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A Novel Low-Cost Multi-Mode Reed Solomon Decoder Design Based on Peterson-Gorenstein-Zierler Algorithm

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Abstract

Reed-Solomon (RS) codes play an important role in providing error protection and data integrity. Among various Reed-Solomon decoding algorithms, the Peterson-Gorenstein-Zierler (PGZ) algorithm in general has the least computational complexity for small t values. However, unlike the iterative approaches (e.g., Berlekamp-Massey and Euclidean algorithms), it will encounter divided-by-zero problems in solving multiple t values. In this paper, we propose a multi-mode hardware architecture for error numbers ranging from zero to three. We first propose a cost-down technique to reduce the hardware complexity of a t = 3 decoder. A Finite-field Inversion (FFI) elimination scheme is also proposed in our PGZ kernel. Next, we perform an algorithmic-level derivation to identify the configurable feature of our design. With those manipulations, we are able to perform multi-mode RS decoding in one unified VLSI architecture with very simple control scheme. The very low cost and simple data-path make our design a good choice in small-footprint embedded VLSI systems such as Error Control Coding (ECC) in memory/storage systems.

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Authors and Affiliations

  1. Graduate Institute of Electronics Engineering, National Taiwan University, Taipei, 106, Taiwan, Republic of China

    Huai-Yi Hsu

  2. Department of Electrical Engineering, National Taiwan University, Taipei, 106, Taiwan, Republic of China

    Sheng-Feng Wang

  3. Graduate Institute of Electronics Engineering and Department of Electrical Engineering, National Taiwan University, Taipei, 106, Taiwan, Republic of China

    An-Yeu (Andy) Wu

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  1. Huai-Yi Hsu
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  2. Sheng-Feng Wang
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  3. An-Yeu (Andy) Wu
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Hsu, HY., Wang, SF. & Wu, AY.(. A Novel Low-Cost Multi-Mode Reed Solomon Decoder Design Based on Peterson-Gorenstein-Zierler Algorithm. The Journal of VLSI Signal Processing-Systems for Signal, Image, and Video Technology 34, 251–259 (2003). https://doi.org/10.1023/A:1023200419497

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  • DOI: https://doi.org/10.1023/A:1023200419497

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