The Redundancy of an Optimal Binary Fix-Free Code Is Not Greater Than 1 bit


Within the context of fix-free codes, the foremost important and immediate consequence of the 3/4-conjecture (if it's proven), is that the redundancy of an optimal binary fix-free code never exceeds one bit, like the optimal prefix-free codes, i.e. Huffman codes. During this paper, this certain on the redundancy is proven while not requiring the conjecture to be true. To try to to thus, we use two known sufficient conditions for the existence of binary fix-free codes to derive an improved higher sure on the redundancy of an optimal fix-free code in terms of the most important symbol likelihood.

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