|Iterative Decoding of Non-Binary Cyclic Codes Using Minimum-Weight Dual Codewords
|Jiongyue Xing, Sun Yat-sen University, China; Martin Bossert, Sebastian Bitzer, Ulm University, Germany; Li Chen, Sun Yat-sen University, China
|C.3: Iterative Decoding
|Coding for Communications
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|This paper proposes a novel shift-sum decoding scheme for non-binary cyclic codes. Using minimum-weight dual codewords and their cyclic shifts, a reliability measure can be yielded as an indicator for the error position and the error magnitude. Based on this shift-sum decoding concept, a hard-decision iterative decoding algorithm is proposed, which can correct errors beyond half of the code's minimum Hamming distance. By utilizing reliability information from the channel, a soft-decision iterative decoding algorithm is further introduced to improve the decoding performance. These two shift-sum based iterative decoding algorithms are realized with polynomial multiplication and integer (or real number) comparisons, which are hardware-friendly. Simulation results on Reed-Solomon codes and non-binary BCH codes show the decoding potential of the proposed algorithms.