zbMATH — the first resource for mathematics

Vectorizing computations at decoding of nonbinary codes with small density of checks. (English. Russian original) Zbl 1355.94097
Autom. Remote Control 77, No. 10, 1781-1791 (2016); translation from Avtom. Telemekh. 2016, No. 10, 109-122 (2016).
Summary: A modification of the decoding \(q\)-ary Sum Product Algorithm (\(q\)-SPA) was proposed for the nonbinary codes with small check density based on the permutation matrices. The algorithm described has a vector realization and operates over the vectors defined on the field \(GF(q)\), rather than over individual symbols. Under certain code parameters, this approach enables significant speedup of modeling.
94B60 Other types of codes
Full Text: DOI
[1] Gallager, R.G., Low Density Parity Check Codes, Cambridge: MIT Press, 1963. Translated under the title Kody s maloi plotnost’yu proverok, Moscow: Mir, 1966. · Zbl 0156.40701
[2] Tanner, M.A., Recursive approach to low complexity codes, IEEE Trans. Inform. Theory, 27, 533-547, (1981) · Zbl 0474.94029
[3] Zyablov, V.V.; Pinsker, M.S., Estimating complexity of error correction by the low-density Gallager codes, Probl. Peredachi Inf., 11, 23-36, (1975) · Zbl 0358.94017
[4] Davey, M.; MacKay, D.J.C., Good error-correcting codes based on very sparse matrices, IEEE Trans. Inform. Theory, 45, 399-432, (1999) · Zbl 0946.94030
[5] Davey, M.; MacKay, D.J.C., Low density parity check codes over GF(q), IEEE Commun. Lett., 2, 165-167, (1998)
[6] Zigangirov, K.Sh.; Pusane, A.E.; Zigangirov, D.K.; Kostello, D.Dz.h, On correctability of codes with lew density of parity checks, Probl. Peredachi Inf., 44, 50-62, (2008)
[7] Rybin, P.S.; Zyablov, V.V., Correction of deletions by low density parity-check codes, Probl. Peredachi Inf., 45, 15-32, (2009) · Zbl 1178.94254
[8] Zyablov, V.V.; Rybin, P.S., Analysis of relations between the properties of the LDPC codes and the tanner graph, Probl. Peredachi Inf., 48, 3-29, (2012) · Zbl 1312.94117
[9] Shridkharan, A.; Lentmaier, M.; Trukhachev, D.V.; etal., On minimal distance of low-density codes with checking matrices of the permutation matrices, Probl. Peredachi Inf., 41, 39-52, (2005)
[10] Frolov, A.A.; Zyablov, V.V., Asymptotic estimate of the part of errors correctable by the q-ary LDPC codes, Probl. Peredachi Inf., 46, 47-65, (2010) · Zbl 1237.94145
[11] Frolov, A.A.; Zyablov, V.V., Boundaries of the minimal code distance for the nonbinary codes on bipartite graphs, Probl. Peredachi Inf., 47, 27-42, (2011) · Zbl 1302.94071
[12] Declercq, D.; Fossorier, M., Decoding algorithms for nonbinary LDPC codes over GF(q), IEEE Trans. Commun., 55, 633-643, (2007)
[13] Lin, S.; Song, S.; Lan, L.; Zeng, L.; Tai, Y.Y., Constructions of nonbinary quasi-cyclic LDPC codes: A finite field approach, IEEE Trans. Commun., 56, 545-554, (2008)
[14] Lin, S.; Song, S.; Zhou, B., Algebraic constructions of non-binary quasi-cyclic LDPC codes: array masking and dispersion, (2007)
[15] Carrasco, R.A. and Johnston, M., Non-binary Error Control Coding for Wireless Communication and Data Storage, New York: Wiley, 2009.
[16] Ivanov, F.I.; Zhilin, I.V.; Zyablov, V.V., An algorithm to decode the low-density codes with high parallellization, Informats.-Upravl. Sist., 6, 49-55, (2012)
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.