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In this correspondence 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 H ? log(H + 1) ? H log(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.doi:10.1109/18.481795 fatcat:eihrufhltnby3du5eezfqssprm