{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,27]],"date-time":"2025-10-27T16:26:52Z","timestamp":1761582412135},"reference-count":33,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2014,4,16]],"date-time":"2014-04-16T00:00:00Z","timestamp":1397606400000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/2.0"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["J Wireless Com Network"],"published-print":{"date-parts":[[2014,12]]},"abstract":"<jats:title>Abstract<\/jats:title>\n          <jats:p>In this paper, a class of state-dependent relay channel with orthogonal channels from the source to the relay and from the source and the relay to the destination is studied. The two orthogonal channels are corrupted by two independent channel states <jats:italic>S<\/jats:italic>\n            <jats:sub>R<\/jats:sub> and <jats:italic>S<\/jats:italic>\n            <jats:sub>D<\/jats:sub>, respectively, which are known to both the source and the relay. The lower bounds on the capacity are established for the channel either with non-causal channel state information or with causal channel state information. Further, we show that the lower bound with non-causal channel state information is tight if the receiver output <jats:italic>Y<\/jats:italic> is a deterministic function of the relay input <jats:italic>X<\/jats:italic>\n            <jats:sub>r<\/jats:sub>, the channel state <jats:italic>S<\/jats:italic>\n            <jats:sub>D,<\/jats:sub> and one of the source inputs <jats:italic>X<\/jats:italic>\n            <jats:sub>D<\/jats:sub>, i.e., <jats:italic>Y<\/jats:italic>\u2009=\u2009<jats:italic>f<\/jats:italic>(<jats:italic>X<\/jats:italic>\n            <jats:sub>D<\/jats:sub>, <jats:italic>X<\/jats:italic>\n            <jats:sub>r<\/jats:sub>, <jats:italic>S<\/jats:italic>\n            <jats:sub>D<\/jats:sub>), and the relay output <jats:italic>Y<\/jats:italic>\n            <jats:sub>r<\/jats:sub> is restricted to be controlled by only the source input <jats:italic>X<\/jats:italic>\n            <jats:sub>R<\/jats:sub> and the channel state <jats:italic>S<\/jats:italic>\n            <jats:sub>R<\/jats:sub>, i.e., the channel from the source to the relay is governed by the conditional probability distribution <jats:inline-formula>\n              <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                <mml:msub>\n                  <mml:mi>P<\/mml:mi>\n                  <mml:mrow>\n                    <mml:msub>\n                      <mml:mi>Y<\/mml:mi>\n                      <mml:mi>r<\/mml:mi>\n                    <\/mml:msub>\n                    <mml:mo>|<\/mml:mo>\n                    <mml:msub>\n                      <mml:mi>X<\/mml:mi>\n                      <mml:mi>R<\/mml:mi>\n                    <\/mml:msub>\n                    <mml:mo>,<\/mml:mo>\n                    <mml:msub>\n                      <mml:mi>S<\/mml:mi>\n                      <mml:mi>R<\/mml:mi>\n                    <\/mml:msub>\n                  <\/mml:mrow>\n                <\/mml:msub>\n              <\/mml:math>\n            <\/jats:inline-formula>. The capacity for this class of semi-deterministic orthogonal relay channel is characterized exactly. The results are then extended to the Gaussian cases, modeling the channel states as additive Gaussian interferences. The capacity is characterized for the channel when the channel state information is known non-causally. However, when the channel state information is known causally, the capacity cannot be characterized in general. In this case, the lower bound on the capacity is established, and the capacity is characterized when the power of the relay is sufficiently large. Some numerical examples of the causal state information case are provided to illustrate the impact of the channel state and the role of the relay in information transmission and in cleaning the channel state.<\/jats:p>","DOI":"10.1186\/1687-1499-2014-59","type":"journal-article","created":{"date-parts":[[2014,4,16]],"date-time":"2014-04-16T07:04:04Z","timestamp":1397631844000},"update-policy":"http:\/\/dx.doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["The capacity of a class of state-dependent relay channel with orthogonal components and side information at the source and the relay"],"prefix":"10.1186","volume":"2014","author":[{"given":"Zhixiang","family":"Deng","sequence":"first","affiliation":[]},{"given":"Baoyun","family":"Wang","sequence":"additional","affiliation":[]},{"given":"Fei","family":"Lang","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2014,4,16]]},"reference":[{"issue":"6","key":"1043_CR1","doi-asserted-by":"publisher","first-page":"44","DOI":"10.1561\/0100000025","volume":"4","author":"G Keshet","year":"2008","unstructured":"Keshet G, Steinberg Y, Merhav N: Channel coding in the presence of side information: subject review. Found. Trends Commun. Inf. Theory 2008, 4(6):44-586.","journal-title":"Found. Trends Commun. Inf. Theory"},{"issue":"4","key":"1043_CR2","doi-asserted-by":"publisher","first-page":"289","DOI":"10.1147\/rd.24.0289","volume":"2","author":"CE Shannon","year":"1958","unstructured":"Shannon CE: Channels with side information at the transmitter. IBM J. Res. Develop. 1958, 2(4):289-293.","journal-title":"IBM J. Res. Develop"},{"issue":"1","key":"1043_CR3","first-page":"19","volume":"9","author":"SI Gel'fand","year":"1980","unstructured":"Gel'fand SI, Pinsker MS: Coding for channel with random parameters. Prob. Contr. Inf. Theory 1980, 9(1):19-31.","journal-title":"Prob. Contr. Inf. Theory"},{"issue":"3","key":"1043_CR4","doi-asserted-by":"publisher","first-page":"439","DOI":"10.1109\/TIT.1983.1056659","volume":"29","author":"MHM Costa","year":"1983","unstructured":"Costa MHM: Writing on dirty paper. IEEE Trans. Inf. Theory 1983, 29(3):439-441. 10.1109\/TIT.1983.1056659","journal-title":"IEEE Trans. Inf. Theory"},{"key":"1043_CR5","first-page":"247","volume-title":"Paper presented at the IEEE International Symposium on Information Theory, U.S.S.R Tashkent, 18\u201322 Sept","author":"SI Gel'fand","year":"1984","unstructured":"Gel'fand SI, Pinsker MS: On Gaussian channel with random parameters. Paper presented at the IEEE International Symposium on Information Theory, U.S.S.R Tashkent, 18\u201322 Sept 1984 247-250."},{"key":"1043_CR6","first-page":"72","volume-title":"Paper presented at the IEEE international symposium on information theory (ISIT), Adelaide, 4\u20139 Sept","author":"S Sigurjonsson","year":"2005","unstructured":"Sigurjonsson S, Kim YH: On multiple user channels with state information at the transmitters. Paper presented at the IEEE international symposium on information theory (ISIT), Adelaide, 4\u20139 Sept 2005 72-76."},{"key":"1043_CR7","first-page":"2184","volume-title":"Paper presented at the IEEE international symposium on information theory (ISIT), Adelaide, SA, 4\u20139 Sept","author":"Y Steinberg","year":"2005","unstructured":"Steinberg Y, Shamai S: (Shitz), Achievable rates for the broadcast channel with states known at the transmitter. Paper presented at the IEEE international symposium on information theory (ISIT), Adelaide, SA, 4\u20139 Sept 2005 2184-2188."},{"issue":"8","key":"1043_CR8","doi-asserted-by":"publisher","first-page":"2867","DOI":"10.1109\/TIT.2005.851727","volume":"51","author":"Y Steinberg","year":"2005","unstructured":"Steinberg Y: Coding for the degraded broadcast channel with random parameters, with causal and noncausal side information. IEEE Trans. Inf. Theory. 2005, 51(8):2867-2877. 10.1109\/TIT.2005.851727","journal-title":"IEEE Trans. Inf. Theory"},{"key":"1043_CR9","unstructured":"Nagananda KG, Murthy CR, Kishore S: nt broadcast channels. (Cornell University Library, 2012). . Accessed 12 Aug 2012 http:\/\/arxiv.org\/abs\/1110.0124"},{"key":"1043_CR10","volume-title":"Paper presented at the Allerton conference on communications, control, and computing, Monticello, IL, USA, 29 Sept\u20131","author":"S Kotagiri","year":"2004","unstructured":"Kotagiri S, Laneman JN: Achievable rates for multiple access channels with state information known at one encoder. Paper presented at the Allerton conference on communications, control, and computing, Monticello, IL, USA, 29 Sept\u20131 Oct 2004"},{"key":"1043_CR11","volume-title":"EURASIP J. Wireless Commun. Netw","author":"S Kotagiri","year":"2008","unstructured":"Kotagiri S, Laneman JN: Multiple access channels with state information known to some encoders and independent messages. EURASIP J. Wireless Commun. Netw. 2008. doi:10.1155\/2008\/450680"},{"issue":"11","key":"1043_CR12","doi-asserted-by":"publisher","first-page":"3392","DOI":"10.1109\/TIT.2005.856981","volume":"51","author":"Y Cemal","year":"2005","unstructured":"Cemal Y, Steinberg Y: The multiple-access channel with partial state information at the encoders. IEEE Trans. Inf. Theory. 2005, 51(11):3392-4003.","journal-title":"IEEE Trans. Inf. Theory"},{"key":"1043_CR13","first-page":"534","volume-title":"Paper presented at the IEEE international symposium on information and theory (ISIT), Chicago, 27 June\u20132","author":"Y Kim","year":"2004","unstructured":"Kim Y, Sutivong A, Sigurjonsson S: Multiple user writing on dirty paper. Paper presented at the IEEE international symposium on information and theory (ISIT), Chicago, 27 June\u20132 July 2004 534."},{"issue":"10","key":"1043_CR14","doi-asserted-by":"publisher","first-page":"4448","DOI":"10.1109\/TIT.2008.928977","volume":"54","author":"A Somekh-Baruch","year":"2008","unstructured":"Somekh-Baruch A, Shamai (Shitz) S, Verd\u00fa S: Cooperative multiple-access encoding with states available at one transmitter. IEEE Trans. Inf. Theory 2008, 54(10):4448-4469.","journal-title":"IEEE Trans. Inf. Theory"},{"issue":"9","key":"1043_CR15","doi-asserted-by":"publisher","first-page":"5640","DOI":"10.1109\/TIT.2012.2202210","volume":"58","author":"SI Bross","year":"2012","unstructured":"Bross SI, Lapidoth A, Wigger M: Dirty-paper coding for the Gaussian multiaccess channel with conferencing. IEEE Trans. Inf. Theory 2012, 58(9):5640-5668.","journal-title":"IEEE Trans. Inf. Theory"},{"issue":"5","key":"1043_CR16","doi-asserted-by":"publisher","first-page":"2272","DOI":"10.1109\/TIT.2010.2043782","volume":"56","author":"A Zaidi","year":"2010","unstructured":"Zaidi A, Kotagiri SP, Nicholas Laneman J, Vandendorpe L: Cooperative relaying with state available noncausally at the relay. IEEE Trans. Inf. Theory 2010, 56(5):2272-2298.","journal-title":"IEEE Trans. Inf. Theory"},{"key":"1043_CR17","volume-title":"EURASIP J. Wireless Commun. Netw","author":"A Zaidi","year":"2009","unstructured":"Zaidi A, Vandendorpe L: Lower bounds on the capacity of the relay channel with states at the source. EURASIP J. Wireless Commun. Netw. 2009. doi:10.1155\/2009\/634296"},{"issue":"5","key":"1043_CR18","doi-asserted-by":"publisher","first-page":"2639","DOI":"10.1109\/TIT.2012.2229780","volume":"59","author":"A Zaidi","year":"2013","unstructured":"Zaidi A, Shamai (Shitz) S, Piantanida P, Vandendorpe L: Bounds on the capacity of the relay channel with noncausal state at source. IEEE Trans. Inf. Theory 2013, 59(5):2639-2672.","journal-title":"IEEE Trans. Inf. Theory"},{"key":"1043_CR19","first-page":"528","volume-title":"Paper presented at the 5th international symposium on wireless pervasive computing (ISWPC), Modena, Italy, 5\u20137","author":"A Zaidi","year":"2010","unstructured":"Zaidi A, Shamai S, Piantanida P, Vandendorpe L: On the capacity of a class of relay channels with orthogonal components and noncausal state information at source. Paper presented at the 5th international symposium on wireless pervasive computing (ISWPC), Modena, Italy, 5\u20137 May 2010 528-533."},{"issue":"4","key":"1043_CR20","doi-asserted-by":"publisher","first-page":"1277","DOI":"10.1109\/TCOMM.2013.020413.110883","volume":"61","author":"K Bakanoglu","year":"2012","unstructured":"Bakanoglu K, Erkip E, Simeone O, Shamai (Shitz) S: Relay channel with orthogonal components and structured interference known at the source. IEEE Trans. Comm. 2012, 61(4):1277-289.","journal-title":"IEEE Trans. Comm"},{"key":"1043_CR21","first-page":"1169","volume-title":"Paper presented at the IEEE international symposium on information theory (ISIT), Seoul, Korea, 28 June\u20133","author":"B Akhbari","year":"2009","unstructured":"Akhbari B, Mirmohseni M, Aref MR: Compress-and-forward strategy for the relay channel with non-causal state information. Paper presented at the IEEE international symposium on information theory (ISIT), Seoul, Korea, 28 June\u20133 July 2009 1169-1173."},{"issue":"4","key":"1043_CR22","doi-asserted-by":"publisher","first-page":"1423","DOI":"10.1109\/18.923725","volume":"47","author":"B Chen","year":"2001","unstructured":"Chen B, Wornell GW: Quantization index modulation: a class of provably good methods for digital watermarking and information embedding. IEEE Trans. Inf. Theory 2001, 47(4):1423-1443. 10.1109\/18.923725","journal-title":"IEEE Trans. Inf. Theory"},{"issue":"6","key":"1043_CR23","doi-asserted-by":"publisher","first-page":"1639","DOI":"10.1109\/TIT.2002.1003844","volume":"48","author":"AS Cohen","year":"2002","unstructured":"Cohen AS, Lapidoth A: The Gaussian watermarking game. IEEE Trans. Inf. Theory 2002, 48(6):1639-1667. 10.1109\/TIT.2002.1003844","journal-title":"IEEE Trans. Inf. Theory"},{"issue":"3","key":"1043_CR24","doi-asserted-by":"publisher","first-page":"563","DOI":"10.1109\/TIT.2002.808134","volume":"49","author":"P Moulin","year":"2003","unstructured":"Moulin P, O'Sullivan JA: Information-theoretic analysis of information hiding. IEEE Trans. Inf. Theory 2003, 49(3):563-593. 10.1109\/TIT.2002.808134","journal-title":"IEEE Trans. Inf. Theory"},{"key":"1043_CR25","first-page":"52","volume":"10","author":"AV Kusnetsov","year":"1974","unstructured":"Kusnetsov AV, Tsybakov BS: Coding in a memory with defective cells. Probl. Predach. Inf. 1974, 10: 52-60.","journal-title":"Probl. Predach. Inf"},{"key":"1043_CR26","volume-title":"Cognitive radio: an integrated agent architecture for software defined radio","author":"J Mitola","year":"2000","unstructured":"Mitola J: Cognitive radio: an integrated agent architecture for software defined radio. KTH Royal Institute of Technology: Dissertation; 2000."},{"issue":"5","key":"1043_CR27","doi-asserted-by":"publisher","first-page":"572","DOI":"10.1109\/TIT.1979.1056084","volume":"IT-25","author":"TM Cover","year":"1979","unstructured":"Cover TM, Gamal AEL: Capacity theorems for the relay channel. IEEE Trans. Inf. Theory 1979, IT-25(5):572-584.","journal-title":"IEEE Trans. Inf. Theory"},{"issue":"3","key":"1043_CR28","doi-asserted-by":"publisher","first-page":"1328","DOI":"10.1109\/TIT.2007.915921","volume":"54","author":"YH Kim","year":"2008","unstructured":"Kim YH: Capacity of a class of relay channels. IEEE Trans. Inf. Theory 2008, 54(3):1328-1329.","journal-title":"IEEE Trans. Inf. Theory"},{"issue":"5","key":"1043_CR29","doi-asserted-by":"publisher","first-page":"1815","DOI":"10.1109\/TIT.2005.846438","volume":"51","author":"A El Gamal","year":"2005","unstructured":"El Gamal A, Zahedi S: Capacity of a class of relay channels with orthogonal components. IEEE Trans. Inf. Theory 2005, 51(5):1815-1817. 10.1109\/TIT.2005.846438","journal-title":"IEEE Trans. Inf. Theory"},{"issue":"6","key":"1043_CR30","doi-asserted-by":"publisher","first-page":"1986","DOI":"10.1109\/18.641562","volume":"43","author":"AJ Goldsmith","year":"1997","unstructured":"Goldsmith AJ, Varaiya PP: Capacity of fading channels with channel side information IEEE Trans. Inf. Theory 1997, 43(6):1986-1992. 10.1109\/18.641562","journal-title":"Inf. Theory"},{"key":"1043_CR31","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9781139030687","volume-title":"Network Information Theory","author":"A El Gamal","year":"2011","unstructured":"El Gamal A, Kim YH: Network Information Theory. Cambridge: Cambridge University Press; 2011."},{"key":"1043_CR32","volume-title":"Elements of Information Theory","author":"TM Cover","year":"2006","unstructured":"Cover TM, Thomas JA: Elements of Information Theory. 2nd edition. New York: Liley; 2006.","edition":"2"},{"key":"1043_CR33","volume-title":"Information Theory: Coding Theorems for Discrete Memoryless Channels","author":"I Csisz\u00e1r","year":"1981","unstructured":"Csisz\u00e1r I, K\u00f6rner J: Information Theory: Coding Theorems for Discrete Memoryless Channels. Waltham: Academic; 1981."}],"container-title":["EURASIP Journal on Wireless Communications and Networking"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1186\/1687-1499-2014-59.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1186\/1687-1499-2014-59\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1186\/1687-1499-2014-59.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,9,2]],"date-time":"2021-09-02T11:07:16Z","timestamp":1630580836000},"score":1,"resource":{"primary":{"URL":"https:\/\/jwcn-eurasipjournals.springeropen.com\/articles\/10.1186\/1687-1499-2014-59"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2014,4,16]]},"references-count":33,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2014,12]]}},"alternative-id":["1043"],"URL":"https:\/\/doi.org\/10.1186\/1687-1499-2014-59","relation":{},"ISSN":["1687-1499"],"issn-type":[{"value":"1687-1499","type":"electronic"}],"subject":[],"published":{"date-parts":[[2014,4,16]]},"assertion":[{"value":"1 February 2013","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"24 March 2014","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"16 April 2014","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}],"article-number":"59"}}