Correction and error detection by Reed–Solomon code based on the spectral description

 

V. A. Vershinin

P. A. Solovyov Rybinsk State Aviation Technical University,
Pushkin str. 53, Rybinsk, Yaroslavl region 152934, Russia

 

The paper is received on December 14, 2016

 

Abstract. The article discusses the spectral description of the Reed – Solomon code. The encoding for error correction and error detection is proposed for the case, when the number of errors in the code word is greater than the number of guaranteed correctable errors. To do this, test items are divided into two groups. The first group is used for error correction, and the second (with the first) – for the detection of uncorrectable errors. The resulting estimate of the probability of undetected error is obtained. Simulation of the decoding process confirms the correctness of the assessment. If the number of errors in the code word is greater than the number of guaranteed correctable errors, it is possible to obtain an acceptable value of probability of undetected value in the case when the length of the code words increases and the value of the code distance is constant.

Key words: spectral description, correction and error detection, Reed – Solomon code.

References

1. Blahut R. Teoriya i praktika kodov, kontroliruyuschih oshibki [Theory and practice of error control codes]. Per. from English.– M.: Mir, 1986.– 576 p. (In Russian)

2. Vershinin V.A. Error detection by Reed–Solomon code based on the spectral description.. Zhurnal Radioelektroniki - Journal of Radio Electronics, 2016, No. 11. Available at http://jre.cplire.ru/jre/nov16/16/text.pdf. (In Russian)

 

Reference to this paper:

Correction and error detection by Reed – Solomon code based on the spectral description. V. A. Vershinin. Zhurnal Radioelektroniki - Journal of Radio Electronics, 2017, No. 1. Available at http://jre.cplire.ru/jre/jan17/13/text.pdf. (In Russian)