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Application of symbol avoidance in Reed–Solomon codes to improve their synchronization

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Abstract

In our previous work we introduced a method for avoiding/excluding some symbols in Reed–Solomon (RS) codes, called symbol avoidance. In this paper, we apply the symbol avoidance method to make synchronization of RS encoded data more effective. We avoid symbols in a RS code and then perform conventional frame synchronization on RS encoded data by appending sync-words on the data. The symbols in the RS code are avoided according to the sync-word used, such that the sync-word has very low probability of being found in the RS codewords, where it was not inserted. Therefore, for different sync-words, different symbols need to be avoided in the RS code. The goal here is to reduce the probability of mistaking data for the sync-word in the RS encoded framed data. Hence, the probability of successful synchronization is improved. Not only does our symbol avoidance code improve probability of successful synchronization, it also reduces the overall amount of redundancy required when the channel is very noisy.

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Authors and Affiliations

  1. Department of Electrical and Electronic Engineering Science, University of Johannesburg, Auckland Park, 2006, P.O. Box 524, Johannesburg, South Africa

    Thokozani Shongwe & Hendrik C. Ferreira

  2. Institute for Experimental Mathematics, University of Duisburg-Essen, Ellernstr. 29, 45326, Essen, Germany

    A. J. Han Vinck

Authors
  1. Thokozani Shongwe
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  2. A. J. Han Vinck
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  3. Hendrik C. Ferreira
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Corresponding author

Correspondence to Thokozani Shongwe.

Appendix

Appendix

Table 6 Results of the \(P_{\text {FAD}}\) for corresponding avoided symbols, for binary sync-words of lengths \(7-11\) written in their octal format
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Shongwe, T., Vinck, A.J.H. & Ferreira, H.C. Application of symbol avoidance in Reed–Solomon codes to improve their synchronization. Telecommun Syst 63, 77–88 (2016). https://doi.org/10.1007/s11235-015-9974-z

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