The Implementation and Improvement of List Decoding of Reed-Solomon Codes 余敏男、胡大湘
E-mail: [email protected]
ABSTRACT
Reed-Solomon codes are known for their powerful correct error capacity. Several years ago, the innovative notion of decoding delivered by Madhu Sudan was probably beyond the original bound. Years later, Ron M. Roth and Gitit Ruckenstein presented a new decoding algorithm according to the Madhu Sudan’s concept. In this paper, the research is based on the list decoding of RS codes which is presented by some predecessors. The list decoding of an RS code is complicated. Consequently, the modified list decoding is proposed and carried out by VDHL language and C program. Eventually, the comparison and analysis of improved decoder are apparently presented the elevated efficiency.
Keywords : list decoding ; interpolation ; factorization
Table of Contents
Inside Front Cover Signature Page Authorized Copyright Statement．．．．．．．．．．．．．．．．．．．．．iii English Abstract．．．．．．．．．．．．．．．．．．．．．．．．．．．．．iv Chinese Abstract．．．．．．．．．．．．．
．．．．．．．．．．．．．．．．v Acknowledgement．．．．．．．．．．．．．．．．．．．．．．．．．．．．
．vi Table of Contents．．．．．．．．．．．．．．．．．．．．．．．．．．．．vii Table of Figures．．．．．．．．
．．．．．．．．．．．．．．．．．．．．ix List of tables．．．．．．．．．．．．．．．．．．．．．．．．．．．
．．x Chapter 1 Introduction 1.1 Historical background．．．．．．．．．．．．．．．．．．．．．．． 1 1.2 Framework
．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．2 Chapter 2 List Decoding of RS Codes 2.1 Encoder．．
．．．．．．．．．．．．．．．．．．．．．．．．．．．．． 3 2.2 Syndrome．．．．．．．．．．．．．．．．．
．．．．．．．．．．．．．．4 2.3 Interpolation．．．．．．．．．．．．．．．．．．．．．．．．．．．．6 2.4 Computing the Polynomial．．．．．．．．．．．．．．．．．．．．11 2.5 Factorization．．．．．．．．．．．．．．
．．．．．．．．．．．．．14 Chapter 3 The Improvement of List Decoding of RS codes 3.1 Simplified Syndrome Polynomial
．．．．．．．．．．．．．．．．． 17 3.2 Modified Process of Decoding．．．．．．．．．．．．．．．．．．．20 Chapter 4 The Implementation of List Decoding of RS codes 4.1 The Implementation by Hardware Program．．．．．．．．．
．．．．． 27 4.1.1 Circuit for Addition and Multiplication．．．．．．．．．． 27 4.1.2 Circuit of Encoder．．．．．．．
．．．．．．．．．．．．．．． 32 4.1.3 Circuit of Decoder．．．．．．．．．．．．．．．．．．．．．．．． 33 4.2 The Implementation by Software Program．．．．．．．．．．．．．． 37 4.2.1 Decoder Designed by C Program．．．．
．．．．．．．．．．．．．． 37 4.2.2 Decode The Text File．．．．．．．．．．．．．．．．．．．．．．． 40 Chapter 5 Conclusion．．．．．．．．．．．．．．．．．．．．．．．．．． 43 Reference ．．．．．．．．．．．．
．．．．．．．．．．．．．．．．．．．． 44 REFERENCES
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