Abstract
In 1989, N.Sourlas used the parallel that exists between the information theory and the statistical physics to bring out that low density parity check (LDPC) codes correspond to spins glass models. Such a correspondence is contributing nowadays to the similarity between the statistical physics and the error correcting codes. Hence, the statistical physics methods have been applied to study the properties of these codes. Among these methods the Thouless-Anderson-Palmer (TAP) is an approach which is proved to be similar to the Belief Propagation (BP) algorithm. Unfortunately, there are no studies made for the other decoding algorithms.
The main purpose of this paper is to provide a statistical physics analysis of LDPC codes performance. First, we investigate the Log-Likelihood Ratios-Belief Propagation (LLR-BP) algorithm as well as its simplified versions the BP-Based algorithm and the λ-min algorithm with the TAP approach. Second, we evaluate the performances of these codes in terms of a statistical physics parameter called the magnetization on the Additive White Gaussian Noise (AWGN) channel. Simulation results obtained in terms of the magnetization show that the λ-min algorithm reduces the complexity of decoding and gets close to LLR-BP performance. Finally, we compare our LLR-BP results with those of the replica method.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
European Telecommunications Standards Institude (ETSI). Digital Video Broadcasting (DVB) Second generation framing structure for broadband satellite applications; Part2: DVB-S2 Extensions (DVB-S2X), EN 302 307-2 (V1.1.1), https://www.dvb.org/standards/dvb-s2x
Mackay, D.J.C.: Good error-correcting codes based on very sparse matrices. IEEE Trans. Inform. Theory 45, 399–431 (1999)
Fossorier, M.P.C., Mihaljevic, M., Imai, I.: Reduced complexity iterative decoding of low density parity check codes based on belief propagation. IEEE Trans. Commun. 47, 673–680 (1999)
Guilloud, F., Boutillon, E., Danger, J.L.: λ-min decoding algorithm of regular and irregular LDPC codes. In: Proc. 3rd Int. Symp. on Turbo Codes & Related Topics (ISTC 2003), pp.451–454. Brest (2003)
Sourlas, N.: Spin glass models as error correcting codes. Nature 339, 693–695 (1989)
Skantzos, N.S., Van Mourik, J., Saad, D.: Magnetization enumerator of real-valued symmetric channels in Gallager error-correcting codes. Phys. Rev. E 67, 037101 (2003)
Mezard, M., Montanari, A.: Information, Physics and Computation. Oxford university Press (2009)
Huang, H.: Code optimization, frozen glassy phase and improved decoding algorithms for low-density parity-check codes. Commun. Theor. Phys. 63, 115–127 (2015)
Neri, I., Skantzos, N.S., Boll, D.: Gallager error-correcting codes for binary asymmetric channels. J. Stat. Mech. 2008, P10018 (2008)
Neri, I., Skantzos, N.S.: On the equivalence of Ising models on small-world networks and LDPC codes on channels with memory. J. Phys. A: Math and Theor. 47, 385002 (2014)
Murayama, T., Kabashima, Y., Saad, D., Vicente, R.: Statistical physics of regular low-density parity-check error-correcting codes. Phys. Rev. E 62, 1577–1591 (2000)
Kabashima, Y., Saad, D.: Belief propagation vs TAP for decoding corrupted messages. Eurphys. Lett. 44, 668–674 (1998)
Thouless, D.J., Anderson, P.W., Palmer, R.G.: Solution of solvable model of a spin glass. Phil. Mag. 35, 593–601 (1977)
Vicente, R., Saad, D., Kabashima, Y.: Finite-connectivity systems as error-correcting codes. Phys. Rev. E 60, 5352–5366 (1999)
Mackay, D.J.C.: Ldpc database, http://www.inference.phy.cam.ac.uk/mackay/codes/data.html
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2015 Springer International Publishing Switzerland
About this paper
Cite this paper
Abdelhedi, M., Hamdi, O., Bouallegue, A. (2015). Performance of LDPC Decoding Algorithms with a Statistical Physics Theory Approach. In: El Hajji, S., Nitaj, A., Carlet, C., Souidi, E. (eds) Codes, Cryptology, and Information Security. C2SI 2015. Lecture Notes in Computer Science(), vol 9084. Springer, Cham. https://doi.org/10.1007/978-3-319-18681-8_25
Download citation
DOI: https://doi.org/10.1007/978-3-319-18681-8_25
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-18680-1
Online ISBN: 978-3-319-18681-8
eBook Packages: Computer ScienceComputer Science (R0)