{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T04:35:36Z","timestamp":1760243736968,"version":"build-2065373602"},"reference-count":45,"publisher":"MDPI AG","issue":"10","license":[{"start":{"date-parts":[[2012,9,28]],"date-time":"2012-09-28T00:00:00Z","timestamp":1348790400000},"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>In recent years, there has been rapid progress on understanding Gaussian networks with multiple unicast connections, and new coding techniques have emerged. The essence of multi-source networks is how to efficiently manage interference that arises from the transmission of other sessions. Classically, interference is removed by orthogonalization (in time or frequency). This means that the rate per session drops inversely proportional to the number of sessions, suggesting that interference is a strong limiting factor in such networks. However, recently discovered interference management techniques have led to a paradigm shift that interference might not be quite as detrimental after all. The aim of this paper is to provide a review of these new coding techniques as they apply to the case of time-varying Gaussian networks with multiple unicast connections. Specifically, we review interference alignment and ergodic interference alignment for multi-source single-hop networks and interference neutralization and ergodic interference neutralization for multi-source multi-hop networks. We mainly focus on the \u201cdegrees of freedom\u201d perspective and also discuss an approximate capacity characterization.<\/jats:p>","DOI":"10.3390\/e14101842","type":"journal-article","created":{"date-parts":[[2012,10,2]],"date-time":"2012-10-02T02:39:08Z","timestamp":1349145548000},"page":"1842-1863","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":27,"title":["A Survey on Interference Networks: Interference Alignment and Neutralization"],"prefix":"10.3390","volume":"14","author":[{"given":"Sang-Woon","family":"Jeon","sequence":"first","affiliation":[{"name":"School of Computer and Communication Sciences, Ecole Polytechnique F\u00e9d\u00e9rale de Lausanne (EPFL), Lausanne 1015, Switzerland"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Michael","family":"Gastpar","sequence":"additional","affiliation":[{"name":"School of Computer and Communication Sciences, Ecole Polytechnique F\u00e9d\u00e9rale de Lausanne (EPFL), Lausanne 1015, Switzerland"},{"name":"Department of Electrical Engineering and Computer Sciences, University of California, Berkeley, CA 94720, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2012,9,28]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"572","DOI":"10.1109\/TIT.1979.1056084","article-title":"Capacity theorems for the relay channel","volume":"IT-25","author":"Cover","year":"1979","journal-title":"IEEE Trans. Inf. Theory"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"569","DOI":"10.1109\/TIT.1975.1055432","article-title":"A case where interference does not reduce capacity","volume":"IT-21","author":"Carleial","year":"1975","journal-title":"IEEE Trans. Inf. Theory"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"49","DOI":"10.1109\/TIT.1981.1056307","article-title":"A new achievable rate region for the interference channel","volume":"IT-27","author":"Han","year":"1981","journal-title":"IEEE Trans. Inf. Theory"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"5534","DOI":"10.1109\/TIT.2008.2006447","article-title":"Gaussian interference channel capacity to within one bit","volume":"54","author":"Etkin","year":"2008","journal-title":"IEEE Trans. Inf. Theory"},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"909","DOI":"10.1109\/TIT.2011.2173711","article-title":"Random access: An information-theoretic perspective","volume":"58","author":"Minero","year":"2012","journal-title":"IEEE Trans. Inf. Theory"},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"3425","DOI":"10.1109\/TIT.2008.926344","article-title":"Interference alignment and degrees of freedom of the K-user interference channel","volume":"54","author":"Cadambe","year":"2008","journal-title":"IEEE Trans. Inf. Theory"},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"3457","DOI":"10.1109\/TIT.2008.926460","article-title":"Communication over MIMO X channels: Interference alignment, decomposition, and performance analysis","volume":"54","author":"Motahari","year":"2008","journal-title":"IEEE Trans. Inf. Theory"},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"3893","DOI":"10.1109\/TIT.2009.2025541","article-title":"Interference alignment and the degrees of freedom of wireless X networks","volume":"54","author":"Cadambe","year":"2009","journal-title":"IEEE Trans. Inf. Theory"},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"6040","DOI":"10.1109\/TIT.2010.2080830","article-title":"Degrees of freedom of the K user M \u00d7 N MIMO interference channel","volume":"56","author":"Gou","year":"2010","journal-title":"IEEE Trans. Inf. Theory"},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"2616","DOI":"10.1109\/TCOMM.2011.070511.100313","article-title":"Downlink interference alignments","volume":"59","author":"Suh","year":"2011","journal-title":"IEEE Trans. Commun."},{"key":"ref_11","doi-asserted-by":"crossref","unstructured":"Suh, C., and Tse, D.N.C. (2008, January 23\u201326). Interference alignment for cellular networks. Proceedings of the Allerton Conference on Communication, Control, and Computing, Monticello, IL, USA.","DOI":"10.1109\/ALLERTON.2008.4797673"},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"2334","DOI":"10.1109\/TIT.2009.2016061","article-title":"Degrees of freedom of wireless networks with relays, feedback, cooperation and full duplex operation","volume":"55","author":"Cadambe","year":"2009","journal-title":"IEEE Trans. Inf. Theory"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"5740","DOI":"10.1109\/TIT.2012.2198614","article-title":"Degrees of freedom of interference channels with CoMP transmission and reception","volume":"58","author":"Annapureddy","year":"2012","journal-title":"IEEE Trans. Inf. Theory"},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"3787","DOI":"10.1109\/TIT.2012.2189197","article-title":"Degrees of freedom region for an interference network with general message demands","volume":"58","author":"Ke","year":"2012","journal-title":"IEEE Trans. Inf. Theory"},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"6355","DOI":"10.1109\/TIT.2012.2205217","article-title":"Ergodic interference alignment","volume":"58","author":"Nazer","year":"2012","journal-title":"IEEE Trans. Inf. Theory"},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"379","DOI":"10.1109\/JSAC.2007.070213","article-title":"Spectral efficient protocols for half- duplex fading relay channels","volume":"25","author":"Rankov","year":"2007","journal-title":"IEEE J. Select. Areas Commun."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"2837","DOI":"10.1109\/TIT.2011.2120210","article-title":"Approximate capacity region for a class of relay-interference networks","volume":"57","author":"Mohajer","year":"2011","journal-title":"IEEE Trans. Inf. Theory"},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"4381","DOI":"10.1109\/TIT.2012.2191388","article-title":"Aligned interference neutralization and the degrees of freedom of the 2 \u00d7 2 \u00d7 2 interference channel","volume":"58","author":"Gou","year":"2012","journal-title":"IEEE Trans. Inf. Theory"},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"3032","DOI":"10.1109\/TIT.2011.2119750","article-title":"Degrees of freedom region of a class of multisource Gaussian relay networks","volume":"57","author":"Jeon","year":"2011","journal-title":"IEEE Trans. Inf. Theory"},{"key":"ref_20","doi-asserted-by":"crossref","unstructured":"Jeon, S.-W., Wang, C.-Y., and Gastpar, M. (2012, January 5\u201310). Approximate Ergodic Capacity of a Class of Fading 2 \u00d7 2 \u00d7 2 Networks. Proceedings of the Information Theory and Applications Workshop, San Diego, CA, USA.","DOI":"10.1109\/ITA.2012.6181774"},{"key":"ref_21","doi-asserted-by":"crossref","unstructured":"Jeon, S.-W., Wang, C.-Y., and Gastpar, M. (2012, January 1\u20136). Approximate ergodic capacity of a class of fading 2-user 2-hop networks. Proceedings of the IEEE International Symposium on Information Theory, Cambridge, MA, USA.","DOI":"10.1109\/ISIT.2012.6284255"},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"2825","DOI":"10.1109\/TIT.2006.874540","article-title":"Coding on demand by an informed source (ISCOD) for efficient broadcast of different supplemental data to caching clients","volume":"52","author":"Birk","year":"2006","journal-title":"IEEE Trans. Inf. Theory"},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"1425","DOI":"10.1109\/TIT.2011.2105003","article-title":"Exact-repair MDS code construction using interference alignment","volume":"57","author":"Suh","year":"2011","journal-title":"IEEE Trans. Inf. Theory"},{"key":"ref_24","unstructured":"Cadambe, V.R., Jafar, S.A., Maleki, H., Ramchandran, K., and Suh, C. (2011). Asymptotic interference alignment for optimal repair of MDS codes in distributed storage. IEEE Trans. Inf. Theory, Submitted."},{"key":"ref_25","doi-asserted-by":"crossref","unstructured":"Maleki, H., Cadambe, V.R., and Jafar, S.A. (2012, January 1\u20136). Index Coding\u2013An Interference Alignment Perspective. Proceedings of the IEEE International Symposium on Information Theory, Cambridge, MA, USA.","DOI":"10.1109\/ISIT.2012.6283851"},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"847","DOI":"10.1109\/LCOMM.2009.090735","article-title":"On the beamforming design for efficient interference alignment","volume":"13","author":"Choi","year":"2009","journal-title":"IEEE Commun. Lett."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"3983","DOI":"10.1109\/TIT.2009.2025530","article-title":"Parallel Gaussian interference channels are not always separable","volume":"55","author":"Cadambe","year":"2009","journal-title":"IEEE Trans. Inf. Theory"},{"key":"ref_28","doi-asserted-by":"crossref","unstructured":"Sankar, L., Shang, X., Erkip, E., and Poor, H.V. (2008, January 23\u201326). Ergodic Two-User Interference Channels: Is Separability Optimal?. Proceedings of the Allerton Conference on Communication, Control, and Computing, Monticello, IL, USA.","DOI":"10.1109\/ALLERTON.2008.4797629"},{"key":"ref_29","unstructured":"Nazer, B., Gastpar, M., Jafar, S.A., and Vishwanath, S. (July, January 28). Ergodic Interference Alignment. Proceedings of the IEEE International Symposium on Information Theory, Seoul, Korea."},{"key":"ref_30","unstructured":"Jeon, S.-W., and Chung, S.-Y. (2009, January 8\u201313). Capacity of a Class of Multi-Source Relay Networks. Proceedings of the Information Theory and Applications Workshop, La Jolla, CA, USA."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"3323","DOI":"10.1109\/TIT.2011.2132430","article-title":"Interference alignment for secrecy","volume":"57","author":"Koyluoglu","year":"2011","journal-title":"IEEE Trans. Inf. Theory"},{"key":"ref_32","doi-asserted-by":"crossref","unstructured":"Johnson, O., Aldridge, M., and Piechocki, R. (2012, January 1\u20136). Delay\u2013Rate Tradeoff in Ergodic Interference Alignment. Proceedings of the IEEE International Symposium on Information Theory, Cambridge, MA, USA.","DOI":"10.1109\/ISIT.2012.6283994"},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"4552","DOI":"10.1109\/TIT.2010.2053895","article-title":"Interference alignment with asymmetric complex signaling\u2014Settling the H\u00f8st-Madsen\u2013Nosratinia conjecture","volume":"56","author":"Cadambe","year":"2010","journal-title":"IEEE Trans. Inf. Theory"},{"key":"ref_34","unstructured":"Motahari, A., Gharan, S., Maddah-Ali, M., and Khandani, A. Real interference alignment: Exploiting the potential of single antenna systems. Available online: arxiv.org\/abs\/0908.2282\/."},{"key":"ref_35","unstructured":"Motahari, A., Gharan, S., and Khandani, A. Real interference alignment with real numbers. Available online: arXiv:cs.IT\/0908.1208\/."},{"key":"ref_36","doi-asserted-by":"crossref","unstructured":"Shomorony, I., and Avestimehr, A. S. (2012). Two-unicast wireless networks: Characterizing the degrees-of-freedom. IEEE Trans. Inf. Theory.","DOI":"10.1109\/TIT.2012.2214024"},{"key":"ref_37","unstructured":"Wang, C., Gou, T., and Jafar, S.A. (2011, January 5\u20139). Multiple Unicast Capacity of 2-source 2-sink Networks. Proceedings of the IEEE Global Telecommunications Conference, Houston, TA, USA."},{"key":"ref_38","doi-asserted-by":"crossref","unstructured":"Vaze, C.S., and Varanasi, M.K. (2012, January 5\u201310). Beamforming and aligned interference neutralization achieve the degrees of freedom region of the 2 \u00d7 2 \u00d7 2 MIMO interference network. Proceedings of the Information Theory and Applications Workshop, San Diego, CA, USA.","DOI":"10.1109\/ITA.2012.6181801"},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"4566","DOI":"10.1109\/TIT.2010.2054590","article-title":"The approximate capacity of the many-to-one and one-to-many Gaussian interference channels","volume":"56","author":"Bresler","year":"2010","journal-title":"IEEE Trans. Inf. Theory"},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"5488","DOI":"10.1109\/TIT.2010.2069150","article-title":"Capacity of the Gaussian two-way relay channel to within \n\t\t\t\t\t\t\t\t          \n\t\t\t\t\t\t\t\t            \n\t\t\t\t\t\t\t\t              \n\t\t\t\t\t\t\t\t              1\n\t\t\t\t\t\t\t\t              2\n\t\t\t\t\t\t\t\t\t\t\t  \n\t\t\t\t\t\t\t\t            \n\t\t\t\t\t\t\t\t          \n\t\t\t\t\t\t\t\t         bit","volume":"56","author":"Nam","year":"2010","journal-title":"IEEE Trans. Inf. Theory"},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"1872","DOI":"10.1109\/TIT.2011.2110110","article-title":"Wireless network information flow: A deterministic approach","volume":"57","author":"Avestimehr","year":"2011","journal-title":"IEEE Trans. Inf. Theory"},{"key":"ref_42","doi-asserted-by":"crossref","first-page":"3132","DOI":"10.1109\/TIT.2011.2119930","article-title":"Noisy network coding","volume":"57","author":"Lim","year":"2011","journal-title":"IEEE Trans. Inf. Theory"},{"key":"ref_43","doi-asserted-by":"crossref","first-page":"6463","DOI":"10.1109\/TIT.2011.2165816","article-title":"Compute-and-forward: Harnessing interference through structured codes","volume":"57","author":"Nazer","year":"2011","journal-title":"IEEE Trans. Inf. Theory"},{"key":"ref_44","doi-asserted-by":"crossref","unstructured":"Niesen, U., Nazer, B., and Whiting, P. (2011, January 28\u201330). Computation alignment: Capacity approximation without noise accumulation. Proceedings of the Allerton Conference on Communication, Control, and Computing, Monticello, IL, USA.","DOI":"10.1109\/Allerton.2011.6120360"},{"key":"ref_45","doi-asserted-by":"crossref","unstructured":"Ordentlich, O., Erez, U., and Nazer, B. (2012, January 1\u20136). The approximate sum capacity of the symmetric Gaussian K-user interference channel. Proceedings of the IEEE International Symposium on Information Theory, Cambridge, MA, USA.","DOI":"10.1109\/ISIT.2012.6283726"}],"container-title":["Entropy"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1099-4300\/14\/10\/1842\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T21:52:37Z","timestamp":1760219557000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1099-4300\/14\/10\/1842"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2012,9,28]]},"references-count":45,"journal-issue":{"issue":"10","published-online":{"date-parts":[[2012,10]]}},"alternative-id":["e14101842"],"URL":"https:\/\/doi.org\/10.3390\/e14101842","relation":{},"ISSN":["1099-4300"],"issn-type":[{"type":"electronic","value":"1099-4300"}],"subject":[],"published":{"date-parts":[[2012,9,28]]}}}