| Summary: | 博士 === 長庚大學 === 電機工程學系 === 105 === In this dissertation, we discuss four types of decoding over (2^m-1,2^m-4) Reed-Solomon (RS) code, and investigate the solutions for finding error locations and error values. Moreover, an algorithm for correcting both an error and an erasure of (2^m,2^m-3) extended RS codes is proposed. Using the algorithm, error locations and error values can be found by skipping the procedures of determining error location polynomial, finding the roots and calculating the deviation of error location polynomial.
In addition, a new decoder for RS codes is proposed. The decoder can correct both errors and erasures without computing the erasure locator, errata locator or errata evaluator polynomials, the computational complexity can be substantially reduced. Herein, complexity comparisons between the proposed decoder and the Truong-Jeng-Hung and Lin-Costello decoders are presented. The (255, 223) and (63, 39) RS codes are used as examples for complexity comparisons under the upper bounded condition of 2v+mu=d_min-1. The new decoder can save about 40% additions and multiplications when mu=d_min-1 as compared with the two related decoders. Furthermore, it can also save 50% of the required inverses for 0<=mu<=d_min-1.
Finally, applying above algorithms, a non-sequential decoding algorithm and an alternative hard-decision decoding algorithm are proposed for (2^m-1,2^m-5)^2 RS turbo product codes (TPCs). Simulation results show that the proposed algorithms have extra coding gain compared to general RS TPCs decoding.
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