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, Volume 77, Issue 4, pp 3093–3104 | Cite as

Construction of (2\(k\), \(k\), 2) Convolutional Codes with Double-Loop Cyclic Codes

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Abstract

In this paper, by taking multiple-time information in blocks into the coding of linear block codes, a new class of (2\(k\), \(k\), 2) convolutional codes is constructed, by which a new way of constructing long codes with short ones is obtained. After that, the type of embedded codes is determined and the optimal values of the linear combination coefficients are derived by using a three-dimensional state transfer matrix to analyze and testify the constructing mechanism of the codes. Finally, the simulation experiment tests the error-correcting performance of the (2\(k\), \(k\), 2) convolutional codes for different value of \(k\), it is shown that the performance of the new convolutional codes compares favorably with that of traditional (2, 1, \(l\)) convolutional codes.

Keywords

Convolutional codes State transition Double-loop cyclic codes  Viterbi decoding 
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Notes

Acknowledgments

The authors would like to thank the editors and the anonymous referees for their suggestions and comments.

References

  1. 1.
    Robinson, J. P. (1967). A class of binary recurrent codes with limited error propagation. IEEE Transactions on Information Theory, 13(1), 106–113.CrossRefMATHGoogle Scholar
  2. 2.
    Lin, S., & Costello, D. J. (2004). Error control coding: Fundamentals and applications (2nd ed.). Upper Saddle River: Pearson Education.Google Scholar
  3. 3.
    Berrou, C., & Glavieux, A. (1996). Near optimum error correcting coding and decoding: Turbo-codes. IEEE Transaction Communication Theory, 44(10), 1261–1271.CrossRefGoogle Scholar
  4. 4.
    Truhachev, D., Zigangirov, K. S., & Costello, D. J. (2010). Distance bounds for periodically time-varying and tail-biting LDPC convolutional codes. IEEE Transactions on Information Theory, 56(9), 4301–4308.CrossRefMathSciNetGoogle Scholar
  5. 5.
    Pusane, A. E., et al. (2011). Deriving good LDPC convolutional codes from LDPC block codes. IEEE Transactions on Information Theory, 57(2), 835–857.CrossRefMathSciNetGoogle Scholar
  6. 6.
    Abu-Surra, S., Divsalar, D., & Ryan, W. E. (2011). Enumerators for protograph-based ensembles of LDPC and generalized LDPC codes. IEEE Transactions on Information Theory, 57(2), 858–886.CrossRefMathSciNetGoogle Scholar
  7. 7.
    Tan, P., & Li, J. (2010). Efficient quantum stabilizer codes: LDPC and LDPC-convolutional constructions. IEEE Transactions on Information Theory, 56(1), 476–491.CrossRefMathSciNetGoogle Scholar
  8. 8.
    Moon, H., & Cox, D. C. (2009). Performance of unequally punctured convolutional codes. IEEE Transactions on Wireless Communications, 8(8), 3903–3909.CrossRefGoogle Scholar
  9. 9.
    Kowarzyk, G., Belanger, N., et al. (2012). Efficient search algorithm for determining optimal R=1/2 systematic convolutional self-doubly orthogonal codes. IEEE Transactions on Communications, 60(1), 3–8.CrossRefGoogle Scholar
  10. 10.
    Wang, X., & Xiao, G. (2001). Error correcting codes-princip1e and method. Xi’an: Xidian University Press.Google Scholar
  11. 11.
    Peng, W., & Xiaobing, W. (2012). A matrix implementation scheme of viterbi decoder. Journal of Circuits and Systems, 17(3), 115–120.Google Scholar
  12. 12.
    Sun, F., & Zhang, T. (2007). Low-power state-parallel relaxed adaptive viterbi decoder. IEEE Transactions on Circuits and Systems, 54(5), 1060–1068.CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  1. 1.Laboratory of Aerocraft Tracking Telemetering and Command and Communication, Ministry of EducationChongqing UniversityChongqingChina
  2. 2.Chongqing Vocational Institute of EngineeringChongqingChina

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