{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,29]],"date-time":"2025-10-29T13:39:34Z","timestamp":1761745174867,"version":"build-2065373602"},"reference-count":47,"publisher":"MDPI AG","issue":"8","license":[{"start":{"date-parts":[[2020,4,17]],"date-time":"2020-04-17T00:00:00Z","timestamp":1587081600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Sri Lanka Technological Campus, Padukka, Sri Lanka","award":["4.2099. \u0417\u0413. 2019"],"award-info":[{"award-number":["4.2099. \u0417\u0413. 2019"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>Secure and reliable information flow is one of the main challenges in social IoT and mobile networks. Information flow and data integrity is still an open research problem. In this paper, we develop new methods of constructing systematic and regular Low-Density Parity-Check Matrices (LDPCM), inspired by the structure of the Sarrus method and geometric designs. Furthermore, these codes have cyclic structure and therefore, are less complex in computation and also require less memory in hardware implementation. Besides, an optimal method of post-processing for deleting girths four is presented. Numerical results show that the codes constructed by these methods perform well over the additive white Gaussian noise (AWGN) channel when decoded with the sum-product LDPC iterative algorithms. The proposed methods can be very efficient in terms of reducing memory consumption and improving the convergence speed of the decoder particularly in IoT and mobile networks.<\/jats:p>","DOI":"10.3390\/s20082300","type":"journal-article","created":{"date-parts":[[2020,4,21]],"date-time":"2020-04-21T04:49:38Z","timestamp":1587444578000},"page":"2300","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":12,"title":["A New Construction of High Performance LDPC Matrices for Mobile Networks"],"prefix":"10.3390","volume":"20","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-1878-546X","authenticated-orcid":false,"given":"Moein","family":"Sarvaghad-Moghaddam","sequence":"first","affiliation":[{"name":"Quantum Design Automation Lab, Amirkabir University of Technology, Tehran 9821, Iran"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5912-0101","authenticated-orcid":false,"given":"Waheed","family":"Ullah","sequence":"additional","affiliation":[{"name":"School of Electrical and Information Engineering, University of the Witwatersrand, WITS 2050, South Africa"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7004-2930","authenticated-orcid":false,"given":"Dushantha Nalin K.","family":"Jayakody","sequence":"additional","affiliation":[{"name":"School of Computer Science and Robotics, National Research Tomsk Polytechnic University Tomsk, 634050 Tomsk, Russia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1729-3503","authenticated-orcid":false,"given":"Sofi\u00e8ne","family":"Affes","sequence":"additional","affiliation":[{"name":"Centre \u00c9nergie, Mat\u00e9riaux et Telecommunications, Institut National de la Recherche Scientifique,  Montreal, QC H5A 1K6, Canada"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2020,4,17]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Lee, H., and Kwon, J. (2015, January 5\u201328). Survey and Analysis of Information Sharing in Social IoT. Proceedings of the 2015 8th International Conference on Disaster Recovery and Business Continuity (DRBC), Jeju Island, Korea.","DOI":"10.1109\/DRBC.2015.13"},{"key":"ref_2","unstructured":"Minh, T.N. (2019). Confidentiality and Integrity for IoT\/Mobile Networks. Recent Trends in Communication Networks, IntechOpen."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"379","DOI":"10.1002\/j.1538-7305.1948.tb01338.x","article-title":"A mathematical theory of communication","volume":"27","author":"Shannon","year":"1948","journal-title":"Bell Syst. Tech. J."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"21","DOI":"10.1109\/TIT.1962.1057683","article-title":"Low-density parity-check codes","volume":"8","author":"Gallager","year":"1962","journal-title":"Ire Trans. Inf. Theory"},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"457","DOI":"10.1049\/el:19970362","article-title":"Near Shannon limit performance of low density parity check codes","volume":"33","author":"MacKay","year":"1997","journal-title":"Electron. Lett."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"399","DOI":"10.1109\/18.748992","article-title":"Good error-correcting codes based on very sparse matrices","volume":"45","author":"MacKay","year":"1999","journal-title":"IEEE Trans. Inf. Theory"},{"key":"ref_7","doi-asserted-by":"crossref","unstructured":"Ullah, W., and FengFan, Y. (2012). Improved Min-Sum Decoding Algorithm for Moderate Length Low Density Parity Check Codes. Computer, Informatics, Cybernetics and Applications, Springer.","DOI":"10.1007\/978-94-007-1839-5_101"},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"76","DOI":"10.1016\/j.phycom.2011.10.006","article-title":"Structured sublinear compressive sensing via belief propagation","volume":"5","author":"Dai","year":"2012","journal-title":"Phys. Commun."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"43","DOI":"10.1016\/j.phycom.2013.01.002","article-title":"Joint physical network coding and LDPC decoding for two way wireless relaying","volume":"6","author":"Xu","year":"2013","journal-title":"Phys. Commun."},{"key":"ref_10","unstructured":"(2020, March 25). Third Generation Partnership Project Document 25.212. Available online: https:\/\/www.etsi.org\/deliver\/etsi_ts\/125200_125299\/125212\/03.02.00_60\/ts_125212v030200p.pdf."},{"key":"ref_11","first-page":"5448","article-title":"QC LDPC Codes for MIMO and Cooperative Networks using Two Way Normalized Min-Sum Decoding","volume":"12","author":"Ullah","year":"2014","journal-title":"Telkomnika Indones. J. Electr. Eng."},{"key":"ref_12","doi-asserted-by":"crossref","unstructured":"Ullah, W., Jiang, T., Yang, F., and Aziz, S.M. (2011, January 23\u201325). Two-way normalization of min-sum decoding algorithm for medium and short length low density parity check codes. Proceedings of the 2011 7th International Conference on Wireless Communications, Networking and Mobile Computing, Wuhan, China.","DOI":"10.1109\/wicom.2011.6040177"},{"key":"ref_13","doi-asserted-by":"crossref","unstructured":"Roth, R.M., and Zeh, A. (2016, January 10\u201315). On spectral design methods for quasi-cyclic codes. Proceedings of the 2016 IEEE International Symposium on Information Theory (ISIT), Barcelona, Spain.","DOI":"10.1109\/ISIT.2016.7541471"},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"533","DOI":"10.1109\/TIT.1981.1056404","article-title":"A recursive approach to low complexity codes","volume":"27","author":"Tanner","year":"1981","journal-title":"IEEE Trans. Inf. Theory"},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"58","DOI":"10.1109\/4234.905935","article-title":"On the design of low-density parity-check codes within 0.0045 dB of the Shannon limit","volume":"5","author":"Chung","year":"2001","journal-title":"IEEE Commun. Lett."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"1788","DOI":"10.1109\/TIT.2004.831841","article-title":"Quasi cyclic low-density parity-check codes from circulant permutation matrices","volume":"50","author":"Fossorier","year":"2004","journal-title":"IEEE Trans. Inf. Theory"},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"585","DOI":"10.1109\/TIT.2011.2173244","article-title":"Quasi-Cyclic LDPC Codes: Influence of Proto- and Tanner-Graph Structure on Minimum Hamming Distance Upper Bounds","volume":"58","author":"Smarandache","year":"2012","journal-title":"IEEE Trans. Inf. Theory"},{"key":"ref_18","unstructured":"Okamura, T. (July, January 29). Designing LDPC codes using cyclic shifts. Proceedings of the IEEE International Symposium on Information Theory, Yokohama, Japan."},{"key":"ref_19","unstructured":"Virmani, S.H.G. (2009, January 22\u201324). LDPC for Wi-Fi and WiMAX technologies. Proceedings of the 2009 International Conference, n Emerging Trends in Electronic and Photonic Devices & Systems, Varanasi, India."},{"key":"ref_20","doi-asserted-by":"crossref","unstructured":"Marchand, C., and Boutillon, E. (2015, January 14\u201316). LDPC decoder architecture for DVB-S2 and DVB-S2X standards. Proceedings of the 2015 IEEE Workshop on Signal Processing Systems (SiPS), Hangzhou, China.","DOI":"10.1109\/SiPS.2015.7345034"},{"key":"ref_21","doi-asserted-by":"crossref","unstructured":"Sybis, M., Wesolowski, K., Jayasinghe, K., Venkatasubramanian, V., and Vukadinovic, V. (2016, January 18\u201321). Channel coding for ultra-reliable low-latency communication in 5G systems. Proceedings of the 2016 IEEE 84th vehicular technology conference (VTC-Fall), Montreal, QC, Canada.","DOI":"10.1109\/VTCFall.2016.7880930"},{"key":"ref_22","doi-asserted-by":"crossref","unstructured":"Ateya, A.A., Muthanna, A., Makolkina, M., and Koucheryavy, A. (2018, January 5\u20139). Study of 5G services standardization: Specifications and requirements. Proceedings of the 2018 10th International Congress on Ultra Modern Telecommunications and Control Systems and Workshops (ICUMT), Moscow, Russia.","DOI":"10.1109\/ICUMT.2018.8631201"},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"e17","DOI":"10.1017\/ATSIP.2019.10","article-title":"An overview of channel coding for 5G NR cellular communications","volume":"8","author":"Bae","year":"2019","journal-title":"Apsipa Trans. Signal Inf. Process."},{"key":"ref_24","doi-asserted-by":"crossref","unstructured":"Chen, P., Xie, Z., Fang, Y., Chen, Z., Mumtaz, S., and Rodrigues, J.J. (2019). Physical-layer network coding: An efficient technique for wireless communications. IEEE Netw.","DOI":"10.1109\/MNET.001.1900289"},{"key":"ref_25","first-page":"1365","article-title":"LCPC Error Correction Code for IoT Applications","volume":"58","author":"Mohd","year":"2010","journal-title":"IEEE Trans. Commun."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"2241","DOI":"10.1109\/JIOT.2018.2887086","article-title":"UAV communications for 5G and beyond: Recent advances and future trends","volume":"6","author":"Li","year":"2018","journal-title":"IEEE Internet Things J."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"619","DOI":"10.1109\/18.910578","article-title":"Design of capacity-approaching irregular low-density parity-check codes","volume":"47","author":"Richardson","year":"2001","journal-title":"IEEE Trans. Inf. Theory"},{"key":"ref_28","unstructured":"Hu, X.Y., Eleftheriou, E., and Arnold, D.M. (2001, January 25\u201329). Progressive edge-growth Tanner graphs. Proceedings of the IEEE Globecom, San Antonio, TX, USA."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"585","DOI":"10.1109\/18.910576","article-title":"Improved low-density parpity-check codes using irregular graphs","volume":"47","author":"Luby","year":"2001","journal-title":"IEEE Trans. Inf. Theory"},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"599","DOI":"10.1109\/18.910577","article-title":"The capacity of low-density parity-check codes under message-passing decoding","volume":"47","author":"Richardson","year":"2001","journal-title":"IEEE Trans. Inf. Theory"},{"key":"ref_31","unstructured":"Kschischang, F.R., Frey, B.J., and Loeliger, H.A. (2001, January 25\u201329). Extended bit-filling and LDPC code design. Proceedings of the IEEE Globecom, San Antonio, TX, USA."},{"key":"ref_32","doi-asserted-by":"crossref","unstructured":"Battaglioni, M., Baldi, M., and Paolini, E. (2017, January 28\u201331). Complexity-constrained spatially coupled LDPC codes based on protographs. Proceedings of the 2017 International Symposium on Wireless Communication Systems (ISWCS), Bologna, Italy.","DOI":"10.1109\/ISWCS.2017.8108160"},{"key":"ref_33","doi-asserted-by":"crossref","unstructured":"Genga, Y., Ogundile, O., Oyerinde, O., and Versfeld, J. (2017, January 18\u201320). A low complexity encoder construction for systematic quasi-cyclic LDPC codes. Proceedings of the 2017 IEEE AFRICON, Cape Town, South Africa.","DOI":"10.1109\/AFRCON.2017.8095475"},{"key":"ref_34","doi-asserted-by":"crossref","unstructured":"Fan, J.L. (2001). Array Codes as LDPC Codes. Constrained Coding and Soft Iterative Decoding, Springer.","DOI":"10.1007\/978-1-4615-1525-8"},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"3126","DOI":"10.1109\/TCOMM.2010.091710.090721","article-title":"Quasi-cyclic LDPC codes: An algebraic construction, rank analysis, and codes on Latin squares","volume":"58","author":"Zhang","year":"2010","journal-title":"IEEE Trans. Commun."},{"key":"ref_36","unstructured":"Recommendation, I., and G9960 (2020, March 28). Unified High-Speed Wireline-Based Home Networking Transceivers\u2013System Architecture and Physical Layer Specification. Available online: https:\/\/www.itu.int\/rec\/T-REC-G.9960."},{"key":"ref_37","unstructured":"CCSDS (2020, March 28). TM Synchronization and Channel Coding. Blue Book 2011. Available online: https:\/\/public.ccsds.org\/Pubs\/131x0b2ec1s.pdf."},{"key":"ref_38","unstructured":"Declercq, D., Fossorier, M., and Biglieri, E. (2014). Channel Coding: Theory, Algorithms, and Applications: Academic Press Library in Mobile and Wireless Communications, Academic Press."},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"1989","DOI":"10.1109\/COMST.2015.2436705","article-title":"A survey on protograph LDPC codes and their applications","volume":"17","author":"Fang","year":"2015","journal-title":"IEEE Commun. Surv. Tutor."},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"853","DOI":"10.1109\/LCOMM.2014.030914.132509","article-title":"Optimization of generalized VDMM for protograph-based LDPC coded BICM","volume":"18","author":"Tang","year":"2014","journal-title":"IEEE Commun. Lett."},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"85","DOI":"10.1109\/MVT.2019.2903343","article-title":"Outage-limit-approaching channel coding for future wireless communications: Root-protograph low-density parity-check codes","volume":"14","author":"Fang","year":"2019","journal-title":"IEEE Veh. Technol. Mag."},{"key":"ref_42","first-page":"211","article-title":"New method to compute determinant of a 3x3 matrix","volume":"3","author":"Hajrizaj","year":"2009","journal-title":"Int. J. Algebra"},{"key":"ref_43","unstructured":"Lin, S., and Costello, D.J. (2004). Error control coding, Pearson Education India."},{"key":"ref_44","first-page":"111","article-title":"Comprehensive Algorithmic Review and Analysis of LDPC Codes","volume":"16","author":"Ullah","year":"2015","journal-title":"Indones. J. Electr. Eng. Comput. Sci."},{"key":"ref_45","first-page":"19","article-title":"Flexible Construction of High-Girth Qc-Ldpc Codes","volume":"1","author":"Malema","year":"2012","journal-title":"Int. J. Comput. Sci. Appl."},{"key":"ref_46","unstructured":"Fan, J., and Xiao, Y. (2006, January 6\u20139). A design of LDPC codes with large girth based on the sub-matrix shifting. Proceedings of the 2006 IET International Conference on Wireless, Mobile and Multimedia Networks, Hangzhou, China."},{"key":"ref_47","doi-asserted-by":"crossref","unstructured":"Ryan, W., and Lin, S. (2009). Channel Codes: Classical and Modern, Cambridge University Press.","DOI":"10.1017\/CBO9780511803253"}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/20\/8\/2300\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,13]],"date-time":"2025-10-13T13:31:25Z","timestamp":1760362285000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/20\/8\/2300"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,4,17]]},"references-count":47,"journal-issue":{"issue":"8","published-online":{"date-parts":[[2020,4]]}},"alternative-id":["s20082300"],"URL":"https:\/\/doi.org\/10.3390\/s20082300","relation":{},"ISSN":["1424-8220"],"issn-type":[{"type":"electronic","value":"1424-8220"}],"subject":[],"published":{"date-parts":[[2020,4,17]]}}}