Distribution of Code Lengths

An ideal variable length code shall adapt the code length of any symbol to the probability for its occurrence. A better graduation will offer a higher efficiency for data compression purposes.

The achievable quality primarily depends on the procedure used to create the code. Some procedures (like Huffman coding) offer a better result than other ones (like Shannon Fano codes).

Most of the coding schemes have limitted capabilities because their code length is restricted to multiples of 1 bit. This is the case for any code based on a binary code tree like Huffman or Shannon Fano codes.

An exception is the arithmetic code which is not restricted to binary limits. Any probability distribution can be realized in an ideal way. But, the arithmetic code cannot be regarded as a prefix code in a general sense and additionally its free usage is prohibited due to patents.