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On the error-correcting capability of LDPC codes. (English. Russian original) Zbl 1173.94010
Probl. Inf. Transm. 44, No. 3, 214-225 (2008); translation from Probl. Peredachi Inf. 44, No. 3, 50-62 (2008).
Summary: We consider the ensemble of low-density parity-check (LDPC) codes introduced by R. G. Gallager [IRE Trans. Inform. Theory IT-8, 21–28 (1962; Zbl 0107.11802)]. The Zyablov-Pinsker majority-logic iterative algorithm [V. V. Zjablov, M. S. Pinsker, Probl. Peredaci Inform. 11, No. 1, 23–26 (1975; Zbl 0358.94017)] for decoding LDPC codes is analyzed on the binary symmetric channel. An analytical lower bound on the error-correcting capability $$\tau _{\max}$$ that grows linearly in the code block length is obtained.

##### MSC:
 94B60 Other types of codes
Full Text:
##### References:
 [1] Gallager, R.G., Low-Density Parity-Check Codes, Cambridge: MIT Press, 1963. Translated under the title Kody s maloi plotnost’yu proverok na chetnost’, Moscow: Mir, 1966. [2] 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 [3] 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 [4] 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 [5] Sridharan, A., Truhachev, D., Lentmaier, M., Costello, D.J., Jr., and Zigangirov, K.Sh., Distance Bounds for an Ensemble of LDPC Convolutional Codes, IEEE Trans. Inform. Theory, 2007, vol. 53, no. 12, pp. 4537–4555. · Zbl 1320.94096 · doi:10.1109/TIT.2007.909113 [6] Zigangirov, D.K. and Zigangirov, K.Sh., Decoding of Low-Density Codes with Parity-Check Matrices Composed of Permutation Matrices in an Erasure Channel Probl. Peredachi Inf., 2006, vol. 42, no. 2, pp. 44–52 [Probl. Inf. Trans. (Engl. Transl.), 2006, vol. 42, no. 2, pp. 106–113]. · Zbl 1237.94142
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