{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T01:39:38Z","timestamp":1760060378724,"version":"build-2065373602"},"reference-count":46,"publisher":"MDPI AG","issue":"9","license":[{"start":{"date-parts":[[2025,8,25]],"date-time":"2025-08-25T00:00:00Z","timestamp":1756080000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"NSFC","doi-asserted-by":"publisher","award":["62271482","22KJA510009","jit-b-202110"],"award-info":[{"award-number":["62271482","22KJA510009","jit-b-202110"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"name":"the Opening Project of Key Laboratory of Fabrication Technologies for Integrated Circuits, Chinese Academy of Sciences, the Key Project of Basic Science (Natural Science) Research in Higher Education Institutions of Jiangsu Province","award":["62271482","22KJA510009","jit-b-202110"],"award-info":[{"award-number":["62271482","22KJA510009","jit-b-202110"]}]},{"name":"JITSF","award":["62271482","22KJA510009","jit-b-202110"],"award-info":[{"award-number":["62271482","22KJA510009","jit-b-202110"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>In modern communication systems, the concatenation of a low-density parity-check (LDPC) code with a cyclic redundancy check (CRC) code is commonly used for error correction. In this paper, we propose a low-complexity two-stage scheme for decoding these codes using their concatenation structures. In the first stage, the traditional belief propagation (BP)-based iterative algorithm with a relative small maximum number of iterations is performed for decoding the LDPC code. If an LDPC codeword is obtained in this stage, the decoding process terminates. Otherwise, the second stage of the decoding process is performed, in which the guessing random additive noise decoding (GRAND) algorithm is applied to the CRC code. A list of information sequences satisfying the CRC check is obtained, each of which is then encoded to an LDPC codeword. The most likely codeword among them is the output of the decoding approach. The simulation results indicate that the proposed two-stage decoding approach can outperform the traditional BP-based iterative algorithm with a large maximum number of iterations. Moreover, the average complexity of the proposed approach is relatively low.<\/jats:p>","DOI":"10.3390\/e27090899","type":"journal-article","created":{"date-parts":[[2025,8,26]],"date-time":"2025-08-26T06:26:31Z","timestamp":1756189591000},"page":"899","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["An Efficient Two-Stage Decoding Scheme for LDPC-CRC Concatenated Codes"],"prefix":"10.3390","volume":"27","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-6452-5322","authenticated-orcid":false,"given":"Lingjun","family":"Kong","sequence":"first","affiliation":[{"name":"Faculty of Network and Telecommunication Engineering, Jinling Institute of Technology, Nanjing 211169, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6567-8603","authenticated-orcid":false,"given":"Haiyang","family":"Liu","sequence":"additional","affiliation":[{"name":"Institute of Microelectronics, Chinese Academy of Sciences, Beijing 100029, China"}]},{"given":"Yuezhuang","family":"Shi","sequence":"additional","affiliation":[{"name":"Institute of Microelectronics, Chinese Academy of Sciences, Beijing 100029, China"},{"name":"University of Chinese Academy of Sciences, Beijing 100049, China"}]},{"ORCID":"https:\/\/orcid.org\/0009-0008-2749-8204","authenticated-orcid":false,"given":"Jiacheng","family":"Miao","sequence":"additional","affiliation":[{"name":"Faculty of Network and Telecommunication Engineering, Jinling Institute of Technology, Nanjing 211169, China"}]}],"member":"1968","published-online":{"date-parts":[[2025,8,25]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"868","DOI":"10.1109\/COMST.2023.3243918","article-title":"Twelve scientific challenges for 6G: Rethinking the foundations of communications theory","volume":"25","author":"Chafii","year":"2023","journal-title":"IEEE Commun. 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