Soft-Decision Decoding of the [23,12] Golay Code Using Covering Polynomials 


Vol. 27,  No. 3, pp. 180-187, Mar.  2002


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  Abstract

The decoding method using covering polynomials is an extended form of error-trapping decoding, and is a simple and effective means to implement decoders for cyclic codes. Covering polynomials can be used for soft-decision decoding as well as for decoding beyond the bounded distance of the code. The implementation complexity is proportional to the number of covering polynomials employed. In this paper, the soft-decision decoding procedure using covering polynomials is described, and the procedure is applied to the [23,12] Golay code. A new set of covering polynomials is derived for the procedure, which is presented as a generalized closed-form solution. The set can be efficiently utilized for decoding a class of cyclic codes including the Golay code. Computer simulation of the described procedure is performed to show the trade-offs between the decoder performance and complexity. It is demonstrated that soft-decision decoding of the Golay code using the derived set of covering polynomials has less than 0.2dB deviation from the optimal performance of maximum-likelihood decoding, with a reduced complexity when compared to the Chase Algorithm 2 combined with hard-decision decoding that has nearly identical performance.

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  Cite this article

[IEEE Style]

W. Sung, "Soft-Decision Decoding of the [23,12] Golay Code Using Covering Polynomials," The Journal of Korean Institute of Communications and Information Sciences, vol. 27, no. 3, pp. 180-187, 2002. DOI: .

[ACM Style]

Wonjin Sung. 2002. Soft-Decision Decoding of the [23,12] Golay Code Using Covering Polynomials. The Journal of Korean Institute of Communications and Information Sciences, 27, 3, (2002), 180-187. DOI: .

[KICS Style]

Wonjin Sung, "Soft-Decision Decoding of the [23,12] Golay Code Using Covering Polynomials," The Journal of Korean Institute of Communications and Information Sciences, vol. 27, no. 3, pp. 180-187, 3. 2002.

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pISSN : 1226 - 4717
eISSN : 2287 - 3880