Skip to main content
Log in

Belief propagation decoding assisted on-the-fly Gaussian elimination for short LT codes

  • Published:
Cluster Computing Aims and scope Submit manuscript

Abstract

Belief propagation (BP) decoding has been widely used for decoding Luby transform (LT) codes which perform very well for a large number of input symbols. However, in reality, small numbers of input symbols are often encountered. In this paper, an efficient BP decoding assisted on-the-fly Gaussian elimination (OFG) decoding process is proposed. Our algorithm exploits XOR operations to get a packet of degree one when the ripple is empty, which gives a small value of overhead. Simulation results show that the proposed algorithm gives a largely improved overhead, about a 0.25 or more, with respect to that of the conventional BP algorithm. The complexity of the proposed algorithm is notably reduced with respect to that of OFG, especially in case of \(k = 150\)–500, while guaranteeing the overhead nearly same as that of OFG.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5

Similar content being viewed by others

References

  1. Luby, M., Codes, L.T., In: IEEE Symposium on Foundations of Computer Science, pp. 271–280 (2002)

  2. Lu, H., Lu, F., Cai, J., Foh, C.H.: LT-W: Improving LT decoding with Wiedemann solver. IEEE Trans. Inf. Theory 59(12), 7887 (2013)

    Article  MathSciNet  Google Scholar 

  3. Chang, L.-J., Wang, C.-H., Zao, J.K.: An error-floor reduction technique for short-length LT codes. In: International Symposium on Information Theory and its Applications (ISITA) 2014, Melbourne, Australia, 26–29 Oct 2014

  4. Kim, S., Ko, K., Chung, S.-Y.: Incremental Gaussian elimination decoding of raptor codes over BEC. IEEE Commun. Lett. 12(4), 307–309 (2008)

    Article  Google Scholar 

  5. Bioglio, V., Grangetto, M., Gaeta, R., Sereno, M.: On the fly gaussian elimination for LT codes. IEEE Commun. Lett. 13(12), 953–955 (2009)

    Article  Google Scholar 

  6. Byers, J., Luby, M., Mitzenmacher, M.: A digital fountain approach to asynchronous reliable multicast. IEEE J. Sel. Areas Commun. 20, 1528–1540 (2002)

    Article  Google Scholar 

  7. Anglano, C., Gaeta, R., Grangetto, M.: Exploiting rateless codes in cloud storage systems. IEEE Trans. Parallel Distrib. Syst. 26(5), 1313–1322 (2015)

    Article  Google Scholar 

  8. Schotsch, B., Garrammone, G., Vary, P.: Analysis of LT codes over finite fields under optimal erasure decoding. IEEE Commun. Lett. 17(7), 1826–1829 (2013)

    Article  Google Scholar 

  9. Bloemer, J., Kalfane, M., Karpinski, M., Karp, R., Luby, M., Zuckerman, D.: An XOR-based erasure-resilient coding scheme. In: ICSI TR-95-048 (1995)

Download references

Acknowledgments

Funding for this paper was provided by Namseoul university.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Kuinam J. Kim.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Cheong, H., Eun, J., Kim, H. et al. Belief propagation decoding assisted on-the-fly Gaussian elimination for short LT codes. Cluster Comput 19, 309–314 (2016). https://doi.org/10.1007/s10586-015-0522-0

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10586-015-0522-0

Keywords

Navigation