{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T03:18:32Z","timestamp":1760239112308,"version":"build-2065373602"},"reference-count":40,"publisher":"MDPI AG","issue":"10","license":[{"start":{"date-parts":[[2020,10,1]],"date-time":"2020-10-01T00:00:00Z","timestamp":1601510400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Key Program of Scientific Research Plan of Universities in Xinjiang Uygur Autonomous Region of China","award":["XJEDU2020I003"],"award-info":[{"award-number":["XJEDU2020I003"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>Polar coding and sparse code multiple access (SCMA) are key technologies for 5G mobile communication, the joint design of them has a great significance to improve the overall performance of the transmitter-receiver symmetric wireless communication system. In this paper, we firstly propose a pruning iterative joint detection and decoding algorithm (PI-JDD) based on the confidence stability of resource nodes. Branches to be updated are dynamically pruned to avoid redundant iterative, which is able to reduce 24~50% complexity while achieving the approximate error performance of traditional serial joint iterative detection and decoding algorithm S-JIDD. Then, to further reduce the bit error rate (BER) of the receiver, a cyclic redundancy check (CRC) termination mechanism is added at the end of each joint iteration to avoid the convergence error caused by decoding deviation. Simulation results show that the addition of an early stopping criterion can achieve a remarkable performance gain compared with the S-JIDD algorithm. More importantly, the combined algorithm of the two proposed schemes can reduce the computational complexity while achieving better error performance.<\/jats:p>","DOI":"10.3390\/sym12101624","type":"journal-article","created":{"date-parts":[[2020,10,1]],"date-time":"2020-10-01T11:28:57Z","timestamp":1601551737000},"page":"1624","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["A Joint Detection and Decoding Scheme for PC-SCMA System Based on Pruning Iteration"],"prefix":"10.3390","volume":"12","author":[{"given":"Yongxing","family":"Zhang","sequence":"first","affiliation":[{"name":"Xinjiang Key Laboratory of Signal Detection and Processing, College of Information Science and Engineering, Xinjiang University, Urumqi 830046, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Wenping","family":"Ge","sequence":"additional","affiliation":[{"name":"Xinjiang Key Laboratory of Signal Detection and Processing, College of Information Science and Engineering, Xinjiang University, Urumqi 830046, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Pengju","family":"Zhang","sequence":"additional","affiliation":[{"name":"Xinjiang Key Laboratory of Signal Detection and Processing, College of Information Science and Engineering, Xinjiang University, Urumqi 830046, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Mengyao","family":"Gao","sequence":"additional","affiliation":[{"name":"Xinjiang Key Laboratory of Signal Detection and Processing, College of Information Science and Engineering, Xinjiang University, Urumqi 830046, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Gecheng","family":"Zhang","sequence":"additional","affiliation":[{"name":"Xinjiang Key Laboratory of Signal Detection and Processing, College of Information Science and Engineering, Xinjiang University, Urumqi 830046, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2020,10,1]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"3051","DOI":"10.1109\/TIT.2009.2021379","article-title":"Channel Polarization: A method for constructing capacity-achieving codes for symmetric binary-input memoryless channels","volume":"55","author":"Arikan","year":"2009","journal-title":"IEEE Trans. Inf. Theory"},{"key":"ref_2","doi-asserted-by":"crossref","unstructured":"Nikopour, H., and Baligh, H. (2013, January 8\u201311). Sparse code multiple access. Proceedings of the 2013 IEEE 24th Annual International Symposium on Personal, Indoor, and Mobile Radio Communications (PIMRC), London, UK.","DOI":"10.1109\/PIMRC.2013.6666156"},{"key":"ref_3","doi-asserted-by":"crossref","unstructured":"Taherzadeh, M., Nikopour, H., Bayesteh, A., and Baligh, H. (2014, January 14\u201317). SCMA Codebook design. Proceedings of the 2014 IEEE 80th Vehicular Technology Conference (VTC2014-Fall), Vancouver, BC, Canada.","DOI":"10.1109\/VTCFall.2014.6966170"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"1420","DOI":"10.1049\/iet-com.2019.0719","article-title":"Low complexity receiver of sparse code multiple access based on dynamic trellis","volume":"14","author":"Peng","year":"2020","journal-title":"IET Commun."},{"key":"ref_5","doi-asserted-by":"crossref","unstructured":"Tan, Y., Gao, Z., Guo, S., and Gao, F. (2017, January 27\u201330). A dynamic multiuser detection scheme for uplink SCMA system. Proceedings of the 2017 IEEE 17th International Conference on Communication Technology (ICCT), Chengdu, China.","DOI":"10.1109\/ICCT.2017.8359713"},{"key":"ref_6","first-page":"1888","article-title":"Multiuser detection scheme for SCMA systems based on serial strategy","volume":"38","author":"Du","year":"2016","journal-title":"Electron. Inf. Technol."},{"key":"ref_7","doi-asserted-by":"crossref","unstructured":"Arikan, E., and Telatar, E. (July, January 28). On the rate of channel polarization. Proceedings of the 2009 IEEE International Symposium on Information Theory, Seoul, Korea.","DOI":"10.1109\/ISIT.2009.5205856"},{"key":"ref_8","doi-asserted-by":"crossref","unstructured":"Hassani, S.H., and Urbanke, R. (2012, January 1\u20136). Polar codes: Robustness of the successive cancellation decoder with respect to quantization. Proceedings of the 2012 IEEE International Symposium on Information Theory, Cambridge, MA, USA.","DOI":"10.1109\/ISIT.2012.6283642"},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"2213","DOI":"10.1109\/TIT.2015.2410251","article-title":"List Decoding of polar codes","volume":"61","author":"Tal","year":"2015","journal-title":"IEEE Trans. Inf. Theory"},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"695","DOI":"10.1049\/el.2012.1459","article-title":"Stack decoding of polar codes","volume":"48","author":"Niu","year":"2012","journal-title":"Electron. Lett."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"3100","DOI":"10.1109\/TCOMM.2013.070213.120789","article-title":"Improved successive cancellation decoding of polar codes","volume":"61","author":"Chen","year":"2013","journal-title":"IEEE Trans. Commun."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"447","DOI":"10.1109\/LCOMM.2008.080017","article-title":"A performance comparison of polar codes and Reed-Muller codes","volume":"12","author":"Arkan","year":"2008","journal-title":"IEEE Commun. Lett."},{"key":"ref_13","doi-asserted-by":"crossref","unstructured":"Elkelesh, A., Ebada, M., Cammerer, S., and Brink, S.T. (2018, January 15\u201318). Belief propagation decoding of polar codes on permuted factor graphs. Proceedings of the 2018 IEEE Wireless Communications and Networking Conference (WCNC), Barcelona, Spain.","DOI":"10.1109\/WCNC.2018.8377158"},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"87","DOI":"10.1109\/TVLSI.2016.2577883","article-title":"Efficient soft cancelation decoder architectures for polar codes","volume":"25","author":"Lin","year":"2017","journal-title":"IEEE Trans. Very Large Scale Integr. (VLSI) Syst."},{"key":"ref_15","doi-asserted-by":"crossref","unstructured":"Fayyaz, U.U., and Barry, J.R. (2013, January 9\u201313). Polar codes for partial response channels. Proceedings of the 2013 IEEE International Conference on Communications (ICC), Budapest, Hungary.","DOI":"10.1109\/ICC.2013.6655247"},{"key":"ref_16","first-page":"2739","article-title":"Joint detection and decoding technology of SCMA and polarization code","volume":"36","author":"Fu","year":"2019","journal-title":"Appl. Res. Comput."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"52014","DOI":"10.1109\/ACCESS.2018.2869906","article-title":"Design and optimization of joint iterative detection and decoding receiver for uplink polar coded SCMA system","volume":"6","author":"Pan","year":"2018","journal-title":"IEEE Access"},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"102283","DOI":"10.1016\/j.yofte.2020.102283","article-title":"The optimization scheme for joint iterative detection and decoding of polar coded SCMA system","volume":"58","author":"Zhang","year":"2020","journal-title":"Opt. Fiber Technol."},{"key":"ref_19","doi-asserted-by":"crossref","unstructured":"Miao, J., Hu, X., and Zhao, Z. (2019, January 11\u201313). A Low Complexity Multiuser Detection Scheme with Dynamic Factor Graph for Uplink SCMA Systems. Proceedings of the 2019 IEEE\/CIC International Conference on Communications Workshops in China (ICCC Workshops), Changchun, China.","DOI":"10.1109\/ICCChina.2019.8855813"},{"key":"ref_20","doi-asserted-by":"crossref","unstructured":"Sun, S., Cho, S.-G., and Zhang, Z. (2016, January 6\u20139). Error patterns in belief propagation decoding of polar codes and their mitigation methods. Proceedings of the 2016 50th Asilomar Conference on Signals, Systems and Computers, Pacific Grove, CA, USA.","DOI":"10.1109\/ACSSC.2016.7869562"},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"6496","DOI":"10.1109\/TSP.2014.2366712","article-title":"Early stopping criteria for energy-efficient low-latency belief-propagation polar code decoders","volume":"62","author":"Yuan","year":"2014","journal-title":"IEEE Trans. Signal. Process."},{"key":"ref_22","doi-asserted-by":"crossref","unstructured":"Nikopour, H., Yi, E., Bayesteh, A., Au, K., Hawryluck, M., Baligh, H., and Ma, J. (2014, January 18\u201312). SCMA for downlink multiple access of 5G wireless networks. Proceedings of the 2014 IEEE Global Communications Conference, Austin, TX, USA.","DOI":"10.1109\/GLOCOM.2014.7037423"},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"33796","DOI":"10.1109\/ACCESS.2018.2842233","article-title":"Enabling high order SCMA systems in downlink scenarios with a serial coding scheme","volume":"6","author":"Han","year":"2018","journal-title":"IEEE Access"},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"1073","DOI":"10.1109\/LWC.2019.2906617","article-title":"BER performance of multicast SCMA systems","volume":"8","author":"Zhang","year":"2019","journal-title":"IEEE Wirel. Commun. Lett."},{"key":"ref_25","doi-asserted-by":"crossref","unstructured":"Wu, Y., Zhang, S., and Chen, Y. (2015, January 8\u201312). Iterative multiuser receiver in sparse code multiple access systems. Proceedings of the 2015 IEEE International Conference on Communications (ICC), London, UK.","DOI":"10.1109\/ICC.2015.7248770"},{"key":"ref_26","unstructured":"Hagenauer, J., and G\u00f6rtz, N. (April, January 31). The turbo principle in joint source-channel coding. Proceedings of the 2003 IEEE Information Theory Workshop (Cat. No.03EX674), Paris, France."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"1046","DOI":"10.1109\/26.774855","article-title":"Iterative (turbo) soft interference cancellation and decoding for coded CDMA","volume":"47","author":"Wang","year":"1999","journal-title":"IEEE Trans. Commun."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"1437","DOI":"10.1109\/TIT.2005.844064","article-title":"LDPC coded MIMO multiple access with iterative joint decoding","volume":"51","author":"Sanderovich","year":"2005","journal-title":"IEEE Trans. Inf. Theory"},{"key":"ref_29","doi-asserted-by":"crossref","unstructured":"Ren, B., Han, S., Meng, W., Li, C., Wu, X., and Sha, X. (2015, January 2\u20134). Enhanced turbo detection for SCMA based on information reliability. Proceedings of the 2015 IEEE\/CIC International Conference on Communications in China (ICCC), Shenzhen, China.","DOI":"10.1109\/ICCChina.2015.7448608"},{"key":"ref_30","doi-asserted-by":"crossref","unstructured":"Zhang, Z., Han, K., Hu, J., and Chen, J. (, January 4\u20138). Joint Detection and Decoding Schemes for Turbo Coded SCMA Systems. Proceedings of the 2016 IEEE Globecom Workshops (GC Wkshps), Washington, DC, USA.","DOI":"10.1109\/GLOCOMW.2016.7848941"},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"115","DOI":"10.1109\/LCOMM.2012.112812.122249","article-title":"EXIT chart based design of irregular LDPC codes for large-MIMO systems","volume":"17","author":"Narasimhan","year":"2012","journal-title":"IEEE Commun. Lett."},{"key":"ref_32","doi-asserted-by":"crossref","unstructured":"Narasimhan, T.L., Chockalingam, A., and Rajan, B.S. (2012, January 6\u20139). Factor graph based joint detection\/decoding for LDPC coded large-MIMO systems. Proceedings of the 2012 IEEE 75th Vehicular Technology Conference (VTC Spring), Yokohama, Japan.","DOI":"10.1109\/VETECS.2012.6240094"},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"1410","DOI":"10.1109\/TIT.2002.1003830","article-title":"Joint message-passing decoding of LDPC codes and partial-response channels","volume":"48","author":"Kurkoski","year":"2002","journal-title":"IEEE Trans. Inf. Theory"},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"707","DOI":"10.1049\/iet-com.2014.0616","article-title":"Joint sparse graph over GF (q) for code division multiple access systems","volume":"9","author":"Wen","year":"2015","journal-title":"IET Commun."},{"key":"ref_35","doi-asserted-by":"crossref","unstructured":"Xiao, B., Xiao, K., Zhang, S., Chen, Z., Xia, B., Liu, H., Baicen, X., Kexin, X., Shutian, Z., and Zhiyong, C. (2015, January 15\u201317). Iterative detection and decoding for SCMA systems with LDPC codes. Proceedings of the 2015 International Conference on Wireless Communications & Signal Processing (WCSP), Nanjing, China.","DOI":"10.1109\/WCSP.2015.7341325"},{"key":"ref_36","doi-asserted-by":"crossref","unstructured":"Han, K., Zhang, Z., Hu, J., and Chen, J. (2016, January 4\u20138). A High performance joint detection and decoding scheme for LDPC coded SCMA system. Proceedings of the 2016 IEEE Globecom Workshops (GC Wkshops), Washington, DC, USA.","DOI":"10.1109\/GLOCOMW.2016.7848813"},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"3571","DOI":"10.1109\/TCSI.2019.2925826","article-title":"An LDPC-coded SCMA receiver with multi-user iterative detection and decoding","volume":"66","author":"Sun","year":"2019","journal-title":"IEEE Trans. Circuits Syst. I Regul. Pap."},{"key":"ref_38","doi-asserted-by":"crossref","unstructured":"Hao, Y., Xiao, K., Chen, Z., and Xia, B. (2017, January 11\u201313). Density evolution analysis of LDPC-coded SCMA systems. Proceedings of the 2017 9th International Conference on Wireless Communications and Signal Processing (WCSP), Nanjing, China.","DOI":"10.1109\/WCSP.2017.8171149"},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"25066","DOI":"10.1109\/ACCESS.2018.2828126","article-title":"Sub-graph based joint sparse graph for sparse code multiple access systems","volume":"6","author":"Lai","year":"2018","journal-title":"IEEE Access"},{"key":"ref_40","unstructured":"Dai, J., Niu, K., Si, Z., and Lin, J. (2015, January 5\u201311). Evaluation and optimization of Gaussian approximation for polar codes. Proceedings of the American Society for Information Science and Technology, St. Louis, MO, USA."}],"container-title":["Symmetry"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2073-8994\/12\/10\/1624\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T10:15:47Z","timestamp":1760177747000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2073-8994\/12\/10\/1624"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,10,1]]},"references-count":40,"journal-issue":{"issue":"10","published-online":{"date-parts":[[2020,10]]}},"alternative-id":["sym12101624"],"URL":"https:\/\/doi.org\/10.3390\/sym12101624","relation":{},"ISSN":["2073-8994"],"issn-type":[{"type":"electronic","value":"2073-8994"}],"subject":[],"published":{"date-parts":[[2020,10,1]]}}}