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Symmetries of the State Diagram of the Syndrome Former of a Binary Rate-1/2 Convolutional Code

  • J. P. M. Schalkwijk
Part of the International Centre for Mechanical Sciences book series (CISM, volume 219)

Abstract

We extend and generalize some earlier results [1] on syndrome decoding of binary rate-1/2 convolutional codes. Figure 1 represents a familiar example of such a code. The additions in Figure 1 are modulo-2 and all binary sequences ...,b−1,b0, b1,... are represented as power series b(α) = ... + b−1α-1 + b0 + b1α + .... The encoder has connection polynomials C1(α) = 1 + α2 and C2(α) = 1 + α + α2.

Keywords

Equivalence Class State Diagram Convolutional Code Bottom Register Nonzero Term 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 1.
    Schalkwijk, J.P.M., and Vinck, A.J., Syndrome decoding of convolutional codes, IEEE Trans. Communications, 23, 789, 1975.CrossRefMATHGoogle Scholar
  2. 2.
    Viterbi, A.J., Convolutional codes and their performance in communication systems, IEEE Trans. Communication Technology, 19, 751, 1971.CrossRefMathSciNetGoogle Scholar
  3. 3.
    Berlekamp, E.R., Algebraic Coding Theory, McGraw Hill, New York, 1968.MATHGoogle Scholar
  4. 4.
    Forney Jr., G.D., Convolutional codes I: Algebraic structure, IEEE Trans. Inform. Theory, 16, 720, 1970; correction appears in 17, 360, 1971.MATHGoogle Scholar
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    Forney Jr., G.D., Structural analysis of convolutional codes via dual codes, IEEE Trans. Inform. Theory, 19, 512, 1973.CrossRefMATHMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Wien 1975

Authors and Affiliations

  • J. P. M. Schalkwijk
    • 1
  1. 1.Department of Electrical EngineeringEindhoven University of TechnologyEindhovenThe Netherlands

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