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Burst Decoding of Cyclic Codes Based on Circulant Parity-Check Matrices

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6 Author(s)
Shumei Song ; Dept. of Electr. & Comput. Eng., Univ. of California, Davis, CA, USA ; Shu Lin ; Abdel-Ghaffar, K. ; Zhi Ding
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An error-burst correcting algorithm is developed based on a circulant parity-check matrix of a cyclic code. The proposed algorithm is more efficient than error trapping if the code rate is less than about 2/3. It is shown that for any (n, k) cyclic code, there is an n × n circulant parity-check matrix such that the algorithm, applied to this matrix, corrects error bursts of lengths up to the error-burst correction limit of the cyclic code. This same matrix can be used to efficiently correct erasure bursts of lengths up to n - k. The error-burst correction capabilities of a class of cyclic low-density parity-check (LDPC) codes constructed from finite geometries are also considered.

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Information Theory, IEEE Transactions on  (Volume:56 ,  Issue: 3 )