provide upper bounds on the expected length of the best code as function of H and the most likely source letter probability.