On decoding (31, 16, 7) quadratic residue code up to its error correcting capacity with bit-error probability estimates

Tsung-Ching Lin; Pei-Yu Shih; Wen-Ku Su; Trieu-Kien Truong

doi:10.1117/12.861076

24 August 2010 On decoding (31, 16, 7) quadratic residue code up to its error correcting capacity with bit-error probability estimates

Tsung-Ching Lin, Pei-Yu Shih, Wen-Ku Su, Trieu-Kien Truong

Author Affiliations +

Proceedings Volume 7814, Free-Space Laser Communications X; 781415 (2010) https://doi.org/10.1117/12.861076
Event: SPIE Optical Engineering + Applications, 2010, San Diego, California, United States

Abstract

The quadratic residue codes are a class of the error correcting codes with interesting mathematics. Among them, the (31, 16, 7) quadratic residue code is the code with reducible generator polynomial and three-error-correcting capacity. The algebraic decoding algorithm for the (32, 16, 8) quadratic residue code is developed by Reed et al. (1990). In this paper, a simplified decoding algorithm is proposed. The algorithm uses bit-error probability estimates, which is first developed by Reed MIT Lincoln Laboratory Report (1959), to cancel the third error and then uses the algebraic decoding algorithm mentioned above to correct the remaining two errors. Simulation results show that this modified decoding algorithm slightly reduces the decoding complexity for correcting the third error while maintaining the same BER performance in additive white Gaussian noise (AWGN). Also, the flowchart of the above decoding algorithm is illustrated with Fig. 1.

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Tsung-Ching Lin, Pei-Yu Shih, Wen-Ku Su, and Trieu-Kien Truong "On decoding (31, 16, 7) quadratic residue code up to its error correcting capacity with bit-error probability estimates", Proc. SPIE 7814, Free-Space Laser Communications X, 781415 (24 August 2010); https://doi.org/10.1117/12.861076

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