# Improved upper bound for the redundancy of fix-free codes

@article{Yekhanin2004ImprovedUB, title={Improved upper bound for the redundancy of fix-free codes}, author={Sergey Yekhanin}, journal={IEEE Transactions on Information Theory}, year={2004}, volume={50}, pages={2815-2818} }

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.

## Topics from this paper

## 18 Citations

Some notes on fix-free codes

- Computer Science2008 42nd Annual Conference on Information Sciences and Systems
- 2008

One lower and one upper bound on the redundancy of the optimal fix-free code are obtained and an upper bound is derived on the length of the most likely source symbol in terms of its probability is derived.

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

- Mathematics, Computer ScienceIEEE Transactions on Information Theory
- 2015

This paper uses two known sufficient conditions for the existence of binary fix-free codes to derive an improved upper bound on the redundancy of an optimal fix- free code in terms of the largest symbol probability.

Some Upper Bounds on the Redundancy of Optimal Binary Fix-Free Codes

- Mathematics, Computer ScienceIEEE Transactions on Information Theory
- 2012

Some upper bounds on the redundancy of the optimal fix-free codes and their difference with the corresponding Huffman codes are presented and a better Huffman-like code is examined.

On Optimal and Achievable Fix-Free Codes

- Mathematics, Computer ScienceIEEE Transactions on Information Theory
- 2012

A variation of the 3/4 conjecture for fix-free codes is introduced and a key idea in the first conjecture and the new one is a definition of how one sequence of nondecreasing natural numbers dominates another.

Weakly Symmetric Fix-Free Codes

- Computer ScienceIEEE Transactions on Information Theory
- 2014

Weakly symmetricfix-free codes can be regarded as an option by which one can to some extent achieve the low redundancy of asymmetric fix- free codes and the low-cost bidirectional decoding of symmetric fix -free codes, simultaneously.

On the Penalty of Optimal Fix-Free Codes

- Mathematics, Computer ScienceIEEE Transactions on Information Theory
- 2015

It is shown that the average penalty of asymmetric fix-free codes is less than 0.21 bit per symbol, and it is proved that when the source alphabet size is sufficiently large, for almost all sources, the penalty is more than or equal to 0.182bit per symbol.

Sufficient conditions for existence of binary fix-free codes

- Mathematics, Computer ScienceIEEE Transactions on Information Theory
- 2005

It is shown that there exists a fix-free code whose codeword lengths are the elements of L if either of the following two conditions holds: i) the smallestinteger in L is at least 2, and no integer in L, except possibly the largest one, occurs more than 2/sup min(L)-2/ times.

Some Tight Lower Bounds on the Redundancy of Optimal Binary Prefix-Free and Fix-Free Codes

- Computer Science, MathematicsIEEE Transactions on Information Theory
- 2020

It is proven that the tight lower bound in terms of the probability of the most likely symbol is the same for optimal prefix-free and optimal fix-free codes.

On the 3/4-Conjecture for Fix-Free Codes -- A Survey

- Computer Science, MathematicsArXiv
- 2007

Since any code has Kraftsum smaller than or equal to one, this answers the question for the second implication of Kraft-McMillan's theorem.

On the capability of the Harada-Kobayashi algorithm in finding fix-free codewords

- Mathematics2008 International Symposium on Information Theory and Its Applications
- 2008

The capability of the Harada-Kobayashi algorithm in finding fix-free codewords is examined. For n les 30, it is observed that this algorithm finds fix-free codewords for more than 99 percent of…

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