Abstract
We survey some recent work on codes based on bipartite expander graphs. The code symbols are associated with the branches and the symbols connected to a given node are restricted to be codewords in certain constituent codes (e.g. Reed–Solomon codes). This class turn out to contain some exellent codes. We give results on the parameters of the codes and methods for their encoding. We also analyze the performance under iterative decoding, partly based on a result on cores in random graphs.
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Zèmor, G.: On expander codes. IEEE Trans. Inform. Theory (Special Issue on Codes on Graphs and iterative Algorithms) 47, 835–837 (2001)
Barg, A., Zèmor, G.: Error exponents of expander codes. IEEE Trans. Inform. Theory 48, 1725–1729 (2002)
Tanner, M.: A Recursive Approach to Low Complexity Codes. IEEE Trans. Inform. Theory 27, 533–547 (1981)
Tanner, M.: Explicit Concentrators from Generalized N–Gons. SIAM J. Alg. Disc. Meth. 5(3), 287–293 (1984)
Tanner, M.: Minimum-Distance Bounds by Graph Analysis. IEEE Trans. Inform. Theory 47, 808–821 (2001)
Sipser, M., Spielman, D.A.: Expander Codes. IEEE Trans. Inform. Theory 42(6), 1710–1722 (1996)
Roth, R.M.: Introduction to Coding Theory. Cambridge University Press, Cambridge (2006)
Janwa, H., Lal, A.K.: On Tanner Codes: Minimum Distance and Decoding. In: AAECC, vol. 13, pp. 335–347 (2003)
Roth, R.M., Skachek, V.: Improved Nearly-MDS Expander Codes. IEEE Trans. Inform. Theory 52(8), 3650–3661 (2006)
Feit, W., Higman, G.: The nonexistence of certain generalized polygons. J. Algebra 1, 114–131 (1964)
van Maldeghem, H.: Generalized Polygons. Birkhäuser, Basel (1998)
McEliece, R., Swanson, L.: On the error probability for Reed-Solomon codes. IEEE Trans. Inform. Theory 32, 701–703 (1986)
Pittel, B., Spencer, J., Wormald, N.: Sudden emergence of a giant k-core in a random graph. J. Comb. Theory, Series B 67, 11–151 (1996)
Janson, S., Luczak, M.J.: A simple solution to the k-core problem. Random Structures Algorithms 30(1-2), 50–62 (2007)
Høholdt, T., Justesen, J.: Graph codes with Reed-Solomon component codes. In: Proceedings ISIT 2006, Seattle, Washington, July 2006, pp. 2022–2026 (2006)
Høholdt, T., Justesen, J.: Iterative decoding of product codes and graph codes with Reed-Solomon component codes. In: Proceedings ITW 2007 (September 2007)
Høholdt, T., Justesen, J.: Graph Codes with Reed-Solomon Component Codes. In: IEEE Trans. Inform. Theory (March 2008) (submitted)
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Høholdt, T. (2008). Codes from Expander Graphs. In: Barbero, Á. (eds) Coding Theory and Applications. Lecture Notes in Computer Science, vol 5228. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-87448-5_9
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DOI: https://doi.org/10.1007/978-3-540-87448-5_9
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-87447-8
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