zbMATH — the first resource for mathematics

Asymptotic bounds on the decoding error probability for two ensembles of LDPC codes. (English. Russian original) Zbl 1367.94469
Probl. Inf. Transm. 51, No. 3, 205-216 (2015); translation from Probl. Peredachi Inf. 51, No. 3, 3-14 (2015).
Summary: Two ensembles of low-density parity-check (LDPC) codes with low-complexity decoding algorithms are considered. The first ensemble consists of generalized LDPC codes, and the second consists of concatenated codes with an outer LDPC code. Error exponent lower bounds for these ensembles under the corresponding low-complexity decoding algorithms are compared. A modification of the decoding algorithm of a generalized LDPC code with a special construction is proposed. The error exponent lower bound for the modified decoding algorithm is obtained. Finally, numerical results for the considered error exponent lower bounds are presented and analyzed.
94B70 Error probability in coding theory
94B05 Linear codes, general
94B35 Decoding
Full Text: DOI
[1] Forney, G.D. Jr., Concatenated Codes, Cambridge: MIT Press, 1966. Translated under the title Kaskadnye kody, Moscow: Mir, 1970.
[2] Blokh, E.L.; Zyablov, V.V., (linear concatenated codes), (1982), Moscow · Zbl 0309.94030
[3] Gallager, R.G., Low-density parity-check codes, (1963), Cambridge · Zbl 0107.11802
[4] Zyablov, V.V.; Pinsker, M.S., Estimation of the error-correction complexity for Gallager low-density codes, Probl. Peredachi Inf., 11, 23-36, (1975) · Zbl 0358.94017
[5] Zyablov, V.V.; Johannesson, R.; Loncar, M., Low-complexity error correction of Hamming-code- based LDPC codes, Probl. Peredachi Inf., 45, 25-40, (2009) · Zbl 1173.94451
[6] Zyablov, V.V.; Rybin, P.S., Analysis of the relation between properties of LDPC codes and the tanner graph, Probl. Peredachi Inf., 48, 3-29, (2012) · Zbl 1312.94117
[7] Rybin, P., On the error-correcting capabilities of low-complexity decoded irregular LDPC codes, 3165-3169, (2014)
[8] Barg, A.; Zémor, G., Error exponents of expander codes, IEEE Trans. Inform. Theory, 48, 1725-1729, (2002) · Zbl 1061.94078
[9] Barg, A.; Zémor, G., Error exponents of expander codes under linear-complexity decoding, SIAM J. Discret. Math., 17, 426-445, (2004) · Zbl 1062.94063
[10] Zyablov, V.V.; Rybin, P.S., Estimation of the exponent of the decoding error probability for a special generalized LDPC code, Inform. Protsessy, 12, 84-97, (2012)
[11] Gallager, R.G. Information Theory and Reliable Communication, New York: Wiley, 1968. Translated under the title Teoriya informatsii i nadezhnaya svyaz’, Moscow: Sov. Radio, 1974. · Zbl 0198.52201
[12] Frolov, A.A.; Zyablov, V.V., Asymptotic estimation of the fraction of errors correctable by q-ary LDPC codes, Probl. Peredachi Inf., 46, 47-65, (2010) · Zbl 1237.94145
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.