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Decoding of low-density codes with parity-check matrices composed of permutation matrices in an erasure channel. (English. Russian original) Zbl 1237.94142
Probl. Inf. Transm. 42, No. 2, 106-113 (2006); translation from Probl. Peredachi Inf. 42, No. 2, 44-52 (2006).
Summary: A lower bound for the number of iteratively correctable erasures is given, with application to the ensemble of LDPC codes with parity-check matrices composed of permutation matrices. We assume that the Zyablov-Pinsker iterative decoding algorithm is used. Its complexity is \(O(N \log N)\), where \(N\) is the block length.

94B35 Decoding
Full Text: DOI
[1] Sridharan, A., Lentmaier, M., Truhachev, D.V., Costello, D.J., Jr., and Zigangirov, K.Sh., On the Minimum Distance of Low-Density Parity-Check Codes with Parity-Check Matrices Constructed from Permutation Matrices, Probl. Peredachi Inf., 2005, vol. 41, no. 1, pp. 39–52 [Probl. Inf. Trans. (Engl. Transl.), 2005, vol. 41, no. 1, pp. 33–44]. · Zbl 1078.94038
[2] Zyablov, V.V. and Pinsker, M.S., Decoding Complexity of Low-Density Codes for Transmission in a Channel with Erasures, Probl. Peredachi Inf., 1974, vol. 10, no. 1, pp. 15–28 [Probl. Inf. Trans. (Engl. Transl.), 1974, vol. 10, no. 1, pp. 10–21]. · Zbl 0326.94011
[3] Gallager, R.G., Low-Density Parity-Check Codes, Cambridge: MIT Press, 1963. · Zbl 0156.40701
[4] Luby, M.G., Mitzenmacher, M., Shokrollahi, M.A., and Spielman, D.A., Efficient Erasure Correcting Codes, IEEE Trans. Inform. Theory, 2001, vol. 47, no. 2, pp. 569–584. · Zbl 1019.94032 · doi:10.1109/18.910575
[5] Zyablov, V.V. and Pinsker, M.S., Estimation of the Error-Correction Complexity for Gallager Low-Density Codes, Probl. Peredachi Inf., 1975, vol. 11, no. 1, pp. 23–36 [Probl. Inf. Trans. (Engl. Transl.), 1975, vol. 11, no. 1, pp. 18–28]. · Zbl 0358.94017
[6] Lentmaier, M., Truhachev, D.V., Zigangirov, K.Sh., and Costello, D.J., Jr., An Analysis of the Block Error Probability Performance of Iterative Decoding, IEEE Trans. Inform. Theory, 2005, vol. 51, no. 11, pp. 3834–3855. · Zbl 1303.94144 · doi:10.1109/TIT.2005.856942
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