{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T04:30:57Z","timestamp":1760243457301,"version":"build-2065373602"},"reference-count":36,"publisher":"MDPI AG","issue":"5","license":[{"start":{"date-parts":[[2013,5,8]],"date-time":"2013-05-08T00:00:00Z","timestamp":1367971200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/3.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>A method of blind recognition of the coding parameters for binary  Bose-Chaudhuri-Hocquenghem (BCH) codes is proposed in this paper. We consider an intelligent communication receiver which can blindly recognize the coding parameters of the received data stream. The only knowledge is that the stream is encoded using binary BCH codes, while the coding parameters are unknown. The problem can be addressed on the context of the non-cooperative communications or adaptive coding and modulations (ACM) for cognitive radio networks. The recognition processing includes two major procedures: code length estimation and generator polynomial reconstruction. A hard decision method has been proposed in a previous literature. In this paper we propose the recognition approach in soft decision situations with Binary-Phase-Shift-Key modulations and Additive-White-Gaussian-Noise (AWGN) channels. The code length is estimated by maximizing the root information dispersion entropy function. And then we search for the code roots to reconstruct the primitive and generator polynomials. By utilizing the soft output of the channel, the recognition performance is improved and the simulations show the efficiency of the proposed algorithm.<\/jats:p>","DOI":"10.3390\/e15051705","type":"journal-article","created":{"date-parts":[[2013,5,8]],"date-time":"2013-05-08T11:26:23Z","timestamp":1368012383000},"page":"1705-1725","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":20,"title":["Information-Dispersion-Entropy-Based Blind Recognition of Binary BCH Codes in Soft Decision Situations"],"prefix":"10.3390","volume":"15","author":[{"given":"Jing","family":"Zhou","sequence":"first","affiliation":[{"name":"School of Mechatronics Engineering and Automation, National University of Defense Technology, Deya Road, Changsha 410073, Hunan Province, China"}]},{"given":"Zhiping","family":"Huang","sequence":"additional","affiliation":[{"name":"School of Mechatronics Engineering and Automation, National University of Defense Technology, Deya Road, Changsha 410073, Hunan Province, China"}]},{"given":"Chunwu","family":"Liu","sequence":"additional","affiliation":[{"name":"School of Mechatronics Engineering and Automation, National University of Defense Technology, Deya Road, Changsha 410073, Hunan Province, China"}]},{"given":"Shaojing","family":"Su","sequence":"additional","affiliation":[{"name":"School of Mechatronics Engineering and Automation, National University of Defense Technology, Deya Road, Changsha 410073, Hunan Province, China"}]},{"given":"Yimeng","family":"Zhang","sequence":"additional","affiliation":[{"name":"School of Mechatronics Engineering and Automation, National University of Defense Technology, Deya Road, Changsha 410073, Hunan Province, China"}]}],"member":"1968","published-online":{"date-parts":[[2013,5,8]]},"reference":[{"key":"ref_1","unstructured":"Horton, J.M., and Riccardi, D.W. (2004). Error Control Coding: Fundamentals and Applications, Pearson Prentice Hall. [2nd ed.]."},{"key":"ref_2","unstructured":"Li, J. (2001). Error correcting coding: principles and methods, Xidian University Press."},{"key":"ref_3","unstructured":"Moreira, J.C., and Farrell, P.G. (2006). Essentials of Error-Control Coding, John Wiley & Sons Ltd."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"459","DOI":"10.1109\/TIT.1960.1057586","article-title":"Encoding and error-correction procedures for Bose-Chaudhuri codes","volume":"9","author":"Peterson","year":"1960","journal-title":"IRE Trans. Inf. Theory"},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"357","DOI":"10.1109\/TIT.1964.1053699","article-title":"Cyclic Decoding procedure for the Bose-Chaudhuri-Hocquenghem Codes","volume":"10","author":"Chien","year":"1964","journal-title":"IEEE Trans. Inf. Theory"},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"13","DOI":"10.1109\/98.788210","article-title":"Cognitive radio: making software radios more personal","volume":"6","author":"Mitola","year":"1999","journal-title":"IEEE Personal Commun."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"64","DOI":"10.3390\/e13010064","article-title":"A pattern construction scheme for neural network-based cognitive communication","volume":"13","author":"Oreay","year":"2011","journal-title":"Entropy"},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"3743","DOI":"10.1109\/TWC.2011.091911.101260","article-title":"Cognitive code-division links with blind primary-system identification","volume":"11","author":"Li","year":"2011","journal-title":"IEEE Trans. Wireless Commun."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"691","DOI":"10.3969\/j.issn.1004-4132.2011.04.020","article-title":"Joint power and spectrum allocation algorithm in cognitive radio networks","volume":"4","author":"Liu","year":"2011","journal-title":"J. Syst. Eng. Electron."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"1309","DOI":"10.1049\/iet-com.2010.0258","article-title":"Efficient exploration in reinforcement learning-based cognitive radio spectrum sharing","volume":"10","author":"Jiang","year":"2011","journal-title":"IET 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 errorneous bitstream","volume":"2","author":"Marazin","year":"2012","journal-title":"IET Signal Process."},{"key":"ref_12","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 54th GLOBECOM, Houston, TX, USA.","DOI":"10.1109\/GLOCOM.2011.6133507"},{"key":"ref_13","unstructured":"Marazin, M., Gautier, R., and Burel, G. (December, January 30). Dual code method for blind identification of convolutional encoder for cognitive radio receiver design. Proceedings of IEEE Globecom Workshops, Honolulu, HI, USA."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"595","DOI":"10.1109\/26.668727","article-title":"Adaptive coded modulation for fading channels","volume":"5","author":"Goldsmith","year":"1998","journal-title":"IEEE Trans. Commun."},{"key":"ref_15","unstructured":"Burel, G., and Gautier, R. (2003, January 17\u201319). Blind estimation of encoder and interleaver characteristics in a non cooperative context. Presented at International Conference on Communications, Internet and Information Technology, Scottsdale, AZ, USA."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"1290","DOI":"10.1109\/TSP.2009.2036062","article-title":"Blind reconstruction of linear space-time block codes: a likelihood-based approach","volume":"3","author":"Choqueuse","year":"2010","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_17","first-page":"1","article-title":"Blind recovery of k\/n rate convolutional encoders in a noisy environment","volume":"168","author":"Marazin","year":"2011","journal-title":"EURASIP J. Wireless Commun. Netw."},{"key":"ref_18","doi-asserted-by":"crossref","unstructured":"Wang, F., Huang, Z., and Zhou, Y. (2007, January 21\u201325). A method for blind recognition of convolution code based on Euclidean algorithm. Proceedings of IEEE WiCom, Shanghai, China.","DOI":"10.1109\/WICOM.2007.358"},{"key":"ref_19","doi-asserted-by":"crossref","unstructured":"Dignel, J., and Hagenauer, J. (2007, January 24\u201329). Parameter estimation of a convolutional encoder from noisy observations. Proceedings of IEEE ISIT, Nice, France.","DOI":"10.1109\/ISIT.2007.4557147"},{"key":"ref_20","first-page":"213","article-title":"Blind recovery of the second convolutional encoder of a turbo-code when its systematic outputs are punctured","volume":"2","author":"Marazin","year":"2009","journal-title":"Military Tech. Acad. Rev."},{"key":"ref_21","first-page":"167","article-title":"Blind recognition method for the Turbo coding parameters","volume":"2","author":"Yongguang","year":"2011","journal-title":"J. Xidian Univ."},{"key":"ref_22","first-page":"30","article-title":"Recognition methods of BCH codes","volume":"6","author":"Wen","year":"2010","journal-title":"Electron. Warf."},{"key":"ref_23","first-page":"69","article-title":"Recognition method of BCH codes on roots information dispersion entropy and roots statistic","volume":"3","author":"Yang","year":"2010","journal-title":"J. Detect. Control."},{"key":"ref_24","first-page":"187","article-title":"Fast recognition method of generator polynomial of BCH codes","volume":"6","author":"Lv","year":"2011","journal-title":"J. Xidian Univ."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"3083","DOI":"10.1109\/18.737537","article-title":"Bit error probability for maximum likelihood decoding of linear block codes and related soft decision decoding methods","volume":"11","author":"Fossorier","year":"1998","journal-title":"IEEE Trans. Inf. Theory."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"320","DOI":"10.1109\/18.312155","article-title":"An effifient maximum likelihood decoding of linear block codes with algebraic decoder","volume":"3","author":"Kaneko","year":"1994","journal-title":"IEEE Trans. Inf. Theory."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"3347","DOI":"10.1109\/TIT.2005.853321","article-title":"Iterative decoding of linear block codes: A parity-check orthogonalization approach","volume":"51","author":"Sankaranarayanan","year":"2005","journal-title":"IEEE Trans. Inf. Theory"},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"3746","DOI":"10.1109\/TIT.2006.878176","article-title":"Iterative soft-input-soft-output decoding of Reed-Solomon codes by adapting the parity check matrix","volume":"8","author":"Jiang","year":"2006","journal-title":"IEEE Trans. Inf. Theory."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"654","DOI":"10.3390\/e14040654","article-title":"A rotated quasi-othogonal space-time block code for asynchronous cooperative discovery","volume":"14","author":"Ni","year":"2012","journal-title":"Entropy"},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"429","DOI":"10.1109\/18.485714","article-title":"Iterative decoding of binary block and convolutional codes","volume":"2","author":"Hagenauer","year":"1996","journal-title":"IEEE Trans. Inf. Theory"},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"1574","DOI":"10.1109\/TCOMM.2009.06.070445","article-title":"Blind frame synchronization for error correcting codes having a sparse parity check matrix","volume":"6","author":"Imad","year":"2009","journal-title":"IEEE Trans. Commun."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"5472","DOI":"10.1109\/TWC.2009.090410","article-title":"Theoretical analysis of a MAP based blind frame synchronizer","volume":"11","author":"Imad","year":"2009","journal-title":"IEEE Trans. Wireless Commun."},{"key":"ref_33","doi-asserted-by":"crossref","unstructured":"Imad, R., Houcke, S., and Jego, C. (2009, January 14\u201318). Blind frame synchronization of product codes based on the adaptation of the parity check matrix. Proceedings of IEEE ICC2009, Dresden, Germany.","DOI":"10.1109\/ICC.2009.5198792"},{"key":"ref_34","doi-asserted-by":"crossref","unstructured":"Imad, R., Poulliat, C., Houcke, S., and Gadat, G. (2010, January 20\u201323). Blind frame synchronization of Reed-Solomon codes: Non-binary vs. binary approach. Proceedings of 2010 IEEE Eleventh International Workshop on Signal Processing Advances in Wireless Communications (SPAWC), Marrakech, Morocco.","DOI":"10.1109\/SPAWC.2010.5670870"},{"key":"ref_35","unstructured":"Moreira, J.C., and Farrell, P.G. (2006). Essentials of Error-Control Coding, John Wiley & Sons Ltd."},{"key":"ref_36","unstructured":"Horton, J.M., and Riccardi, D.W. (2004). Error Control Coding: Fundamentals and Applications, Pearson Prentice Hall. [2nd ed.]."}],"container-title":["Entropy"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1099-4300\/15\/5\/1705\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T21:46:37Z","timestamp":1760219197000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1099-4300\/15\/5\/1705"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2013,5,8]]},"references-count":36,"journal-issue":{"issue":"5","published-online":{"date-parts":[[2013,5]]}},"alternative-id":["e15051705"],"URL":"https:\/\/doi.org\/10.3390\/e15051705","relation":{},"ISSN":["1099-4300"],"issn-type":[{"type":"electronic","value":"1099-4300"}],"subject":[],"published":{"date-parts":[[2013,5,8]]}}}