On the overall performance of the Uniform code

It is known that most n-tuple distributions have a large entropy around log n-0.61. In this paper, it is shown that more than 100n/n+1 percent of n-tuple distributions have entropy greater than log n-1.387. Consequently, for more than 100n/n+1 percent of memoryless information sources with n symbols, the redundancy of a fixed-length code (with code-length [log n]) is less than 2.387. This upper bound decreases to 1.620 for the Uniform code (i.e. the Huffman code for the uniform distribution). Therefore, both the Uniform code and the fixed-length code have good performance. This point can be regarded as another benefit of these codes besides their simplicity.