Efficient Decoding Algorithm for Binary Quadratic Residue Codes Using Reduced Permutation Sets
- 1 Department of Web and Mobile Engineering, ENSIAS College of Engineering, Mohammed V University, in Rabat, Morocco
- 2 Department of Computer Science, Ecole Supérieure de Technologie Moulay-Ismail University, Meknes, Morocco
Abstract
The Quadratic Residue (QR) codes have a rich mathematic structure. Unfortunately, their Algebraic Decoding (AD) is not generalizable for all QR codes. In this study, an efficient hard decoding algorithm is proposed to generalize the decoding of the binary systematic Quadratic Residue (QR) codes. The proposed decoder corrects t erroneous bits or less, in the received word, based on a reduced set of permutations derived from the large automorphism group of QR codes. This set of permutations is applied to the received word to move the error positions and trap all of them in redundancy. Then, to evaluate the proposed method, we applied it to many binary QR codes of moderate code length starting with 17 until 113 with reducible and irreducible generator polynomials. The proposed decoder was validated by inserting all possible error patterns, that have t or less erroneous positions, as input of the proposed decoder and the output is always a correct codeword. The complexity study, in terms of the number of operations used, reveals that the light permutation decoding LPD algorithm significantly decreases decoding complexity without performance loss. So, it is qualified to be a good competitor to decode QR codes with lower lengths but is the best for QR codes with higher lengths.
DOI: https://doi.org/10.3844/jcssp.2023.526.539
Copyright: © 2023 Hamza Boualame, Mostafa Belkasmi and Idriss Chana. This is an open access article distributed under the terms of the
Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.
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Keywords
- Automorphism Group
- Permutation Decoding
- Quadratic Residue Codes
- Syndrome Decoding