{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T04:10:43Z","timestamp":1760242243151,"version":"build-2065373602"},"reference-count":13,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2017,2,4]],"date-time":"2017-02-04T00:00:00Z","timestamp":1486166400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"the Major Frontier Project of Sichuan Province","award":["2015JY0282"],"award-info":[{"award-number":["2015JY0282"]}]},{"name":"the National High Technology Research and Development Program of China (863 Program)","award":["2015AA01A710"],"award-info":[{"award-number":["2015AA01A710"]}]},{"name":"the National Science Foundation of China","award":["61325005"],"award-info":[{"award-number":["61325005"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>In this paper, we investigate the effect of output quantization on the secrecy capacity of the binary-input Gaussian wiretap channel. As a result, a closed-form expression with infinite summation terms of the secrecy capacity of the binary-input Gaussian wiretap channel is derived for the case when both the legitimate receiver and the eavesdropper have unquantized outputs. In particular, computable tight upper and lower bounds on the secrecy capacity are obtained. Theoretically, we prove that when the legitimate receiver has unquantized outputs while the eavesdropper has binary quantized outputs, the secrecy capacity is larger than that when both the legitimate receiver and the eavesdropper have unquantized outputs or both have binary quantized outputs. Further, numerical results show that in the low signal-to-noise ratio (SNR) (of the main channel) region, the secrecy capacity of the binary input Gaussian wiretap channel when both the legitimate receiver and the eavesdropper have unquantized outputs is larger than the capacity when both the legitimate receiver and the eavesdropper have binary quantized outputs; as the SNR increases, the secrecy capacity when both the legitimate receiver and the eavesdropper have binary quantized outputs tends to overtake.<\/jats:p>","DOI":"10.3390\/e19020059","type":"journal-article","created":{"date-parts":[[2017,2,6]],"date-time":"2017-02-06T11:29:27Z","timestamp":1486380567000},"page":"59","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["On the Binary Input Gaussian Wiretap Channel with\/without Output Quantization"],"prefix":"10.3390","volume":"19","author":[{"given":"Chao","family":"Qi","sequence":"first","affiliation":[{"name":"Information Security and National Computing Grid Laboratory, Southwest Jiaotong University, 611756 Chengdu, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yanling","family":"Chen","sequence":"additional","affiliation":[{"name":"Institute of Digital Signal Processing, University of Duisburg-Essen, 47057 Duisburg, Germany"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"A.","family":"Vinck","sequence":"additional","affiliation":[{"name":"Institute of Digital Signal Processing, University of Duisburg-Essen, 47057 Duisburg, Germany"},{"name":"Center for Telecommunications, University of Johannesburg, Auckland Park 2006, South Africa"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2017,2,4]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"656","DOI":"10.1002\/j.1538-7305.1949.tb00928.x","article-title":"Communication theory of secrecy systems","volume":"28","author":"Shannon","year":"1949","journal-title":"Bell Syst. Tech. J."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"1355","DOI":"10.1002\/j.1538-7305.1975.tb02040.x","article-title":"The wire-tap channel","volume":"54","author":"Wyner","year":"1975","journal-title":"Bell Syst. Tech. J."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"339","DOI":"10.1109\/TIT.1978.1055892","article-title":"Broadcast channels with confidential messages","volume":"24","year":"1978","journal-title":"IEEE Trans. Inf. Theory"},{"key":"ref_4","doi-asserted-by":"crossref","unstructured":"Rodrigues, M.R.D., Somekh-Baruch, A., and Bloch, M. (2010, January 12\u201315). On Gaussian wiretap channels with M-PAM inputs. Proceedings of the 2010 European Wireless Conference, Lucca, Italy.","DOI":"10.1109\/EW.2010.5483475"},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"527","DOI":"10.1109\/LCOMM.2011.032811.102539","article-title":"On the secrecy rate of multi-antenna wiretap channel under finite-alphabet input","volume":"15","author":"Bashar","year":"2011","journal-title":"IEEE Commun. Lett."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"3816","DOI":"10.1109\/TCOMM.2012.091212.110199","article-title":"On secrecy rate analysis of MIMO wiretap channels driven by finite-alphabet input","volume":"60","author":"Bashar","year":"2012","journal-title":"IEEE Trans. Commun."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"551","DOI":"10.1109\/TIFS.2011.2139208","article-title":"Secret-sharing LDPC codes for the BPSK-constrained Gaussian wiretap channel","volume":"6","author":"Wong","year":"2011","journal-title":"IEEE Trans. Inf. Forensics Secur."},{"key":"ref_8","doi-asserted-by":"crossref","unstructured":"Bloch, M., and Barros, J. (2011). Physical-Layer Security: From Information Theory to Security Engineering, Cambridge University Press.","DOI":"10.1017\/CBO9780511977985"},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"451","DOI":"10.1109\/TIT.1978.1055917","article-title":"The Gaussian wire-tap channel","volume":"24","author":"Hellman","year":"1978","journal-title":"IEEE Trans. Inf. Theory"},{"key":"ref_10","unstructured":"Proakis, J.G. (2007). Digital Communications, McGraw-Hill Education. [5th ed.]."},{"key":"ref_11","unstructured":"Nasif, A., and Karystinos, G.N. (2005, January 16\u201318). Binary transmissions over additive Gaussian noise: A closed-form expression for the channel capacity. Proceedings of the 2005 Conference on Information Sciences and Systems (CISS), Dayton, OH, USA."},{"key":"ref_12","unstructured":"Cover, T.M., and Thomas, J.A. (2006). Elements of Information Theory, John Wiley and Sons. [2nd ed.]."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"625","DOI":"10.1109\/TIT.1977.1055763","article-title":"On a special class of wiretap channels","volume":"23","year":"1977","journal-title":"IEEE Trans. Inf. Theory"}],"container-title":["Entropy"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1099-4300\/19\/2\/59\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T18:27:28Z","timestamp":1760207248000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1099-4300\/19\/2\/59"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2017,2,4]]},"references-count":13,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2017,2]]}},"alternative-id":["e19020059"],"URL":"https:\/\/doi.org\/10.3390\/e19020059","relation":{},"ISSN":["1099-4300"],"issn-type":[{"type":"electronic","value":"1099-4300"}],"subject":[],"published":{"date-parts":[[2017,2,4]]}}}