{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T02:19:12Z","timestamp":1760149152030,"version":"build-2065373602"},"reference-count":16,"publisher":"MDPI AG","issue":"7","license":[{"start":{"date-parts":[[2023,7,11]],"date-time":"2023-07-11T00:00:00Z","timestamp":1689033600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"National Natural Science Foundation of China","award":["U19B2015","62271386","61801371"],"award-info":[{"award-number":["U19B2015","62271386","61801371"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>Spatially coupled low density parity check (SC-LDPC) are prominent candidates for future communication standards due to their \u201cthreshold saturation\u201d properties. To evaluate the finite-length performance of SC-LDPC codes, a general and efficient finite-length analysis from the perspective of the base matrix is proposed. We analyze the evolution of the residual graphs resulting at each iteration during the decoding process based on the base matrix and then derive the expression for the error probability. To verify the effectiveness of the proposed finite-length analysis, we consider the SC-LDPC code ensembles constructed by parallelly connecting multiple chains (PC-MSC-LDPC). The analysis results show that the predicted error probabilities obtained by using the derived expression for the error probability match the simulated error probabilities. The proposed finite-length analysis provides a useful engineering tool for practical SC-LDPC code design and for analyzing the effects of the code parameters on the performances.<\/jats:p>","DOI":"10.3390\/e25071041","type":"journal-article","created":{"date-parts":[[2023,7,12]],"date-time":"2023-07-12T00:50:41Z","timestamp":1689123041000},"page":"1041","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Finite-Length Analysis for Spatially Coupled LDPC Codes Based on Base Matrix"],"prefix":"10.3390","volume":"25","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-1859-6300","authenticated-orcid":false,"given":"Yang","family":"Liu","sequence":"first","affiliation":[{"name":"School of Communication and Information Engineering, Xi\u2019an University of Science and Technology, Xi\u2019an 710054, China"}]},{"given":"Sha","family":"Sun","sequence":"additional","affiliation":[{"name":"School of Communication and Information Engineering, Xi\u2019an University of Science and Technology, Xi\u2019an 710054, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1311-9786","authenticated-orcid":false,"given":"Yuzhi","family":"Zhang","sequence":"additional","affiliation":[{"name":"School of Communication and Information Engineering, Xi\u2019an University of Science and Technology, Xi\u2019an 710054, China"}]},{"given":"Bin","family":"Wang","sequence":"additional","affiliation":[{"name":"School of Communication and Information Engineering, Xi\u2019an University of Science and Technology, Xi\u2019an 710054, China"}]}],"member":"1968","published-online":{"date-parts":[[2023,7,11]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"803","DOI":"10.1109\/TIT.2010.2095072","article-title":"Threshold saturation via spatial coupling: Why convolutional LDPC ensembles perform so well over the BEC","volume":"57","author":"Kudekar","year":"2011","journal-title":"IEEE Trans. Inf. Theory"},{"key":"ref_2","doi-asserted-by":"crossref","unstructured":"Schmalen, L., and Aref, V. (2019, January 25\u201328). Spatially Coupled LDPC Codes with Non-uniform Coupling for Improved Decoding Speed. Proceedings of the IEEE Information Theory Workshop (ITW), Visby, Sweden.","DOI":"10.1109\/ITW44776.2019.8989360"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"3485","DOI":"10.1109\/TCOMM.2021.3060797","article-title":"Construction of Time Invariant Spatially Coupled LDPC Codes Free of Small Trapping Sets","volume":"69","author":"Naseri","year":"2021","journal-title":"IEEE Trans. Commun."},{"key":"ref_4","doi-asserted-by":"crossref","unstructured":"Amiri, B., Reisizadeh, A., Kliewer, J., and Dolecek, L. (2015, January 14\u201319). Optimized array-based spatially-coupled LDPC Codes: An absorbing set approach. 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