To investigate the cost of replacing well-established prefix-free codes with fix-free codes in order to benefit from their desired properties , the redundancy of optimal binary fix-free codes is studied under two criteria ``maximum value " and ``average value" . In particular , it is proved that the redundancy of an optimal binary fix-free code never exceeds it . This shows that the performance of optimal binary fix-free codes in the worst case is identical to that of prefix-free codes . By the second criterion , the average redundancy of optimal fix-free codes over all sources with ymbols is examined . It is proved that the average redundancy of optimal fix-free codes is less than it when is sufficiently large . To do so , a suboptimal fix-free encoding scheme is proposed and employed for all sources . The interesting property of this encoding scheme is that , for almost all sources with ymbols , its redundancy is less than it for sufficiently large . By comparing this result with one for Huffman codes , it can be proved that the cost of employing optimal fix-free codes instead of optimal prefix-free codes is less than it for almost all memoryless sources with a large alphabet. key word : Huffman codes , fix-free codes, average distribution, redundancy, video compressin standard,kraft condition
