On the redundancy of binary Huffman codes (Corresp.)

Some properties of Huffman codes are presented. It is shown that knowing the probability
P_{1}
of the most likely source letter, there exist new lower and upper bounds on the redundancy of the Huffman code which are tighter for
P_{1} \geq 0.4
than those given by Shannon's first theorem or by the more recent results of Gallager. It is also shown that the new bounds are the tightest possible for
P_{1} \geq 0.4
when it is supposed that PI is the only known probability.