Binary Burst Error Correcting Cyclic Codes Designed with the Circulant Parity Check Matrix

The letter presents binary cyclic codes with the maximum burst error correction capability. This is achieved based on the properties of circulant parity check matrix. Results conclude existence of codes with high minimum weight and rate greater than 0.28. It also gives cyclic product codes suitable for multiple burst and random error corrections.

[1]  Zhi Ding,et al.  Burst Decoding of Cyclic Codes Based on Circulant Parity-Check Matrices , 2010, IEEE Transactions on Information Theory.

[2]  E. J. Weldon,et al.  Cyclic product codes , 1965, IEEE Trans. Inf. Theory.

[3]  Khaled A. S. Abdel-Ghaffar,et al.  On the existence of optimum cyclic burst-correcting codes , 1986, IEEE Trans. Inf. Theory.

[4]  L. Javier García-Villalba,et al.  Efficient Shortened Cyclic Codes Correcting Either Random Errors or Bursts , 2011, IEEE Communications Letters.

[5]  Marc André Armand,et al.  Interleaved LDPC codes, reduced-complexity inner decoder and an iterative decoder for the Davey-MacKay construction , 2011, 2011 IEEE International Symposium on Information Theory Proceedings.

[6]  Shu Lin,et al.  Error control coding : fundamentals and applications , 1983 .

[8]  James L. Massey,et al.  Determining the burst-correcting limit of cyclic codes , 1980, IEEE Trans. Inf. Theory.

[9]  Stafford E. Tavares,et al.  Detecting and correcting multiple bursts for binary cyclic codes (Corresp.) , 1970, IEEE Trans. Inf. Theory.

[10]  Qin Huang,et al.  Quasi-cyclic LDPC codes: an algebraic construction , 2010, IEEE Transactions on Communications.

[11]  Dan Raphaeli,et al.  The burst error correcting capabilities of a simple array code , 2005, IEEE Transactions on Information Theory.

[12]  L. Javier García-Villalba,et al.  Use of Gray codes for optimizing the search of (shortened) cyclic single burst-correcting codes , 2011, 2011 IEEE International Symposium on Information Theory Proceedings.