Improved upper bound for the redundancy of fix-free codes

A variable-length code is a fix-free code if no codeword is a prefix or a suffix of any other codeword. In a fix-free code, any finite sequence of codewords can be decoded in both directions, which can improve the robustness to channel noise and speed up the decoding process. In this paper, we prove a new sufficient condition of the existence of fix-free codes and improve the upper bound on the redundancy of optimal fix-free codes.