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

S. Song , S. Lin , K. Abdel-Ghaffar , Z. Ding , W.H. Fong , Marc Fossorier (1)

1 ICI

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.

S. Song, S. Lin, K. Abdel-Ghaffar, Z. Ding, W.H. Fong, et al.. Burst Decoding of Cyclic Codes Based on Circulant Parity-Check Matrices. IEEE Transactions on Information Theory, 2010, 56 (3), pp.1038 - 1047. ⟨10.1109/TIT.2009.2039043⟩. ⟨hal-00865902⟩