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Generalized Silver Codes
For an nt transmit, nr receive antenna system ( nt × nr system), a full-rate space time block code (STBC) transmits at least nmin = min ( nt , nr ) complex symbols per channel use. The well-known Golden code is an example of a full-rate, full-diversity STBC for two transmit antennas. Its ML-decoding...
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| Published in: | IEEE transactions on information theory 2011-09, Vol.57 (9), p.6134-6147 |
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| Main Authors: | , |
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| Language: | English |
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| container_end_page | 6147 |
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| container_title | IEEE transactions on information theory |
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| creator | Srinath, K. P. Rajan, B. S. |
| description | For an nt transmit, nr receive antenna system ( nt × nr system), a full-rate space time block code (STBC) transmits at least nmin = min ( nt , nr ) complex symbols per channel use. The well-known Golden code is an example of a full-rate, full-diversity STBC for two transmit antennas. Its ML-decoding complexity is of the order of M 2.5 for square M -QAM. The Silver code for two transmit antennas has all the desirable properties of the Golden code except its coding gain, but offers lower ML-decoding complexity of the order of M 2 . Importantly, the slight loss in coding gain is negligible compared to the advantage it offers in terms of lowering the ML-decoding complexity. For higher number of transmit antennas, the best known codes are the Perfect codes, which are full-rate, full-diversity, information lossless codes (for nr ≥ nt ) but have a high ML-decoding complexity of the order of M n t n min (for n r |
| doi_str_mv | 10.1109/TIT.2011.2162276 |
| format | article |
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P. ; Rajan, B. S.</creator><creatorcontrib>Srinath, K. P. ; Rajan, B. S.</creatorcontrib><description>For an nt transmit, nr receive antenna system ( nt × nr system), a full-rate space time block code (STBC) transmits at least nmin = min ( nt , nr ) complex symbols per channel use. The well-known Golden code is an example of a full-rate, full-diversity STBC for two transmit antennas. Its ML-decoding complexity is of the order of M 2.5 for square M -QAM. The Silver code for two transmit antennas has all the desirable properties of the Golden code except its coding gain, but offers lower ML-decoding complexity of the order of M 2 . Importantly, the slight loss in coding gain is negligible compared to the advantage it offers in terms of lowering the ML-decoding complexity. For higher number of transmit antennas, the best known codes are the Perfect codes, which are full-rate, full-diversity, information lossless codes (for nr ≥ nt ) but have a high ML-decoding complexity of the order of M n t n min (for n r <; nt, the punctured Perfect codes are considered). In this paper, a scheme to obtain full-rate STBCs for 2a transmit antennas and any n r with reduced ML-decoding complexity of the order of M n t ( n min-3/4)-0.5 is presented. The codes constructed are also information lossless for nr ≥ nt , like the Perfect codes, and allow higher mutual information than the comparable punctured Perfect codes for nr <; nt . These codes are referred to as the generalized Silver codes, since they enjoy the same desirable properties as the comparable Perfect codes (except possibly the coding gain) with lower ML-decoding complexity, analogous to the Silver code and the Golden code for two transmit antennas. Simulation results of the symbol error rates for four and eight transmit antennas show that the generalized Silver codes match the punctured Perfect codes in error performance while offering lower ML- decoding complexity.</description><identifier>ISSN: 0018-9448</identifier><identifier>EISSN: 1557-9654</identifier><identifier>DOI: 10.1109/TIT.2011.2162276</identifier><identifier>CODEN: IETTAW</identifier><language>eng</language><publisher>New York, NY: IEEE</publisher><subject>Antennas ; Anticommuting matrices ; Applied sciences ; Block codes ; Coding theory ; Coding, codes ; Complexity theory ; Data transmission ; Encoding ; ergodic capacity ; Exact sciences and technology ; full-rate space-time block codes ; information losslessness ; Information theory ; Information, signal and communications theory ; low ML- decoding complexity ; MIMO ; Mutual information ; Radiocommunications ; Receiving antennas ; Signal and communications theory ; Silver ; Simulation ; Systems, networks and services of telecommunications ; Telecommunications ; Telecommunications and information theory ; Transmission and modulation (techniques and equipments) ; Transmitting antennas</subject><ispartof>IEEE transactions on information theory, 2011-09, Vol.57 (9), p.6134-6147</ispartof><rights>2015 INIST-CNRS</rights><rights>Copyright The Institute of Electrical and Electronics Engineers, Inc. (IEEE) Sep 2011</rights><lds50>peer_reviewed</lds50><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c362t-72bea402326f7a9550a11d8319d1b03c48ab8583e6a85bb6d84bb9a15241c4ad3</citedby><cites>FETCH-LOGICAL-c362t-72bea402326f7a9550a11d8319d1b03c48ab8583e6a85bb6d84bb9a15241c4ad3</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktohtml>$$Uhttps://ieeexplore.ieee.org/document/6006602$$EHTML$$P50$$Gieee$$H</linktohtml><link.rule.ids>314,776,780,27903,27904,54774</link.rule.ids><backlink>$$Uhttp://pascal-francis.inist.fr/vibad/index.php?action=getRecordDetail&idt=24554486$$DView record in Pascal Francis$$Hfree_for_read</backlink></links><search><creatorcontrib>Srinath, K. P.</creatorcontrib><creatorcontrib>Rajan, B. S.</creatorcontrib><title>Generalized Silver Codes</title><title>IEEE transactions on information theory</title><addtitle>TIT</addtitle><description>For an nt transmit, nr receive antenna system ( nt × nr system), a full-rate space time block code (STBC) transmits at least nmin = min ( nt , nr ) complex symbols per channel use. The well-known Golden code is an example of a full-rate, full-diversity STBC for two transmit antennas. Its ML-decoding complexity is of the order of M 2.5 for square M -QAM. The Silver code for two transmit antennas has all the desirable properties of the Golden code except its coding gain, but offers lower ML-decoding complexity of the order of M 2 . Importantly, the slight loss in coding gain is negligible compared to the advantage it offers in terms of lowering the ML-decoding complexity. For higher number of transmit antennas, the best known codes are the Perfect codes, which are full-rate, full-diversity, information lossless codes (for nr ≥ nt ) but have a high ML-decoding complexity of the order of M n t n min (for n r <; nt, the punctured Perfect codes are considered). In this paper, a scheme to obtain full-rate STBCs for 2a transmit antennas and any n r with reduced ML-decoding complexity of the order of M n t ( n min-3/4)-0.5 is presented. The codes constructed are also information lossless for nr ≥ nt , like the Perfect codes, and allow higher mutual information than the comparable punctured Perfect codes for nr <; nt . These codes are referred to as the generalized Silver codes, since they enjoy the same desirable properties as the comparable Perfect codes (except possibly the coding gain) with lower ML-decoding complexity, analogous to the Silver code and the Golden code for two transmit antennas. Simulation results of the symbol error rates for four and eight transmit antennas show that the generalized Silver codes match the punctured Perfect codes in error performance while offering lower ML- decoding complexity.</description><subject>Antennas</subject><subject>Anticommuting matrices</subject><subject>Applied sciences</subject><subject>Block codes</subject><subject>Coding theory</subject><subject>Coding, codes</subject><subject>Complexity theory</subject><subject>Data transmission</subject><subject>Encoding</subject><subject>ergodic capacity</subject><subject>Exact sciences and technology</subject><subject>full-rate space-time block codes</subject><subject>information losslessness</subject><subject>Information theory</subject><subject>Information, signal and communications theory</subject><subject>low ML- decoding complexity</subject><subject>MIMO</subject><subject>Mutual information</subject><subject>Radiocommunications</subject><subject>Receiving antennas</subject><subject>Signal and communications theory</subject><subject>Silver</subject><subject>Simulation</subject><subject>Systems, networks and services of telecommunications</subject><subject>Telecommunications</subject><subject>Telecommunications and information theory</subject><subject>Transmission and modulation (techniques and equipments)</subject><subject>Transmitting antennas</subject><issn>0018-9448</issn><issn>1557-9654</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2011</creationdate><recordtype>article</recordtype><recordid>eNo9kNFLwzAQh4MoOKfvA1-G4GNrLk3S5FGKzsHAB-dzuLRX6KjrTDZB_3pTNvZ0HPf97viOsRnwHIDbp_VynQsOkAvQQpT6gk1AqTKzWslLNuEcTGalNNfsJsZNaqUCMWGzBW0pYN_9UTP_6PofCvNqaCjesqsW-0h3pzpln68v6-otW70vltXzKqsLLfZZKTyh5KIQui3RKsURoDEF2AY8L2pp0BtlCtJolPe6MdJ7i6CEhFpiU0zZw3HvLgzfB4p7txkOYZtOOmMl2FKWNkH8CNVhiDFQ63ah-8Lw64C7Ud8lfTfqu5N-ijye9mKssW8DbusunnNCKpW-MXL3R64jovNYc651svoHy8RgHg</recordid><startdate>20110901</startdate><enddate>20110901</enddate><creator>Srinath, K. P.</creator><creator>Rajan, B. S.</creator><general>IEEE</general><general>Institute of Electrical and Electronics Engineers</general><general>The Institute of Electrical and Electronics Engineers, Inc. (IEEE)</general><scope>97E</scope><scope>RIA</scope><scope>RIE</scope><scope>IQODW</scope><scope>AAYXX</scope><scope>CITATION</scope><scope>7SC</scope><scope>7SP</scope><scope>8FD</scope><scope>JQ2</scope><scope>L7M</scope><scope>L~C</scope><scope>L~D</scope></search><sort><creationdate>20110901</creationdate><title>Generalized Silver Codes</title><author>Srinath, K. P. ; Rajan, B. S.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c362t-72bea402326f7a9550a11d8319d1b03c48ab8583e6a85bb6d84bb9a15241c4ad3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2011</creationdate><topic>Antennas</topic><topic>Anticommuting matrices</topic><topic>Applied sciences</topic><topic>Block codes</topic><topic>Coding theory</topic><topic>Coding, codes</topic><topic>Complexity theory</topic><topic>Data transmission</topic><topic>Encoding</topic><topic>ergodic capacity</topic><topic>Exact sciences and technology</topic><topic>full-rate space-time block codes</topic><topic>information losslessness</topic><topic>Information theory</topic><topic>Information, signal and communications theory</topic><topic>low ML- decoding complexity</topic><topic>MIMO</topic><topic>Mutual information</topic><topic>Radiocommunications</topic><topic>Receiving antennas</topic><topic>Signal and communications theory</topic><topic>Silver</topic><topic>Simulation</topic><topic>Systems, networks and services of telecommunications</topic><topic>Telecommunications</topic><topic>Telecommunications and information theory</topic><topic>Transmission and modulation (techniques and equipments)</topic><topic>Transmitting antennas</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Srinath, K. P.</creatorcontrib><creatorcontrib>Rajan, B. S.</creatorcontrib><collection>IEEE All-Society Periodicals Package (ASPP) 2005-present</collection><collection>IEEE All-Society Periodicals Package (ASPP) 1998-Present</collection><collection>IEEE/IET Electronic Library (IEL)</collection><collection>Pascal-Francis</collection><collection>CrossRef</collection><collection>Computer and Information Systems Abstracts</collection><collection>Electronics & Communications Abstracts</collection><collection>Technology Research Database</collection><collection>ProQuest Computer Science Collection</collection><collection>Advanced Technologies Database with Aerospace</collection><collection>Computer and Information Systems Abstracts Academic</collection><collection>Computer and Information Systems Abstracts Professional</collection><jtitle>IEEE transactions on information theory</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Srinath, K. P.</au><au>Rajan, B. S.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Generalized Silver Codes</atitle><jtitle>IEEE transactions on information theory</jtitle><stitle>TIT</stitle><date>2011-09-01</date><risdate>2011</risdate><volume>57</volume><issue>9</issue><spage>6134</spage><epage>6147</epage><pages>6134-6147</pages><issn>0018-9448</issn><eissn>1557-9654</eissn><coden>IETTAW</coden><abstract>For an nt transmit, nr receive antenna system ( nt × nr system), a full-rate space time block code (STBC) transmits at least nmin = min ( nt , nr ) complex symbols per channel use. The well-known Golden code is an example of a full-rate, full-diversity STBC for two transmit antennas. Its ML-decoding complexity is of the order of M 2.5 for square M -QAM. The Silver code for two transmit antennas has all the desirable properties of the Golden code except its coding gain, but offers lower ML-decoding complexity of the order of M 2 . Importantly, the slight loss in coding gain is negligible compared to the advantage it offers in terms of lowering the ML-decoding complexity. For higher number of transmit antennas, the best known codes are the Perfect codes, which are full-rate, full-diversity, information lossless codes (for nr ≥ nt ) but have a high ML-decoding complexity of the order of M n t n min (for n r <; nt, the punctured Perfect codes are considered). In this paper, a scheme to obtain full-rate STBCs for 2a transmit antennas and any n r with reduced ML-decoding complexity of the order of M n t ( n min-3/4)-0.5 is presented. The codes constructed are also information lossless for nr ≥ nt , like the Perfect codes, and allow higher mutual information than the comparable punctured Perfect codes for nr <; nt . These codes are referred to as the generalized Silver codes, since they enjoy the same desirable properties as the comparable Perfect codes (except possibly the coding gain) with lower ML-decoding complexity, analogous to the Silver code and the Golden code for two transmit antennas. Simulation results of the symbol error rates for four and eight transmit antennas show that the generalized Silver codes match the punctured Perfect codes in error performance while offering lower ML- decoding complexity.</abstract><cop>New York, NY</cop><pub>IEEE</pub><doi>10.1109/TIT.2011.2162276</doi><tpages>14</tpages><oa>free_for_read</oa></addata></record> |
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| ispartof | IEEE transactions on information theory, 2011-09, Vol.57 (9), p.6134-6147 |
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| source | IEEE Electronic Library (IEL) Journals |
| subjects | Antennas Anticommuting matrices Applied sciences Block codes Coding theory Coding, codes Complexity theory Data transmission Encoding ergodic capacity Exact sciences and technology full-rate space-time block codes information losslessness Information theory Information, signal and communications theory low ML- decoding complexity MIMO Mutual information Radiocommunications Receiving antennas Signal and communications theory Silver Simulation Systems, networks and services of telecommunications Telecommunications Telecommunications and information theory Transmission and modulation (techniques and equipments) Transmitting antennas |
| title | Generalized Silver Codes |
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