Abstract
Reed–Solomon (RS) codes are mainly powerful subclass of cyclic non-binary BCH codes which are widely employed to detect and correct both the burst and random errors in different digital transmission systems and storage media. In RS codes, the most important and complex block is key equation solver (KES) which is responsible to compute the unknown error location polynomial and magnitude polynomial. The designers mostly prefer the Berlekamp–Massey (BM)-based algorithms for computation of this KES block. In this paper, we have analyzed and implemented Berlekamp–Massey algorithm-based three important algorithms, namely inversionless Berlekamp–Massey (iBM) algorithm, reformulated inversionless Berlekamp–Massey (riBM) algorithm and extended reformulated inversionless Berlekamp–Massey (RiBM) algorithm. These three algorithms have been simulated and evaluated using both FPGA and ASIC platforms. The KES blocks based on three algorithms are compared in terms of area occupied and propagation delay. It is observed that iBM algorithm-based KES block requires lesser area with higher delay. On the other way, the RiBM algorithm-based KES block has lowest delay with larger area. This analysis will help the design engineer to implement resource constraints application in digital communication systems and storage systems.
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Samanta, J., Maity, R.K., Ghosh, D., Bardhan, S. (2022). Performance Analysis of Berlekamp–Massey-Based KES Block for 3-Byte RS Decoder. In: Sikdar, B., Prasad Maity, S., Samanta, J., Roy, A. (eds) Proceedings of the 3rd International Conference on Communication, Devices and Computing. ICCDC 2021. Lecture Notes in Electrical Engineering, vol 851. Springer, Singapore. https://doi.org/10.1007/978-981-16-9154-6_2
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DOI: https://doi.org/10.1007/978-981-16-9154-6_2
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