Design of Short Irregular LDPC Codes for a Markov-modulated Gaussian Channel

W. Proß, M. Otesteanu, F. Quint

2012

Abstract

This paper deals with the design of short irregular Low-Density Parity-Check (LDPC) codes. An optimization method for the underlying symbol-node degree-distribution (SNDD) of an irregular LDPC code is introduced, which is based on the Downhill-Simplex (DHS) algorithm. In order to compare our method with the optimization described in (Hu et al., 2005), which is based on a simplified version of the DHS algorithm, we first designed a rate 0.5 irregular LDPC code of length n = 504 for an Additive White Gaussian Noise Channel (AWGNC). The proposed optimization method was then used to design an irregular LDPC code for a Markov-modulated Gaussian Channel (MMGC). The decoding performance of the resulting LDPC code is then compared to the design based on the Density-Evolution (DE) method.

References

  1. Amin, T. R., Richardson, T., Shokrollahi, A., and Urbanke, R. (1999). Design of provably good low-density parity check codes. In IEEE Transactions on Information Theory.
  2. Eckford, A. W. (2004). Low-density parity-check codes for Gilbert-Elliott and Markov-modulated channels. PhD thesis, University of Toronto.
  3. Gallager, R. G. (1962). Low density parity check codes. IRE Trans on Information Theory, 1:21-28.
  4. Hu, X. Y., Eleftheriou, E., and Arnold, D. M. (2005). Regular and irregular progressive edge-growth tanner graphs. Information Theory, IEEE Transactions on, 51(1):386-398.
  5. Hu, X. Y., Eleftheriou, E., Arnold, D. M., and Dholakia, A., editors (2002). Efficient implementations of the sumproduct algorithm for decoding LDPC codes, volume 2.
  6. Luby, M., Mitzenmacher, M., Shokrollah, A., and Spielman, D. (1998). Analysis of low density codes and improved designs using irregular graphs. In Proceedings of the thirtieth annual ACM symposium on Theory of computing, pages 249-258.
  7. Luby, M. G., Mitzenmacher, M., Shokrollahi, M. A., and Spielman, D. A. (2001). Improved low-density paritycheck codes using irregular graphs. Information Theory, IEEE Transactions on, 47(2):585-598.
  8. MacKay, D. and Neal, R. (1995). Good codes based on very sparse matrices. Cryptography and Coding, pages 100-111.
  9. MacKay, D. J. C., Wilson, S. T., and Davey, M. C. (1999). Comparison of constructions of irregular gallager codes. Communications, IEEE Transactions on, 47(10):1449-1454.
  10. Nelder, J. A. and Mead, R. (1965). A simplex method for function minimization. The computer journal, 7(4):308.
  11. Proß, W., Quint, F., and Otesteanu, M. (2010). Estimationdecoding of short blocklength ldpc codes on a markov-modulated gaussian channel. In 3rd IEEE International Conference on Signal Processing Systems (ICSPS2011) Proceedings, pages 383-387.
  12. Richardson, T. J., Shokrollahi, M. A., and Urbanke, R. L. (2001). Design of capacity-approaching irregular lowdensity parity-check codes. Information Theory, IEEE Transactions on, 47(2):619-637.
  13. Richardson, T. J. and Urbanke, R. L. (2001). The capacity of low-density parity-check codes under messagepassing decoding. Information Theory, IEEE Transactions on, 47(2):599-618.
  14. Tanner, R. M. (1981). A recursive approach to low complexity codes. IEEE Transactions on Information Theory, 27:533-547.
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Paper Citation


in Harvard Style

Proß W., Otesteanu M. and Quint F. (2012). Design of Short Irregular LDPC Codes for a Markov-modulated Gaussian Channel . In Proceedings of the International Conference on Signal Processing and Multimedia Applications and Wireless Information Networks and Systems - Volume 1: SIGMAP, (ICETE 2012) ISBN 978-989-8565-25-9, pages 31-34. DOI: 10.5220/0004017000310034


in Bibtex Style

@conference{sigmap12,
author={W. Proß and M. Otesteanu and F. Quint},
title={Design of Short Irregular LDPC Codes for a Markov-modulated Gaussian Channel},
booktitle={Proceedings of the International Conference on Signal Processing and Multimedia Applications and Wireless Information Networks and Systems - Volume 1: SIGMAP, (ICETE 2012)},
year={2012},
pages={31-34},
publisher={SciTePress},
organization={INSTICC},
doi={10.5220/0004017000310034},
isbn={978-989-8565-25-9},
}


in EndNote Style

TY - CONF
JO - Proceedings of the International Conference on Signal Processing and Multimedia Applications and Wireless Information Networks and Systems - Volume 1: SIGMAP, (ICETE 2012)
TI - Design of Short Irregular LDPC Codes for a Markov-modulated Gaussian Channel
SN - 978-989-8565-25-9
AU - Proß W.
AU - Otesteanu M.
AU - Quint F.
PY - 2012
SP - 31
EP - 34
DO - 10.5220/0004017000310034