On the construction of prefix-free and fix-free codes with specified codeword compositions

We investigate the construction of prefix-free and fix-free codes with specified codeword compositions. We present a polynomial time algorithm which constructs a fix-free code with the same codeword compositions as a given code for a special class of codes called distinct codes. We consider the construction of optimal fix-free codes which minimize the average codeword cost for general letter costs with uniform distribution of the codewords and present an approximation algorithm to find a near optimal fix-free code with a given constant cost.