a variable-length code is a fix-free code if no codeword is a prefix or a s
uffix of any other codeword. This class of codes is applied to speed up the
decoding process, for the decoder can decode from both sides of the compre
ssed file simultaneously. In this paper, we study some basic properties of
fix-free codes. We prove a sufficient and a necessary condition for the exi
stence of fix-free codes, and we obtain some new upper bounds on the redund
ancy of optimal fix-free codes.