Low-complexity encoding of binary quasi-cyclic codes based on Galois Fourier transform

Li Tang, Qin Huang, Zulin Wang, Zixiang Xiong

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3 Citations (Scopus)


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.

Original languageEnglish
Title of host publication2013 IEEE International Symposium on Information Theory, ISIT 2013
PublisherIEEE, Institute of Electrical and Electronics Engineers
Number of pages5
ISBN (Print)9781479904464
Publication statusPublished - 2013
Externally publishedYes
EventIEEE International Symposium on Information Theory 2013 - Istanbul, Turkey
Duration: 7 Jul 201312 Jul 2013
https://ieeexplore.ieee.org/xpl/conhome/6597029/proceeding (Proceedings)


ConferenceIEEE International Symposium on Information Theory 2013
Abbreviated titleISIT 2013
Internet address

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