Efficient variable-length coding under an assigned maximum code-length constraint

Given a maximum allowable codeword length for a source S, an algorithm is developed to produce a set of optimal variable-length binary codes for the symbols in S. It is shown that no matter what the maximum size of the codewords is the algorithm always generates a set of optimal variable-length codes. And if no limit for the maximum code-length is specified the variable-length code becomes ultimately Huffman code. A maximum allowable codeword length is often necessary for data compression and transmission used in different applications. The limit for the codeword size might be necessary and essential because of the data-word size, the data buffers or even the data transmission rate. The ability to optimally control the length of the codewords provides a definite advantage over either a fixed code-length or a full variable-length code. Depending on particular applications and constraints, in the former case, one is able to choose the growth of the codewords that best suits the application and resources