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The cost of the encoders of QC\u2010LDPC codes mainly depends on the number of non\u2010zero entries in the SC generator matrices. This study introduces a novel construction of SC generator matrices based on matrix transformations via Galois Fourier transform. By revealing the structure of SC generator matrices in the transform domain, an algorithm is proposed to reduce the density of the generator matrices of QC\u2010LDPC codes. Furthermore, a tight upper bound on ranks of QC matrices is derived. Based on the bound, rank distributions of parity\u2010check matrices and generator matrices in the transform domain illustrate the efficiency of the proposed algorithm. Simulation results show that the density of their SC generator matrices can be significantly decreased with moderate computational complexity.<\/jats:p>","DOI":"10.1049\/iet-com.2014.0178","type":"journal-article","created":{"date-parts":[[2014,8,4]],"date-time":"2014-08-04T16:09:59Z","timestamp":1407168599000},"page":"2547-2555","source":"Crossref","is-referenced-by-count":3,"title":["Density optimisation of generator matrices of quasi\u2010cyclic low\u2010density parity\u2010check codes and their rank analysis"],"prefix":"10.1049","volume":"8","author":[{"given":"Mu","family":"Zhang","sequence":"first","affiliation":[{"name":"School of Electronic and Information Engineering Beihang University Beijing 100191 People's Republic of China"}]},{"given":"Qin","family":"Huang","sequence":"additional","affiliation":[{"name":"School of Electronic and Information Engineering Beihang University Beijing 100191 People's Republic of China"}]},{"given":"Zulin","family":"Wang","sequence":"additional","affiliation":[{"name":"School of Electronic and Information Engineering Beihang University Beijing 100191 People's Republic of China"}]},{"given":"Shuai","family":"Yuan","sequence":"additional","affiliation":[{"name":"School of Electronic and Information Engineering Beihang University Beijing 100191 People's Republic of China"}]},{"given":"Zhe","family":"Liu","sequence":"additional","affiliation":[{"name":"School of Electronic and Information Engineering Beihang University Beijing 100191 People's Republic of China"}]}],"member":"265","published-online":{"date-parts":[[2014,9]]},"reference":[{"key":"e_1_2_8_2_1","doi-asserted-by":"publisher","DOI":"10.1109\/TIT.2004.831841"},{"key":"e_1_2_8_3_1","doi-asserted-by":"publisher","DOI":"10.1109\/TCSI.2005.844113"},{"key":"e_1_2_8_4_1","doi-asserted-by":"publisher","DOI":"10.1109\/TVLSI.2007.891098"},{"key":"e_1_2_8_5_1","doi-asserted-by":"publisher","DOI":"10.1109\/TIT.2007.899516"},{"key":"e_1_2_8_6_1","doi-asserted-by":"publisher","DOI":"10.1109\/TIT.2007.892770"},{"key":"e_1_2_8_7_1","doi-asserted-by":"publisher","DOI":"10.1109\/TCOMM.2003.822172"},{"key":"e_1_2_8_8_1","doi-asserted-by":"publisher","DOI":"10.1109\/JSAC.2009.090803"},{"key":"e_1_2_8_9_1","doi-asserted-by":"publisher","DOI":"10.1109\/18.910579"},{"key":"e_1_2_8_10_1","unstructured":"IEEE 802 LAN\/MAN Standards Committee:\u2018Wireless LAN medium access control (MAC) and physical layer (PHY) specifications\u2019 IEEE Standard 802.11 1999 edition 1999"},{"key":"e_1_2_8_11_1","doi-asserted-by":"publisher","DOI":"10.1109\/MCOM.2009.5273821"},{"key":"e_1_2_8_12_1","unstructured":"WangJ. 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