IJPAM: Volume 97, No. 1 (2014)

DECODING OF 2-D CONVOLUTIONAL CODES
BASED ON ALGEBRAIC APPROACH

Pramote Jangisarakul$^1$, Chalie Charoenlarpnopparut$^2$
$^{1,2}$ School of Information
Computer and Communication Technology
Sirindhorn International Institute of Technology
Thammasat University
Klong Luang, Pathum-Thani 12121, THAILAND


Abstract. In this paper, we apply the decoding matrix for $2$-D convolution codes to reconstruct information sequences. It is suitable for non-square matrices with multivariate polynomial elements. Next, development of a syndrome decoder for $2$-D convolutional codes based on Gröbner bases is introduced. The computation of the syndrome vector employs the computation of the syzygy module, found by means of the Gröbner basis of a certain module. Then, estimated error vector can be identified by using $m$-variate division algorithm. Simulation results show error-correcting capability of decoding process.

Received: May 11, 2014

AMS Subject Classification: 94B10, 94B35

Key Words and Phrases: Groebner bases, convolutional codes, decoding matrix, syndrome decoder

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DOI: 10.12732/ijpam.v97i1.3 How to cite this paper?

Source:
International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2014
Volume: 97
Issue: 1
Pages: 21 - 30


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