New Distance Concept and Graph Theory Approach for Certain Coding Techniques Design and Analysis

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Abstract

A New graph distance concept introduced for certain coding techniques helped in their design and analysis as in the case of distance-preserving mappings and spectral shaping codes. A graph theoretic construction, mapping binary sequences to permutation sequences and inspired from the k-cube graph has reached the upper bound on the sum of the distances for certain values of the length of the permutation sequence. The new introduced distance concept in the k-cube graph helped better understanding and analyzing for the first time the concept of distance-reducing mappings. A combination of distance and the index-permutation graph concepts helped uncover and verify certain properties of spectral null codes, which were previously difficult to analyze.

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  • 1. N. Deo Graph Theory with Applications to Engineering and Computer Science. Dover Publications 2016.

  • 2. J. Susymary and R. Lawrance Graph theory analysis of protein-protein interaction graphs through clustering method in 2017 IEEE International Conference on Intellignet Techniques in Control Optimization and Signal Processing pp. 1–5 Srivilliputhur India March 23–25 2017.

  • 3. K. Ouahada and H. Ferreira A similation and graph theoretical analysis of certain porperties of spectrall null codebooks SAIEE Africa Research Journal vol. 103 no. 3 pp. 106–115 2012.

  • 4. K. Ouahada and H. C. Ferreira A graph theoretic approach for spectral null codes in Proceedings of the Information Theory Workshop pp. 369–373 Taormina Sicily Italy October 11-16 2009.

  • 5. A. K. Singh Error detection and correction by hamming codel in Proceedings of the 2016 International Conference on Global Trends in Signal Processing Information Computing and Communication pp. 35–37 Bambhori Jalgoan India December 22-24 2016.

  • 6. A. Wachter-Zeh List decoding of insertions and deletions IEEE Transactions on Information Theory vol. PP no. 99 p. 1 2017.

  • 7. K. Ouahada T. G. Swart and H. C. Ferreira Binary permutation sequences as subsets of levenshtein codes and higher order spectral nulls codes in 2006 IEEE Information Theory Workshop - ITW ’06 Chengdu pp. 535–539 Chengdu China Oct. 2006.

  • 8. A. Viterbi and J. Omura Principles of Digital Communication and Coding. McGraw-Hill Kogakusha LTD Tokyo Japan 1979.

  • 9. A. J. H. Vinck and H. C. Ferreira Permutation trellis codes in in Proceedings of the International Symposium on Information Theory (ISIT 2001) p. 279 Washington DCUSA June 24-29 2001.

  • 10. A. J. H. Vinck Coded modulation for powerline communications AEU International Journal of Electronics and Communications vol. 54 no. 1 pp. 45–49 2000.

  • 11. H. C. Ferreira A. J. H. Vinck T. G. Swart and I. de Beer Permutation trellis codes IEEE Trans. Commun. vol. 53 no. 11 pp. 1782–1789 2005.

  • 12. T. G. Swart and H. C. Ferreira A generalized upper bound and a multilevel construction for distance-preserving mappings IEEE Trans. Inf. Theory vol. 52 no. 8 pp. 3685–3695 2006.

  • 13. K. Ouahada and H. C. Ferreira k-cube construction mappings from binary vectors to permutation sequences in in proceedings of IEEE International Symposium on Information Theory p. 279 Seoul South Korea June 28–July 3 2009.

  • 14. W. J. Dally Express cubes: Improving the performance of k-ary n-cube interconnection networks IEEE Trans. On Computers vol. 40 no. 9 pp. 1016–1023 Sept. 1991.

  • 15. M. Haynes Magnetic recording techniques for buried servos IEEE Transactions on Magnetics vol. 17 no. 6 pp. 2730–2734 Nov. 198.

  • 16. H. C. Ferreira I. de Beer and A. J. H. Vinck Distance preserving mappings onto convolutional codes revisited in Proceedings of the IEEE Information Theory Workshop pp. 23–26 Breisach Germany Apr. 26–29 2002.

  • 17. E. Gorog Alphabets with desirable frequency spectrum properties IBM J. Res. Develop vol. 12 pp. 234–241 May 1968.

  • 18. K. Ouahada T. G. Swart and H. C. Ferreira Spectral shaping permutation distance-preserving mappings codes in IEEE Proc. ITW’07 Conf. California USA pp. 36–41 California USA Sept. 2Ö6 2007.

  • 19. K. A. S. Immink Codes for mass data storage systems. Shannon Foundation Publishers The Netherlands 1999.

  • 20. K. A. S. Immink Spectral null codes IEEE Transactions on Magnetics vol. 26 no. 2 pp. 1130–1135 Mar. 1990.

  • 21. C. Yeh and B. Parhami ‘parallel algorithms for index-permutation graphs. an extension of cayley graphs for multiple chip-multiprocessors (mcmp) in International Conference on Parallel Processing pp. 3–12 California USA Sept. 2001.

  • 22. L.-H. Chang C. Wang P.-N. Chen Y. S. Han and V. Y. F. Tan Distance spectrum formula for the largest minimum hamming distance of finite-length binary block codes in 2017 IEEE Information Theory Workshop - ITW 2017 Kaohsiung pp. 419–423 Kaohsiung Taiwan Nov. 6–10 2017.

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CiteScore 2018: 0.95

SCImago Journal Rank (SJR) 2018: 0.324
Source Normalized Impact per Paper (SNIP) 2018: 0.73

Mathematical Citation Quotient (MCQ) 2018: 0.27

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