Research Article Open Access

Reed-Muller Codec Simulation Performance

O. O. Khalifa1, A. H. Abdullah1, N. Suriyana1, S. Zawanah1 and S. A. Hameed1
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Journal of Computer Science
Volume 4 No. 10, 2008, 792-798

DOI: https://doi.org/10.3844/jcssp.2008.792.798

Submitted On: 4 February 2008 Published On: 31 October 2008

How to Cite: Khalifa, O. O., Abdullah, A. H., Suriyana, N., Zawanah, S. & Hameed, S. A. (2008). Reed-Muller Codec Simulation Performance. Journal of Computer Science, 4(10), 792-798. https://doi.org/10.3844/jcssp.2008.792.798

Abstract

The approach to error correction coding taken by modern digital communication systems started in the late 1940's with the ground breaking work of Shannon, Hamming and Golay. Reed-Muller (RM) codes were an important step beyond the Hamming and Golay codes because they allowed more flexibility in the size of the code word and the number of correctable errors per code word. Whereas the Hamming and Golay codes were specific codes with particular values for q; n; k; and t, the RM codes were a class of binary codes with a wide range of allowable design parameters. Binary Reed-Muller codes are among the most prominent families of codes in coding theory. They have been extensively studied and employed for practical applications. In this research, the performance simulation of Reed-Muller Codec was presented. An introduction on Reed-Muller codes, were introduced that consists of defining the key terms and operation used with the binary numbers. Reed-Muller codes were defined and encoding matrices were discussed. The decoding process was given and some examples were demonstrated to clarify the method. The results and the performance of Reed-Muller encoding were presented and the messages been encoded using the defined matrices were shown. The simulation of the decoding part also been shown. The performance of Reed-Muller codes were then analyzed in terms of its code rate, code length and minimum Hamming distance. The analysis that performed also successfully examines the relationship between the parameters of Reed-Muller coding. The decoding part of the Reed-Muller codes can detect one error and correct it as shown in the examples.

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Keywords

  • Reed-Muller
  • code length
  • minimum Hamming distance
  • code rate