{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T02:05:55Z","timestamp":1760234755021,"version":"build-2065373602"},"reference-count":35,"publisher":"MDPI AG","issue":"6","license":[{"start":{"date-parts":[[2021,6,21]],"date-time":"2021-06-21T00:00:00Z","timestamp":1624233600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>Forward error correction codes (FEC) are one of the vital sections of modern communication systems; therefore, recognition of the coding type is an important issue in non-cooperative communication. At present, the recognition of FEC codes is mainly concentrated in the field of semi-blind identification with known types of codes. However, based on information asymmetry, the receiver cannot know the types of channel coding previously used in non-cooperative systems such as cognitive radio and remote sensing of communication. Therefore, it is important to recognize the error-correcting encoding type with no prior information. Although the traditional algorithm can also recognize the type of codes, it is only applicable to the case without errors, and its practicability is poor. In the paper, we propose a new method to identify the types of FEC codes based on depth distribution in non-cooperative communication. The proposed algorithm can effectively recognize linear block codes, convolutional codes, and Turbo codes under a low error probability level, and has a higher robustness to noise transmission environment. In addition, an improved matrix estimation algorithm based on Gaussian elimination was adopted in this paper, which effectively improves the parameter identification in a noisy environment. Finally, we used a general framework to unify all the reconstruction algorithms to simplify the complexity of the algorithm. The simulation results show that, compared with the traditional algorithm based on matrix rank, the proposed algorithm has a better anti-interference performance. The method proposed is simple and convenient for engineering and practical applications.<\/jats:p>","DOI":"10.3390\/sym13061094","type":"journal-article","created":{"date-parts":[[2021,6,21]],"date-time":"2021-06-21T04:21:21Z","timestamp":1624249281000},"page":"1094","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Blind Recognition of Forward Error Correction Codes Based on a Depth Distribution Algorithm"],"prefix":"10.3390","volume":"13","author":[{"given":"Fan","family":"Mei","sequence":"first","affiliation":[{"name":"School of Electronic Countermeasures, National University of Defense Technology, Hefei 230000, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Hong","family":"Chen","sequence":"additional","affiliation":[{"name":"School of Electronic Countermeasures, National University of Defense Technology, Hefei 230000, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yingke","family":"Lei","sequence":"additional","affiliation":[{"name":"School of Electronic Countermeasures, National University of Defense Technology, Hefei 230000, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2021,6,21]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"595","DOI":"10.1109\/26.668727","article-title":"Adaptive coded modulation for fading channels","volume":"46","author":"Goldsmith","year":"1998","journal-title":"IEEE Trans. Commun."},{"key":"ref_2","doi-asserted-by":"crossref","unstructured":"Moosavi, R., and Larsson, E.G. (2011, January 5\u20139). A fast scheme for blind identification of channel codes. Proceedings of the IEEE Global Telecommunications Conference, Houston, TX, USA.","DOI":"10.1109\/GLOCOM.2011.6133507"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"1917","DOI":"10.1109\/LCOMM.2012.102612.121473","article-title":"Novel blind encoder parameter estimation for Turbo codes","volume":"16","author":"Debessu","year":"2012","journal-title":"IEEE Commun. Lett."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"1301","DOI":"10.1109\/LCOMM.2013.051313.130462","article-title":"Identification of non-binary LDPC codes using average LLR of syndrome a posteriori probability","volume":"17","author":"Xia","year":"2013","journal-title":"IEEE Commun. Lett."},{"key":"ref_5","first-page":"1","article-title":"Blind identification of the code word length for non-binary error-correcting codes in noisy transition","volume":"43","author":"Zrelli","year":"2015","journal-title":"EURASIP J. Wirel. Commun. Netw."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"2572","DOI":"10.1109\/TSP.2018.2816587","article-title":"Classification based on Euclidean distance distribution for blind identification of error correcting codes in noncooperative contexts","volume":"66","author":"Bonvard","year":"2018","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"199","DOI":"10.1016\/S0166-218X(00)00353-X","article-title":"Detection and recognition of a binary linear code","volume":"111","author":"Valembois","year":"2001","journal-title":"Discret. Appl. Math."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"2693","DOI":"10.1109\/TCOMM.2016.2561931","article-title":"Blind reconstruction of binary cyclic codes from unsynchronized bitstream","volume":"64","author":"Yardi","year":"2016","journal-title":"IEEE Trans. Commun."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"6151","DOI":"10.1109\/ACCESS.2017.2684189","article-title":"Parameter estimation of convolutional and helical interleavers in a noisy environment","volume":"5","author":"Ramabadran","year":"2017","journal-title":"IEEE Access"},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"260","DOI":"10.12720\/jcm.10.4.260-267","article-title":"Blind recognition of (n\u22121)\/n rate punctured convolutional encoders in a noisy environment","volume":"10","author":"Wengu","year":"2015","journal-title":"J. Commun."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"122","DOI":"10.1049\/iet-spr.2010.0343","article-title":"Algebraic method for blind recovery of punctured convolutional encoders from an erroneous bitstream","volume":"6","author":"Marazin","year":"2012","journal-title":"IET Signal Process."},{"key":"ref_12","doi-asserted-by":"crossref","unstructured":"C\u00f4te, M., and Sendrier, N. (2010, January 13\u201318). Reconstruction of a turbo-code interleaver from noisy observation. Proceedings of the 2010 IEEE International Symposium on Information Theory, Austin, TX, USA.","DOI":"10.1109\/ISIT.2010.5513364"},{"key":"ref_13","doi-asserted-by":"crossref","unstructured":"Barbier, J., and Letessier, J. (2009, January 13\u201315). Forward error correcting codes characterization based on rank properties. Proceedings of the IEEE International Conference on Wireless Communications & Signal Processing, Nanjing, China.","DOI":"10.1109\/WCSP.2009.5371733"},{"key":"ref_14","first-page":"1205","article-title":"Blind Identifying of Type of Linear Block Code and Convolutional Code Based on Run Feature","volume":"30","author":"Xinhao","year":"2015","journal-title":"J. Data Acquis. Proc."},{"key":"ref_15","unstructured":"Yisen, L. (2014). Research on the Technology of Turbo Coding Recognition in Non-Cooperative Communication, Xidian University."},{"key":"ref_16","unstructured":"Jing, Z. (2014). Research of Recognition and Analyzation Methods of Channel Codes, National University of Defense Technology."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"463","DOI":"10.1109\/TBC.2017.2704436","article-title":"Classification of error correcting codes and estimation of interleaver parameters in a noisy transmission environment","volume":"63","author":"Swaminathan","year":"2017","journal-title":"IEEE Trans. Broadcast."},{"key":"ref_18","doi-asserted-by":"crossref","unstructured":"Kwon, S., and Shin, D.J. (2021). Blind Classification of Error-Correcting Codes for Enhancing Spectral Efficiency of Wireless Networks. IEEE Trans. Broadcast., 1\u201313.","DOI":"10.1109\/TBC.2021.3061984"},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"102668","DOI":"10.1016\/j.dsp.2020.102668","article-title":"Fine-grained recognition of error correcting codes based on 1-D convolutional neural network","volume":"99","author":"Wang","year":"2020","journal-title":"Digit. Signal Process."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"102986","DOI":"10.1016\/j.dsp.2021.102986","article-title":"Recognition of error correcting codes based on CNN with block mechanism and embedding","volume":"111","author":"Li","year":"2021","journal-title":"Digit. Signal Process."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"1361","DOI":"10.1109\/18.605610","article-title":"The depth distribution\u2014A new characterization for linear codes","volume":"43","author":"Etzion","year":"1997","journal-title":"IEEE Trans. Inform. Theory"},{"key":"ref_22","unstructured":"Jingli, T. (2018). Research on Blind Recognition Technology for Linear Block Code, Hebei University."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"450","DOI":"10.1016\/j.sigpro.2008.09.012","article-title":"Blind detection of interleaver parameters","volume":"89","author":"Sicot","year":"2009","journal-title":"Signal Process."},{"key":"ref_24","first-page":"1","article-title":"Blind recovery of rate convolutional encoders in a noisy environment","volume":"168","author":"Marazin","year":"2015","journal-title":"EURASIP J. Wirel. Commun. Netw."},{"key":"ref_25","unstructured":"Chao, L., and Jin, G. (2006). Depth Distribution of Linear Block Codes over Finite Fields, National University of Defense Technology."},{"key":"ref_26","unstructured":"Daofu, Z. (2008). Research on Depth Distribution of Linear Codes and Generalized Derivatives of Binary Sequences, Hefei University of Technology."},{"key":"ref_27","unstructured":"Liye, S. (2007). Depth Distribution of Cyclic Codes, Central China Normal University."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"3146","DOI":"10.1109\/18.737545","article-title":"On integer-valued rational polynomials and depth distributions of binary codes","volume":"44","author":"Mitchell","year":"1998","journal-title":"IEEE Trans. Inform. Theory"},{"key":"ref_29","first-page":"68","article-title":"Research on Depth Distribution of Linear Codes","volume":"25","author":"Zhentao","year":"2002","journal-title":"J. Beijing Univ. Posts Telecommun."},{"key":"ref_30","unstructured":"Zhang, Y.G., Lou, C.Y., and Wang, T. (2014). A Blind Parameters Identification Method for Linear Block Code. (CN201010131103)."},{"key":"ref_31","doi-asserted-by":"crossref","unstructured":"Cluzeau, M. (2006, January 9\u201314). Block code reconstruction using iterative decoding techniques. Proceedings of the IEEE International Symposium on Information Theory, Seattle, WA, USA.","DOI":"10.1109\/ISIT.2006.261971"},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"140","DOI":"10.1109\/49.661103","article-title":"Turbo decoding as an instance of Pearl\u2019s belief propagation algorithm","volume":"16","author":"McEliece","year":"1998","journal-title":"IEEE J. Sel. Areas Commun."},{"key":"ref_33","unstructured":"Dandan, L. (2014). Research on Blind Recognition of Turbo Codes and Compressed Sensing System Based on LDPC Codes, Shandong University."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"1288","DOI":"10.1109\/TCOMM.2005.852852","article-title":"Reduced-Complexity Decoding of LDPC Codes","volume":"53","author":"Chen","year":"2005","journal-title":"IEEE Trans. Commun."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"673","DOI":"10.1109\/26.768759","article-title":"Reduced Complexity Iterative Decoding of Low-Density Parity Check Codes Based on Belief Propagation","volume":"47","author":"Fossorier","year":"1999","journal-title":"IEEE Trans. Commun."}],"container-title":["Symmetry"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2073-8994\/13\/6\/1094\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T06:19:53Z","timestamp":1760163593000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2073-8994\/13\/6\/1094"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,6,21]]},"references-count":35,"journal-issue":{"issue":"6","published-online":{"date-parts":[[2021,6]]}},"alternative-id":["sym13061094"],"URL":"https:\/\/doi.org\/10.3390\/sym13061094","relation":{},"ISSN":["2073-8994"],"issn-type":[{"type":"electronic","value":"2073-8994"}],"subject":[],"published":{"date-parts":[[2021,6,21]]}}}