Binary Cyclic Pearson Codes

  • Ari Dwi Hartanto Universitas Gadjah Mada, Yogyakarta, Indonesia
  • Al. Sutjijana Universitas Gadjah Mada, Yogyakarta, Indonesia
Keywords: Pearson distance, Pearson code, Cyclic code

Abstract

The phenomena of unknown gain or offset on communication systems and modern storages such as optical data storage and non-volatile memory (flash) becomes a serious problem. This problem can be handled by Pearson distance applied to the detector because it offers immunity to gain and offset mismatch. This distance can only be used for a specific set of codewords, called Pearson codes. An interesting example of Pearson code can be found in T-constrained code class. In this paper, we present binary 2-constrained codes with cyclic property. The construction of this code is adopted from cyclic codes, but it cannot be considered as cyclic codes.

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References

K. A. S. Immink and J. H. Weber, “Minimum pearson distance detection for multilevel channels with gain and/or offset mismatch,” IEEE Trans. Inf. Theory, vol. 60, no. 10, pp. 5966–5974, 2014, doi: 10.1109/TIT.2014.2342744.

F. Sala, K. A. S. Immink, and L. Dolecek, “Error Control Schemes for Modern Flash Memories,” IEEE Consum. Electron., vol. 4, no. 1, pp. 66–73, 2015.

J. H. Weber, K. A. S. Immink, and S. R. Blackburn, “Pearson codes,” IEEE Trans. Inf. Theory, vol. 62, no. 1, pp. 131–135, 2016, doi: 10.1109/TIT.2015.2490219.

K. A. S. Immink and J. H. Weber, “Hybrid Minimum Pearson and Euclidean Distance Detection,” IEEE Trans. Commun., vol. 63, no. 9, pp. 3290–3298, 2015, doi: 10.1109/TCOMM.2015.2458319.

J. H. Weber, T. G. Swart, and K. A. S. Immink, “Simple systematic Pearson coding,” IEEE Int. Symp. Inf. Theory - Proc., vol. 2016-Augus, pp. 385–389, 2016, doi: 10.1109/ISIT.2016.7541326.

S. A. Vanstone and P. C. Oorschot, An Introduction to Error Correcting Codes with Applications. Springer US, 1989.

S. Ling and C. Xing, Coding Theory. Cambridge University Press, 2004.

A. Betten, M. Braun, H. Fripertinger, A. Kerber, A. Kohnert, and A. Wassermann, Error-Correcting Linear Codes. Springer Berlin Heidelberg, 2006.

K. A. S. Immink, “Coding schemes for multi-level channels with unknown gain and/or offset,” IEEE Int. Symp. Inf. Theory - Proc., pp. 709–713, 2013, doi: 10.1109/ISIT.2013.6620318.

K. A. S. Immink, “Coding schemes for multi-level Flash memories that are intrinsically resistant against unknown gain and/or offset using reference symbols,” Electron. Lett., vol. 50, no. 1, pp. 20–22, 2014, doi: 10.1049/el.2013.3558.

“MAGMA Handbook.” http://magma.maths.usyd.edu.au/magma/handbook/ (accessed Nov. 05, 2018).

CROSSMARK
Published
2021-03-18
DIMENSIONS
How to Cite
HartantoA. D., & SutjijanaA. (2021). Binary Cyclic Pearson Codes. Jurnal Matematika MANTIK, 7(1), 1-8. https://doi.org/10.15642/mantik.2021.7.1.1-8