Low-Complexity Encoding of Binary Quasi-Cyclic Codes Based on Galois Fourier Transform Conference Paper uri icon


  • 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.

name of conference

  • 2013 IEEE International Symposium on Information Theory

published proceedings


author list (cited authors)

  • Tang, L. i., Huang, Q., Wang, Z., & Xiong, Z.

citation count

  • 4

complete list of authors

  • Tang, Li||Huang, Qin||Wang, Zulin||Xiong, Zixiang

publication date

  • July 2013