Sufficient Conditions for the Existence of an (n, 1) Mother Code and Its Puncturing Pattern to Generating a Given Convolutional Code

- Journal title : The Journal of Korean Institute of Communications and Information Sciences
- Volume 41, Issue 4, 2016, pp.379-386
- Publisher : The Korean Institute of Communications and Information Sciences
- DOI : 10.7840/kics.2016.41.4.379

Title & Authors

Sufficient Conditions for the Existence of an (n, 1) Mother Code and Its Puncturing Pattern to Generating a Given Convolutional Code

Chung, Habong; Seong, Jinwoo;

Chung, Habong; Seong, Jinwoo;

Abstract

Puncturing is the most common way of increasing the rate of convolutional codes. The puncturing process is done to the original code called the mother code by a specific puncturing pattern. In this article, we investigate into the question whether any convolutional code is obtainable by puncturing some (n, 1) mother codes. We present two sufficient conditions for the mother code and the puncturing pattern to satisfy in order that the punctured code is equivalent to the given (N, K) convolutional code.

Keywords

Punctured Convolutional Code;Mother Code;Puncturing Pattern;Polynomial Generator Matrix;Reconstruction Algorithm;

Language

Korean

References

1.

J. Barbier, G. Sicot, and S. Houcke, "Algebraic approach for the reconstruction of linear and convolutional error correcting codes," in Proc. CISE'06, pp. 66-71, Venice, Italia, Nov. 2006.

2.

A. Canteaut and F. Chabaud, "A new algorithm for finding minimum-weight words in a linear code: application to primitive narrow-sense BCH codes of length 511," IEEE Trans. Inf. Theory, vol. 44, no. 1, pp. 367-378, Jan. 1998.

3.

M. Cote and N. Sendrier, "Reconstruction of convolutional codes from noisy observation," in Proc. IEEE ISIT'09, pp. 546-550, Seoul, Korea, Jun. 2009.

4.

E. Filiol, "Reconstruction of convolutionnal encoders over GF(q)," Lecture Notes in Com. Sci., Crypt. and Coding, vol. 1355, pp. 101-109, Dec. 1997.

5.

E. Filiol, "Reconstruction of punctured convolutional encoders", in Proc. ISITA'00, Hawaii, USA, Nov. 2000.

6.

J. H. Lee, et al., "Recognition of convolutional code with performance analysis," J. KICS, vol. 37A, no. 04, pp. 260-268, Apr. 2012.

7.

M. Marazin, et al., "Blind recovery if k/n rate convolutional encoders in a noisy environment," EURASIP J. Wireless Commun. Netw., vol. 2011, pp. 1186-1687, Nov. 2011.

8.

S. Su, et al., "Blind identification of convolutional encoder parameters," The Scientific World J., vol. 2014, no. 798612, p. 9, May 2014.

9.

M. Cluzeau and M. Finiasz, "Reconstruction of punctured convolutional codes," in Proc ITW'09, pp. 75-79, Taormina, Italy, Oct. 2009.

10.

G. Karpilovsky, Topics in field theory, 1st Ed., Elsevier, 1989.

11.

H. S. Jang, H. B. Chung, and J. W. Seong, "On the existence of the (2,1) mother code of (n,n-1) convolutional code," J. KICS, vol. 39A, no. 04, pp. 165-171, Apr. 2014.