Low-Complexity Encoding of Binary Quasi-Cyclic Codes Based on Galois Fourier Transform
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This paper presents a novel low-complexity encoding algorithm for binary quasi-cyclic (QC) codes based on matrix transformation. First, a message vector is encoded into a transformed codeword in the transform domain. Then, the transmitted codeword is obtained from the transformed codeword by the inverse Galois Fourier transform. Moreover, a simple and fast mapping is devised to post-process the transformed codeword such that the transmitted codeword is binary as well. The complexity of our proposed encoding algorithm is less than ek(n-k)log2 e+ne(log22 e+log2 e)+ n/2 elog32 e bit operations for binary codes. This complexity is much lower than its traditional complexity 2e2(n - k)k. In the examples of encoding the binary (4095, 2016) and (15500, 10850) QC codes, the complexities are 12.09% and 9.49% of those of traditional encoding, respectively. © 2013 IEEE.
author list (cited authors)
Tang, L. i., Huang, Q., Wang, Z., & Xiong, Z.