Density Evolution of Low Density Parity Check codes over different channels

International Journal of VLSI & Signal Processing
© 2017 by SSRG - IJVSP Journal
Volume 4 Issue 2
Year of Publication : 2017
Authors : P.Ravikiran and Mehul C. Patel
pdf
How to Cite?

P.Ravikiran and Mehul C. Patel, "Density Evolution of Low Density Parity Check codes over different channels," SSRG International Journal of VLSI & Signal Processing, vol. 4,  no. 2, pp. 39-44, 2017. Crossref, https://doi.org/10.14445/23942584/IJVSP-V4I4P101

Abstract:

LDPC codes are originally invented by Robert G. Gallager. Later these codes are rediscovered by multiple groups has become the best known forward error correcting codes.We will discuss about density evolution of regular LDPC codes over Binary Erasure Channel(BEC) and Binary Symmetry channel(BSC) under message passing decoding algorithm in this paper. Density Evolution is a technic used to evaluate how good the LDPC codes are working on the given channel and to evaluate how far away the performance is from the Shannon limit.

Keywords:

 

      LDPC codes, BEC, BSC and Density Evolution.

References:

[1] R. G. Gallager “Low Density Parity Check codes.” IRE Transactions on Information Theory, vol 8, no. 1, pp. 21-28, 1962.
[2] D. J. C. MacKay and R. M. Neal, "Near Shannon limit performance of low density parity check codes," in Electronics Letters, vol. 32, no. 18, pp. 1645-1646, 1996.
[3] C. E. Shannon, “A Mathematical Theory of Communication”. CSLI publications, 1948. [online] Available: http://math.harvard.edu/~ctm/home/text/others/shannon/entropy /entropy.pdf
[4] Luby, Michael, et al. "Analysis of low density codes and improved designs using irregular graphs." Proceedings of the thirtieth annual ACM symposium on Theory of computing. ACM, 1998.
[5] M. C. Davey and D. MacKay, "Low-density parity check codes over GF(q)," in IEEE Communications Letters, vol. 2, no. 6, pp. 165-167, June 1998.
[6] T. J. Richardson, M. A. Shokrollahi and R. L. Urbanke, "Design of capacity-approaching irregular low-density parity-check codes," in IEEE Transactions on Information Theory, vol. 47, no. 2, pp. 619-637, Feb 2001.
[7] Johnson, Sarah J.”Introducing low-density parity-check codes.” University of Newcastle, Australia, 2006.
[8] Valenti, Matthew C., Shi Cheng, and Rohit Iyer Seshadri. "Turbo and LDPC codes for digital video broadcasting." Turbo Code Applications. Springer Netherlands, 2005. 301-319.
[9] Morello, Alberto, and Vittoria Mignone. "DVB-S2: The second generation standard for satellite broad-band services." Proceedings of the IEEE 94.1 (2006): 210-227.
[10] Biglieri, Ezio. Coding for wireless channels. Springer Science & Business Media, 2005.
[11] Johnson, Sarah J. Iterative error correction: Turbo, low-density parity-check and repeat-accumulate codes. Cambridge University Press, 2009.
[12] Loeliger, H-A. "An introduction to factor graphs." IEEE Signal Processing Magazine 21.1 (2004): 28-41.
[13] Zhang, Xiaojie, and Paul H. Siegel. "Quantized iterative message passing decoders with low error floor for LDPC codes." IEEE Transactions on Communications 62.1 (2014): 1- 14.