Near-ellipsoidal Voronoi coding
We consider a special case of Voronoi coding, where a lattice /spl Lambda/ in /spl Ropf//sup n/ is shaped (or truncated) using a lattice /spl Lambda/'={(m/sub 1/x/sub 1/,...,m/sub n/x/sub n/)|(x/sub 1/,...,x/sub n/)/spl isin//spl Lambda/} for a fixed m_=(m/sub 1/,...,m/sub n/)/spl isin/(/spl No...
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| Veröffentlicht in: | IEEE transactions on information theory 2003-07, Vol.49 (7), p.1815-1820 |
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| container_title | IEEE transactions on information theory |
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| creator | Ragot, S. Minjie Xie Lefebvre, R. |
| description | We consider a special case of Voronoi coding, where a lattice /spl Lambda/ in /spl Ropf//sup n/ is shaped (or truncated) using a lattice /spl Lambda/'={(m/sub 1/x/sub 1/,...,m/sub n/x/sub n/)|(x/sub 1/,...,x/sub n/)/spl isin//spl Lambda/} for a fixed m_=(m/sub 1/,...,m/sub n/)/spl isin/(/spl Nopf//spl bsol/{0,1})/sup n/. Using this technique, the shaping boundary is near-ellipsoidal. It is shown that the resulting codes can be indexed by standard Voronoi indexing algorithms plus a conditional modification step, as far as /spl Lambda/' is a sublattice of /spl Lambda/. We derive the underlying conditions on m_ and present generic near-ellipsoidal Voronoi indexing algorithms. Examples of constraints on m_ and conditional modification are provided for the lattices A/sub 2/, D/sub n/ (n/spl ges/2) and 2D/sub n//sup +/ (n even /spl ges/4). |
| doi_str_mv | 10.1109/TIT.2003.813484 |
| format | Article |
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Using this technique, the shaping boundary is near-ellipsoidal. It is shown that the resulting codes can be indexed by standard Voronoi indexing algorithms plus a conditional modification step, as far as /spl Lambda/' is a sublattice of /spl Lambda/. We derive the underlying conditions on m_ and present generic near-ellipsoidal Voronoi indexing algorithms. Examples of constraints on m_ and conditional modification are provided for the lattices A/sub 2/, D/sub n/ (n/spl ges/2) and 2D/sub n//sup +/ (n even /spl ges/4).</description><identifier>ISSN: 0018-9448</identifier><identifier>EISSN: 1557-9654</identifier><identifier>DOI: 10.1109/TIT.2003.813484</identifier><identifier>CODEN: IETTAW</identifier><language>eng</language><publisher>New York: IEEE</publisher><subject>Algorithm design and analysis ; Algorithms ; Boundaries ; Code standards ; Codes ; Coding ; Error correction codes ; Indexing ; Information systems ; Information theory ; Lattices ; Libraries ; Modulation coding ; Speech coding ; Vectors ; Wideband</subject><ispartof>IEEE transactions on information theory, 2003-07, Vol.49 (7), p.1815-1820</ispartof><rights>Copyright Institute of Electrical and Electronics Engineers, Inc. (IEEE) Jul 2003</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c350t-931e585a62a224e4c951f48817a9edc307b0e0c8d985177de01c19f6926393b53</citedby><cites>FETCH-LOGICAL-c350t-931e585a62a224e4c951f48817a9edc307b0e0c8d985177de01c19f6926393b53</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktohtml>$$Uhttps://ieeexplore.ieee.org/document/1207381$$EHTML$$P50$$Gieee$$H</linktohtml><link.rule.ids>314,776,780,792,27903,27904,54736</link.rule.ids><linktorsrc>$$Uhttps://ieeexplore.ieee.org/document/1207381$$EView_record_in_IEEE$$FView_record_in_$$GIEEE</linktorsrc></links><search><creatorcontrib>Ragot, S.</creatorcontrib><creatorcontrib>Minjie Xie</creatorcontrib><creatorcontrib>Lefebvre, R.</creatorcontrib><title>Near-ellipsoidal Voronoi coding</title><title>IEEE transactions on information theory</title><addtitle>TIT</addtitle><description>We consider a special case of Voronoi coding, where a lattice /spl Lambda/ in /spl Ropf//sup n/ is shaped (or truncated) using a lattice /spl Lambda/'={(m/sub 1/x/sub 1/,...,m/sub n/x/sub n/)|(x/sub 1/,...,x/sub n/)/spl isin//spl Lambda/} for a fixed m_=(m/sub 1/,...,m/sub n/)/spl isin/(/spl Nopf//spl bsol/{0,1})/sup n/. Using this technique, the shaping boundary is near-ellipsoidal. It is shown that the resulting codes can be indexed by standard Voronoi indexing algorithms plus a conditional modification step, as far as /spl Lambda/' is a sublattice of /spl Lambda/. We derive the underlying conditions on m_ and present generic near-ellipsoidal Voronoi indexing algorithms. Examples of constraints on m_ and conditional modification are provided for the lattices A/sub 2/, D/sub n/ (n/spl ges/2) and 2D/sub n//sup +/ (n even /spl ges/4).</description><subject>Algorithm design and analysis</subject><subject>Algorithms</subject><subject>Boundaries</subject><subject>Code standards</subject><subject>Codes</subject><subject>Coding</subject><subject>Error correction codes</subject><subject>Indexing</subject><subject>Information systems</subject><subject>Information theory</subject><subject>Lattices</subject><subject>Libraries</subject><subject>Modulation coding</subject><subject>Speech coding</subject><subject>Vectors</subject><subject>Wideband</subject><issn>0018-9448</issn><issn>1557-9654</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2003</creationdate><recordtype>article</recordtype><sourceid>RIE</sourceid><recordid>eNp9kE1LAzEQhoMoWKtnDx4sHsTLtjP52CRHKX4Uil6q15Bms7Jlu6lJe_DfN3UFwYOnYeB5X2YeQi4RxoigJ4vZYkwB2Fgh44ofkQEKIQtdCn5MBgCoCs25OiVnKa3yygXSAbl-8TYWvm2bTQpNZdvRe4ihC83IharpPs7JSW3b5C9-5pC8PT4sps_F_PVpNr2fF44J2BaaoRdK2JJaSrnnTgusuVIorfaVYyCX4MGpSiuBUlYe0KGuS01LptlSsCG57Xs3MXzufNqadZNcvst2PuySoYpLUIpm8O5fEIEh1VJ8ozd_0FXYxS6_YVALpUoAnaFJD7kYUoq-NpvYrG38yk3mINZkseYg1vRic-KqTzTe-1-agmSZ2ANCLHBS</recordid><startdate>20030701</startdate><enddate>20030701</enddate><creator>Ragot, S.</creator><creator>Minjie Xie</creator><creator>Lefebvre, R.</creator><general>IEEE</general><general>The Institute of Electrical and Electronics Engineers, Inc. (IEEE)</general><scope>RIA</scope><scope>RIE</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><scope>F28</scope><scope>FR3</scope></search><sort><creationdate>20030701</creationdate><title>Near-ellipsoidal Voronoi coding</title><author>Ragot, S. ; Minjie Xie ; Lefebvre, R.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c350t-931e585a62a224e4c951f48817a9edc307b0e0c8d985177de01c19f6926393b53</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2003</creationdate><topic>Algorithm design and analysis</topic><topic>Algorithms</topic><topic>Boundaries</topic><topic>Code standards</topic><topic>Codes</topic><topic>Coding</topic><topic>Error correction codes</topic><topic>Indexing</topic><topic>Information systems</topic><topic>Information theory</topic><topic>Lattices</topic><topic>Libraries</topic><topic>Modulation coding</topic><topic>Speech coding</topic><topic>Vectors</topic><topic>Wideband</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Ragot, S.</creatorcontrib><creatorcontrib>Minjie Xie</creatorcontrib><creatorcontrib>Lefebvre, R.</creatorcontrib><collection>IEEE All-Society Periodicals Package (ASPP) 1998–Present</collection><collection>IEEE Electronic Library (IEL)</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><collection>ANTE: Abstracts in New Technology & Engineering</collection><collection>Engineering Research Database</collection><jtitle>IEEE transactions on information theory</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext_linktorsrc</fulltext></delivery><addata><au>Ragot, S.</au><au>Minjie Xie</au><au>Lefebvre, R.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Near-ellipsoidal Voronoi coding</atitle><jtitle>IEEE transactions on information theory</jtitle><stitle>TIT</stitle><date>2003-07-01</date><risdate>2003</risdate><volume>49</volume><issue>7</issue><spage>1815</spage><epage>1820</epage><pages>1815-1820</pages><issn>0018-9448</issn><eissn>1557-9654</eissn><coden>IETTAW</coden><abstract>We consider a special case of Voronoi coding, where a lattice /spl Lambda/ in /spl Ropf//sup n/ is shaped (or truncated) using a lattice /spl Lambda/'={(m/sub 1/x/sub 1/,...,m/sub n/x/sub n/)|(x/sub 1/,...,x/sub n/)/spl isin//spl Lambda/} for a fixed m_=(m/sub 1/,...,m/sub n/)/spl isin/(/spl Nopf//spl bsol/{0,1})/sup n/. Using this technique, the shaping boundary is near-ellipsoidal. It is shown that the resulting codes can be indexed by standard Voronoi indexing algorithms plus a conditional modification step, as far as /spl Lambda/' is a sublattice of /spl Lambda/. We derive the underlying conditions on m_ and present generic near-ellipsoidal Voronoi indexing algorithms. Examples of constraints on m_ and conditional modification are provided for the lattices A/sub 2/, D/sub n/ (n/spl ges/2) and 2D/sub n//sup +/ (n even /spl ges/4).</abstract><cop>New York</cop><pub>IEEE</pub><doi>10.1109/TIT.2003.813484</doi><tpages>6</tpages></addata></record> |
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| source | IEEE Electronic Library (IEL) |
| subjects | Algorithm design and analysis Algorithms Boundaries Code standards Codes Coding Error correction codes Indexing Information systems Information theory Lattices Libraries Modulation coding Speech coding Vectors Wideband |
| title | Near-ellipsoidal Voronoi coding |
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