{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T00:58:53Z","timestamp":1760057933582,"version":"build-2065373602"},"reference-count":28,"publisher":"MDPI AG","issue":"3","license":[{"start":{"date-parts":[[2025,2,28]],"date-time":"2025-02-28T00:00:00Z","timestamp":1740700800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Spectrum Relocation Fund (SRF)","award":["IRIG-106"],"award-info":[{"award-number":["IRIG-106"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>This paper examines the iterative decoding of low-density parity check (LDPC) codes concatenated with continuous phase modulation (CPM). As relevant case studies, we focus on the family of three CPM waveforms that are embodied in the IRIG-106 aeronautical telemetry standard. Two of these CPMs have recently had LDPC codes designed for them for the first time, and thus the decoding complexity of these new schemes is of interest when considering adoption into the standard. We provide comprehensive numerical results that characterize the performance and iteration statistics of the joint LDPC\u2013CPM decoder. These results identify the most advantageous decoder configurations and also expose a key design challenge, which is that LDPC-CPM decoders must deal with a large \u201cpeak to average\u201d ratio in terms of global iterations. We show how a properly designed reference simulation can be used as a design tool to explore the performance of a large range of candidate systems without need for further simulation. We develop a real-time decoder architecture with fixed complexity and show how such a decoder can still achieve a relatively large maximum number of global iterations by introducing a trade-off between decoding latency and maximum global iterations. Our discussion shows that this scheme is generally applicable to LDPC-based schemes. We conclude with a comprehensive design study that demonstrates the accuracy of our methodology and its attractive performance\u2013complexity trade-off.<\/jats:p>","DOI":"10.3390\/e27030255","type":"journal-article","created":{"date-parts":[[2025,2,28]],"date-time":"2025-02-28T10:12:33Z","timestamp":1740737553000},"page":"255","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Real-Time Decoder Architecture for LDPC\u2013CPM"],"prefix":"10.3390","volume":"27","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-3596-4523","authenticated-orcid":false,"given":"Erik","family":"Perrins","sequence":"first","affiliation":[{"name":"Department of Electrical Engineering and Computer Science, University of Kansas, Lawrence, KS 66049, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2025,2,28]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Anderson, J.B., Aulin, T., and Sundberg, C.E. (1986). Digital Phase Modulation, Plenum Press.","DOI":"10.1007\/978-1-4899-2031-7"},{"key":"ref_2","unstructured":"(2025, January 18). Range Commanders Council Telemetry Group, Range Commanders Council, White Sands Missile Range, New Mexico. IRIG Standard 106-2022: Telemetry Standards, Available online: https:\/\/www.irig106.org."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"956","DOI":"10.1109\/26.774833","article-title":"A Serial Concatenation Approach to Iterative Demodulation and Decoding","volume":"47","author":"Narayanan","year":"1999","journal-title":"IEEE Trans. Commun."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"1901","DOI":"10.1109\/26.966054","article-title":"Serially Concatenated Continuous Phase Modulation with Iterative Decoding","volume":"49","author":"Moqvist","year":"2001","journal-title":"IEEE Trans. Commun."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"1283","DOI":"10.1109\/TCOMM.2003.815076","article-title":"Design of Serial Concatenated MSK Schemes Based on Density Evolution","volume":"51","author":"Narayanan","year":"2003","journal-title":"IEEE Trans. Commun."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"1354","DOI":"10.1109\/TCOMM.2007.900614","article-title":"Reduced-Complexity Approach to Iterative Detection of Coded SOQPSK","volume":"55","author":"Perrins","year":"2007","journal-title":"IEEE Trans. Commun."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"1521","DOI":"10.1109\/TIT.2010.2040861","article-title":"Capacity-Achieving CPM Schemes","volume":"56","author":"Perotti","year":"2010","journal-title":"IEEE Trans. Inform. Theory"},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"2340","DOI":"10.1109\/TAES.2013.6621820","article-title":"FEC Systems for Aeronautical Telemetry","volume":"49","author":"Perrins","year":"2013","journal-title":"IEEE Trans. Aerosp. Electron. Syst."},{"key":"ref_9","doi-asserted-by":"crossref","unstructured":"Benaddi, T., Poulliat, C., Boucheret, M.L., Gadat, B., and Lesthievent, G. (July, January 29). Design of Unstructured and Protograph-Based LDPC Coded Continuous Phase Modulation. Proceedings of the 2014 IEEE International Symposium on Information Theory, Honolulu, HI, USA.","DOI":"10.1109\/ISIT.2014.6875180"},{"key":"ref_10","doi-asserted-by":"crossref","unstructured":"Xue, R., Wang, T., Sun, Y., and Tang, H. (2020). Optimized Design for NB-LDPC-Coded High-Order CPM: Power and Iterative Efficiencies. Symmetry, 12.","DOI":"10.3390\/sym12081353"},{"key":"ref_11","unstructured":"Perrins, E. (2023, January 23\u201326). LDPC Codes for IRIG-106 Waveforms: Part I\u2013Code Design. Proceedings of the International Telemetry Conference, Las Vegas, NV, USA."},{"key":"ref_12","unstructured":"Perrins, E. (2023, January 23\u201326). LDPC Codes for IRIG-106 Waveforms: Part II\u2013Receiver Design. Proceedings of the International Telemetry Conference, Las Vegas, NV, USA."},{"key":"ref_13","unstructured":"Perrins, E. (November, January 28). Spectrum-Efficient LDPC Codes for CPM. Proceedings of the IEEE Military Communications Conference, Washington, DC, USA."},{"key":"ref_14","unstructured":"Perrins, E. (2025). Protomatrix-Based LDPC Codes for Continuous Phase Modulation. IEEE Trans. Commun., submitted."},{"key":"ref_15","doi-asserted-by":"crossref","unstructured":"Hung, J.H., and Chen, S.G. (2011, January 14\u201315). A 16Gbps Real-Time BF-based LDPC Decoder for IEEE 802.3an Standard. Proceedings of the 2011 International Conference on Multimedia and Signal Processing, Guilin, China.","DOI":"10.1109\/CMSP.2011.19"},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"102832","DOI":"10.1016\/j.sysarc.2023.102832","article-title":"High-performance hard-input LDPC decoding on multi-core devices for optical space links","volume":"137","author":"Jego","year":"2023","journal-title":"J. Syst. Archit."},{"key":"ref_17","unstructured":"Zimmermann, E., Pattisapu, P., and Fettweis, G. (2005, January 4\u20138). Bit-flipping post-processing for forced convergence decoding of LDPC codes. Proceedings of the 2005 13th European Signal Processing Conference, Antalya, Turkey."},{"key":"ref_18","first-page":"91","article-title":"FPGA Implementation of 5G NR LDPC Codes","volume":"9","author":"Zekry","year":"2023","journal-title":"Adv. Sci. Technol. Eng. Syst. J."},{"key":"ref_19","doi-asserted-by":"crossref","unstructured":"Falcao, G., Andrade, J., Silva, V., and Sousa, L. (2011, January 22\u201327). Real-time DVB-S2 LDPC decoding on many-core GPU accelerators. Proceedings of the 2011 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), Prague, Czech Republic.","DOI":"10.1109\/ICASSP.2011.5946824"},{"key":"ref_20","unstructured":"Li, B., Zheng, J., Fang, Y., Yang, M., and Yan, Z. (2020). Dynamic Maximum Iteration Number Scheduling LDPC Decoder for Space-Based Internet of Things. IoT as a Service, Proceedings of the 5th EAI International Conference, IoTaaS 2019, Xi\u2019an, China, 16\u201317 November 2019, Springer International Publishing."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"260","DOI":"10.1109\/18.2634","article-title":"A Decomposition Approach to CPM","volume":"34","author":"Rimoldi","year":"1988","journal-title":"IEEE Trans. Inform. Theory"},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"286","DOI":"10.1109\/TAES.2007.357134","article-title":"Reduced Complexity Detectors for Multi-h CPM in Aeronautical Telemetry","volume":"43","author":"Perrins","year":"2007","journal-title":"IEEE Trans. Aerosp. Electron. Syst."},{"key":"ref_23","first-page":"4274","article-title":"PAM Decomposition of Ternary CPM With Duobinary Encoding","volume":"65","author":"Othman","year":"2017","journal-title":"IEEE Trans. Commun."},{"key":"ref_24","unstructured":"Perrins, E., and Rice, M. (2018, January 5\u20138). Unification of Signal Models for SOQPSK. Proceedings of the International Telemetering Conference, Glendale, AZ, USA."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"22","DOI":"10.1109\/4234.552145","article-title":"A Soft-Input Soft-Output APP Module for Iterative Decoding of Concatenated Codes","volume":"1","author":"Benedetto","year":"1997","journal-title":"IEEE Commun. Lett."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"2142","DOI":"10.1109\/JPROC.2007.905132","article-title":"The Development of Turbo and LDPC Codes for Deep-Space Applications","volume":"95","author":"Andrews","year":"2007","journal-title":"Proc. IEEE"},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"876","DOI":"10.1109\/JSAC.2009.090806","article-title":"Capacity-Approaching Protograph Codes","volume":"27","author":"Divsalar","year":"2009","journal-title":"IEEE J. Select. Areas Commun."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"338","DOI":"10.1109\/TCOM.1985.1096301","article-title":"Linear Receivers for Correlatively Coded MSK","volume":"33","author":"Galko","year":"1985","journal-title":"IEEE Trans. Commun."}],"container-title":["Entropy"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1099-4300\/27\/3\/255\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,9]],"date-time":"2025-10-09T16:44:42Z","timestamp":1760028282000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1099-4300\/27\/3\/255"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,2,28]]},"references-count":28,"journal-issue":{"issue":"3","published-online":{"date-parts":[[2025,3]]}},"alternative-id":["e27030255"],"URL":"https:\/\/doi.org\/10.3390\/e27030255","relation":{},"ISSN":["1099-4300"],"issn-type":[{"type":"electronic","value":"1099-4300"}],"subject":[],"published":{"date-parts":[[2025,2,28]]}}}