Sufficient conditions for existence of binary fix-free codes

Two sufficient conditions are given for the existence of binary fix-free codes (i.e., both prefix-free and suffix-free). Let L be a finite multiset of positive integers whose Kraft sum is at most 3/4. 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 smallest integer 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. ii) No integer in L, except possibly the largest one, occurs more than twice. The results move closer to the Ahlswede-Balkenhol-Khachatrian conjecture that Kraft sums of at most 3/4 suffice for the existence of fix-free codes.

[1]  John D. Villasenor,et al.  On design of error-correcting reversible variable length codes , 2002, IEEE Communications Letters.

[2]  Y. Sergey.  Sufficient conditions of existence of fix-free codes , 2001, Proceedings. 2001 IEEE International Symposium on Information Theory (IEEE Cat. No.01CH37252).

[3]  J. L. H. Webb,et al.  Efficient table access for reversible variable-length decoding , 2001, IEEE Trans. Circuits Syst. Video Technol..

[4]  Shmuel Tomi Klein,et al.  Bidirectional Huffman Coding , 1990, Comput. J..

[5]  John D. Villasenor,et al.  An algorithm for construction of efficient fix-free codes , 2003, IEEE Communications Letters.

[6]  Susanna Kaiser,et al.  . Soft source decoding with applications , 2001, IEEE Trans. Circuits Syst. Video Technol..

[7]  Umberto Eco,et al.  Theory of Codes , 1976 .

[8]  John D. Villasenor,et al.  Reversible variable length codes for efficient and robust image and video coding , 1998, Proceedings DCC '98 Data Compression Conference (Cat. No.98TB100225).

[9]  M. Wada,et al.  Reversible variable length codes , 1995, IEEE Trans. Commun..

[10]  Bernd Girod.  Bidirectionally decodable streams of prefix code-words , 1999, IEEE Communications Letters.

[11]  Rudolf Ahlswede,et al.  Some properties of fix-free codes , 1996 .

[12]  John D. Villasenor,et al.  A class of reversible variable length codes for robust image and video coding , 1997, Proceedings of International Conference on Image Processing.

[13]  Raymond W. Yeung,et al.  Some basic properties of fix-free codes , 2001, IEEE Trans. Inf. Theory.

[14]  Ja-Ling Wu,et al.  Modified symmetrical reversible variable-length code and its theoretical bounds , 2001, IEEE Trans. Inf. Theory.

[15]  E. F. Moore,et al.  Variable-length binary encodings , 1959 .

[16]  Guo-Fang Tu,et al.  Robust H.263+ video transmission using partial backward decodable bit stream (PBDBS) , 2003, IEEE Trans. Circuits Syst. Video Technol..

[17]  Ja-Ling Wu,et al.  On constructing the Huffman-code-based reversible variable-length codes , 2001, IEEE Trans. Commun..

[18]  Ja-Ling Wu,et al.  A hybrid and flexible H.263-based error resilient and testing system , 2001, Proceedings of IEEE Region 10 International Conference on Electrical and Electronic Technology. TENCON 2001 (Cat. No.01CH37239).

[19]  M. Schützenberger.  On a special class of recurrent events , 1961 .

[20]  Sergey Yekhanin.  Improved upper bound for the redundancy of fix-free codes , 2004, IEEE Transactions on Information Theory.

[21]  Thomas M. Cover,et al.  Elements of Information Theory , 2005 .

[22]  Leon Gordon Kraft,et al.  A device for quantizing, grouping, and coding amplitude-modulated pulses , 1949 .

[23]  Ronald L. Rivest,et al.  Complete variable-length “fix-free” codes , 1995, Des. Codes Cryptogr..

[24]  Susanna Kaiser,et al.  Soft decoding of variable-length codes , 2000, 2000 IEEE International Conference on Communications. ICC 2000. Global Convergence Through Communications. Conference Record.

[25]  Joachim Hagenauer,et al.  Iterative source/channel-decoding using reversible variable length codes , 2000, Proceedings DCC 2000. Data Compression Conference.