{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,28]],"date-time":"2025-10-28T10:50:21Z","timestamp":1761648621862,"version":"build-2065373602"},"reference-count":38,"publisher":"MDPI AG","issue":"3","license":[{"start":{"date-parts":[[2019,3,12]],"date-time":"2019-03-12T00:00:00Z","timestamp":1552348800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/100010661","name":"Horizon 2020","doi-asserted-by":"publisher","award":["694630"],"award-info":[{"award-number":["694630"]}],"id":[{"id":"10.13039\/100010661","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>We consider the problem of channel coding over multiterminal state-dependent channels in which neither transmitters nor receivers but only a helper node has a non-causal knowledge of the state. Such channel models arise in many emerging communication schemes. We start by investigating the parallel state-dependent channel with the same but differently scaled state corrupting the receivers. A cognitive helper knows the state in a non-causal manner and wishes to mitigate the interference that impacts the transmission between two transmit\u2013receive pairs. Outer and inner bounds are derived. In our analysis, the channel parameters are partitioned into various cases, and segments on the capacity region boundary are characterized for each case. Furthermore, we show that for a particular set of channel parameters, the capacity region is entirely characterized. In the second part of this work, we address a similar scenario, but now each channel is corrupted by an independent state. We derive an inner bound using a coding scheme that integrates single-bin Gel\u2019fand\u2013Pinsker coding and Marton\u2019s coding for the broadcast channel. We also derive an outer bound and further partition the channel parameters into several cases for which parts of the capacity region boundary are characterized.<\/jats:p>","DOI":"10.3390\/e21030273","type":"journal-article","created":{"date-parts":[[2019,3,13]],"date-time":"2019-03-13T04:07:37Z","timestamp":1552450057000},"page":"273","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["MIMO Gaussian State-Dependent Channels with a State-Cognitive Helper"],"prefix":"10.3390","volume":"21","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-0498-273X","authenticated-orcid":false,"given":"Michael","family":"Dikshtein","sequence":"first","affiliation":[{"name":"Department of Electrical Engineering, Technion-Israel Institute of Technology, Haifa 32000, Israel"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ruchen","family":"Duan","sequence":"additional","affiliation":[{"name":"Samsung Semiconductor Inc., San Jose, CA 95134, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yingbin","family":"Liang","sequence":"additional","affiliation":[{"name":"Department of ECE, The Ohio State University, Columbus, OH 43210, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Shlomo","family":"Shamai (Shitz)","sequence":"additional","affiliation":[{"name":"Department of Electrical Engineering, Technion-Israel Institute of Technology, Haifa 32000, Israel"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2019,3,12]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Vaezi, M., and Vincent Poor, H. (2019). NOMA: An Information-Theoretic Perspective. Multiple Access Techniques for 5G Wireless Networks and Beyond, Springer International Publishing.","DOI":"10.1007\/978-3-319-92090-0"},{"key":"ref_2","first-page":"19","article-title":"Coding for channels with ramdom parameters","volume":"9","author":"Pinsker","year":"1980","journal-title":"Probl. Contr. Inf. Theory"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"439","DOI":"10.1109\/TIT.1983.1056659","article-title":"Writing on dirty paper (Corresp.)","volume":"29","author":"Costa","year":"1983","journal-title":"IEEE Trans. Inf. Theory"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"289","DOI":"10.1147\/rd.24.0289","article-title":"Channels with Side Information at the Transmitter","volume":"2","author":"Shannon","year":"1958","journal-title":"IBM J. Res. Dev."},{"key":"ref_5","unstructured":"Cohen, A.S., and Lapidoth, A. (July, January 30). Generalized writing on dirty paper. Proceedings of the IEEE International Symposium on Information Theory, Lausanne, Switzerland."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"2","DOI":"10.1109\/TIT.1972.1054727","article-title":"Broadcast channels","volume":"18","author":"Cover","year":"1972","journal-title":"IEEE Trans. Inf. Theory"},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"306","DOI":"10.1109\/TIT.1979.1056046","article-title":"A coding theorem for the discrete memoryless broadcast channel","volume":"25","author":"Marton","year":"1979","journal-title":"IEEE Trans. Inf. Theory"},{"key":"ref_8","unstructured":"Liang, Y. (2005). Multiuser Communications with Relaying and User Cooperation. [Ph.D. Thesis, University of Illinois]."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"350","DOI":"10.1109\/TIT.2006.887492","article-title":"An Outer Bound to the Capacity Region of the Broadcast Channel","volume":"53","author":"Nair","year":"2007","journal-title":"IEEE Trans. Inf. Theory"},{"key":"ref_10","first-page":"3","article-title":"Capacity and coding for degraded broadcast channels","volume":"10","author":"Gallager","year":"1974","journal-title":"Probl. Pereda. Inf."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"279","DOI":"10.1109\/TIT.1974.1055184","article-title":"A simple converse for broadcast channels with additive white Gaussian noise (Corresp.)","volume":"20","author":"Bergmans","year":"1974","journal-title":"IEEE Trans. Inf. Theory"},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"3936","DOI":"10.1109\/TIT.2006.880064","article-title":"The Capacity Region of the Gaussian Multiple-Input Multiple-Output Broadcast Channel","volume":"52","author":"Weingarten","year":"2006","journal-title":"IEEE Trans. Inf. Theory"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"1839","DOI":"10.1109\/TIT.2007.894680","article-title":"An Extremal Inequality Motivated by Multiterminal Information-Theoretic Problems","volume":"53","author":"Liu","year":"2007","journal-title":"IEEE Trans. Inf. Theory"},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"2087","DOI":"10.1109\/TIT.2014.2304457","article-title":"The Capacity Region of the Two-Receiver Gaussian Vector Broadcast Channel with Private and Common Messages","volume":"60","author":"Geng","year":"2014","journal-title":"IEEE Trans. Inf. Theory"},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"2867","DOI":"10.1109\/TIT.2005.851727","article-title":"Coding for the degraded broadcast channel with random parameters, with causal and noncausal side information","volume":"51","author":"Steinberg","year":"2005","journal-title":"IEEE Trans. Inf. Theory"},{"key":"ref_16","doi-asserted-by":"crossref","unstructured":"Steinberg, Y., and Shamai, S. (2005, January 4\u20139). Achievable rates for the broadcast channel with states known at the transmitter. Proceedings of the International Symposium on Information Theory, Adelaide, Australia.","DOI":"10.1109\/ISIT.2005.1523734"},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"787","DOI":"10.1049\/iet-com.2017.0300","article-title":"On the capacity of a class ofK-user Gaussian broadcast channel with states known at the transmitter","volume":"12","author":"Ghabeli","year":"2018","journal-title":"IET Commun."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"1814","DOI":"10.1109\/TIT.2007.894693","article-title":"Carbon Copying Onto Dirty Paper","volume":"53","author":"Khisti","year":"2007","journal-title":"IEEE Trans. Inf. Theory"},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"5907","DOI":"10.1109\/TIT.2017.2708112","article-title":"On the Capacity of the Carbon Copy onto Dirty Paper Channel","volume":"63","author":"Rini","year":"2017","journal-title":"IEEE Trans. Inf. Theory"},{"key":"ref_20","doi-asserted-by":"crossref","unstructured":"Khosravi-Farsani, R., and Marvasti, F. (2011, January 16\u201320). Capacity bounds for multiuser channels with non-causal channel state information at the transmitters. Proceedings of the 2011 IEEE Information Theory Workshop, Paraty, Brazil.","DOI":"10.1109\/ITW.2011.6089375"},{"key":"ref_21","unstructured":"Kotagiri, S., and Laneman, J.N. (October, January 29). Achievable rates for multiple access channels with state information known at one encoder. Proceedings of the Allerton Conference on Communications, Control, and Computing, Monticello, IL, USA."},{"key":"ref_22","doi-asserted-by":"crossref","unstructured":"Kotagiri, S., and Laneman, J.N. (2007, January 24\u201329). Multiaccess Channels with State Known to One Encoder: A Case of Degraded Message Sets. Proceedings of the 2007 IEEE International Symposium on Information Theory, Nice, France.","DOI":"10.1109\/ISIT.2007.4557445"},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"26:1","DOI":"10.1155\/2008\/450680","article-title":"Multiaccess Channels with State Known to Some Encoders and Independent Messages","volume":"2008","author":"Kotagiri","year":"2008","journal-title":"EURASIP J. Wirel. Commun. Netw."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"4448","DOI":"10.1109\/TIT.2008.928977","article-title":"Cooperative Multiple-Access Encoding With States Available at One Transmitter","volume":"54","author":"Shamai","year":"2008","journal-title":"IEEE Trans. Inf. Theory"},{"key":"ref_25","doi-asserted-by":"crossref","unstructured":"Zaidi, A., Kotagiri, S.P., Laneman, J.N., and Vandendorpe, L. (July, January 28). Multiaccess channels with state known to one encoder: Another case of degraded message sets. Proceedings of the 2009 IEEE International Symposium on Information Theory, Seoul, Korea.","DOI":"10.1109\/ISIT.2009.5205986"},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"7866","DOI":"10.1109\/TIT.2018.2839643","article-title":"State-Dependent Gaussian Multiple Access Channels: New Outer Bounds and Capacity Results","volume":"64","author":"Yang","year":"2018","journal-title":"IEEE Trans. Inf. Theory"},{"key":"ref_27","unstructured":"Mallik, S., and Koetter, R. (2008, January 14\u201316). Helpers for Cleaning Dirty Papers. Proceedings of the 7th International ITG Conference on Source and Channel Coding, Ulm, Germany."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"7123","DOI":"10.1109\/TIT.2016.2614320","article-title":"Capacity Characterization for State-Dependent Gaussian Channel With a Helper","volume":"62","author":"Sun","year":"2016","journal-title":"IEEE Trans. Inf. Theory"},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"2272","DOI":"10.1109\/TIT.2010.2043782","article-title":"Cooperative Relaying with State Available Noncausally at the Relay","volume":"56","author":"Zaidi","year":"2010","journal-title":"IEEE Trans. Inf. Theory"},{"key":"ref_30","doi-asserted-by":"crossref","unstructured":"Li, M., Simeone, O., and Yener, A. (ArXiv, 2011). Message and State Cooperation in a Relay Channel When Only the Relay Knows the State, ArXiv.","DOI":"10.1109\/ITA.2011.5743602"},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"776","DOI":"10.1049\/iet-com.2017.1192","article-title":"Impact of relay side information on the coverage region for the wireless relay channel with correlated noises","volume":"12","author":"Boostanpour","year":"2018","journal-title":"IET Commun."},{"key":"ref_32","doi-asserted-by":"crossref","unstructured":"Ghasemi-Goojani, S., and Papadimitratos, P. (2018, January 21\u201323). On the capacity of Gaussian \u201cdirty\u201d Z-interference channel with common state. Proceedings of the 2018 52nd Annual Conference on Information Sciences and Systems (CISS), Princeton, NJ, USA.","DOI":"10.1109\/CISS.2018.8362247"},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"445","DOI":"10.1561\/0100000025","article-title":"Channel coding in the presence of side information","volume":"4","author":"Keshet","year":"2008","journal-title":"Found. Trends Commun. Inf. Theory"},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"6680","DOI":"10.1109\/TIT.2015.2487455","article-title":"State-Dependent Parallel Gaussian Networks With a Common State-Cognitive Helper","volume":"61","author":"Duan","year":"2015","journal-title":"IEEE Trans. Inf. Theory"},{"key":"ref_35","doi-asserted-by":"crossref","unstructured":"Dikshtein, M., Duan, R., Liang, Y., and Shamai, S. (2018, January 12\u201314). Parallel Gaussian Channels Corrupted by Independent States With a State-Cognitive Helper. Proceedings of the IEEE International Conference on the Science of Electrical Engineering (ICSEE), Eilat, Israel.","DOI":"10.1109\/ICSEE.2018.8646036"},{"key":"ref_36","doi-asserted-by":"crossref","unstructured":"Dikshtein, M., Duan, R., Liang, Y., and Shamai, S. (2018, January 21\u201323). State-Dependent Parallel Gaussian Channels with a State-Cognitive Helper. Proceedings of the International Zurich Seminar on Information and Communication (IZS 2018), ETH Zurich, Zurich, Switzerland.","DOI":"10.3390\/e21030273"},{"key":"ref_37","doi-asserted-by":"crossref","unstructured":"El Gamal, A., and Kim, Y. (2011). Network Information Theory, Cambridge University Press.","DOI":"10.1017\/CBO9781139030687"},{"key":"ref_38","unstructured":"Pozrikidis, C. (2014). An Introduction to Grids, Graphs, and Networks, Oxford University Press."}],"container-title":["Entropy"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1099-4300\/21\/3\/273\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T12:38:16Z","timestamp":1760186296000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1099-4300\/21\/3\/273"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,3,12]]},"references-count":38,"journal-issue":{"issue":"3","published-online":{"date-parts":[[2019,3]]}},"alternative-id":["e21030273"],"URL":"https:\/\/doi.org\/10.3390\/e21030273","relation":{},"ISSN":["1099-4300"],"issn-type":[{"type":"electronic","value":"1099-4300"}],"subject":[],"published":{"date-parts":[[2019,3,12]]}}}