Quaternary Unequal Error Protection Codes

We consider codes that offer unequal error protection to different information symbols, as measured by the so-called separation vector (a generalisation of the minimum Hamming distance). We determine the parameters of all optimal linear quaternary codes of length at most eleven.

[1]  Robert H. Morelos-Zaragoza,et al.  The Art of Error Correcting Coding: Morelos-Zaragoza/The Art of Error Correcting Coding, Second Edition , 2006 .

[2]  Y. Edel,et al.  New Codes via the Lengthening of BCH Codes with UEP Codes , 1999 .

[3]  Wil J. van Gils.  Linear unequal error protection codes from shorter codes , 1984, IEEE Trans. Inf. Theory.

[4]  Rolf Johannesson,et al.  Unequal error protection for convolutional codes , 2006, IEEE Transactions on Information Theory.

[5]  I. M. Boyarinov,et al.  Linear unequal error protection codes , 1981, IEEE Trans. Inf. Theory.

[6]  Willis C. Gore,et al.  A class of cyclic unequal error protection codes (Corresp.) , 1972, IEEE Trans. Inf. Theory.

[7]  Jack K. Wolf,et al.  On linear unequal error protection codes , 1967, IEEE Trans. Inf. Theory.

[8]  Larry A. Dunning,et al.  Optimal Encodings of Linear Block Codes for Unequal Error Protection , 1978, Inf. Control..

[9]  Werner Henkel,et al.  Unequal error protection multilevel codes and hierarchical modulation for multimedia transmission , 2008, 2008 IEEE International Symposium on Information Theory.

[10]  Simon Litsyn,et al.  Improved upper bounds for codes with unequal error protection , 2005, ISIT.

[11]  Shu Lin,et al.  On primitive BCH codes with unequal error protection capabilities , 1995, IEEE Trans. Inf. Theory.

[12]  L. M. H. E. Driessen.  On an infinite series of [4n, 2n] binary codes , 1984, IEEE Trans. Inf. Theory.

[13]  Shu Lin,et al.  On a class of optimal nonbinary linear unequal-error-protection codes for two sets of messages , 1994, IEEE Trans. Inf. Theory.

[14]  Shu Lin,et al.  Computer search for binary cyclic UEP codes of odd length up to 65 , 1990, IEEE Trans. Inf. Theory.

[15]  David M. Mandelbaum.  Unequal error protection codes derived from difference sets (Corresp.) , 1972, IEEE Trans. Inf. Theory.

[16]  F. MacWilliams,et al.  The Theory of Error-Correcting Codes , 1977 .

[17]  Nazanin Rahnavard,et al.  Nonuniform error correction using low-density parity-check codes , 2005, IEEE Transactions on Information Theory.

[18]  R. Morelos-Zaragoza.  The art of error correcting coding , 2002 .

[19]  R. Hill,et al.  Optimal linear codes over GF(4) , 1994, Discret. Math..

[20]  Henning Stichtenoth,et al.  Constructing linear unequal error protection codes from algebraic curves , 2003, IEEE Trans. Inf. Theory.

[21]  Larry A. Dunning.  Encoding and decoding for the minimization of message symbol error rates in linear block codes , 1987, IEEE Trans. Inf. Theory.

[22]  Eva K. Englund.  Nonlinear unequal error-protection codes are sometimes better than linear ones , 1991, IEEE Trans. Inf. Theory.

[23]  Hideki Imai,et al.  Multilevel coded modulation for unequal error protection and multistage decoding .I. Symmetric constellations , 2000, IEEE Trans. Commun..

[24]  Wil J. van Gils,et al.  Two topics on linear unequal error protection codes: Bounds on their length and cyclic code classes , 1983, IEEE Trans. Inf. Theory.