Symbol-intersecting codes
We consider codes consisting of arrays over an alphabet F, in which certain intersecting subsets of n/spl times/m coordinates are required to form codewords of length n in prescribed codes over the alphabet F/sup m/. Two specific cases are studied. In the first case, referred to as a singly-intersec...
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| Veröffentlicht in: | IEEE transactions on information theory 2005-07, Vol.51 (7), p.2266-2281 |
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| creator | Roth, R.M. Seroussi, G. |
| description | We consider codes consisting of arrays over an alphabet F, in which certain intersecting subsets of n/spl times/m coordinates are required to form codewords of length n in prescribed codes over the alphabet F/sup m/. Two specific cases are studied. In the first case, referred to as a singly-intersecting coding scheme, the user data is mapped into n/spl times/(2m-1) arrays over an alphabet F, such that the n/spl times/m subarray that consists of the left (respectively, right) m columns forms a codeword of a prescribed code of length n over F/sup m/; in particular, the center column is shared by the left and right subarrays. Bounds are obtained on the achievable redundancy region of singly-intersecting coding schemes, and constructions are presented that approach-and sometimes meet-these bounds. It is shown that singly-intersecting coding schemes can be applied in a certain model of broadcast channels to guarantee reliable communication. The second setting, referred to as a fully-intersecting coding scheme, maps the user data into n/spl times/m/spl times/m three-dimensional arrays in which parallel n/spl times/m subarrays are all codewords of the same prescribed code over F/sup m/. Bounds and constructions are presented for these codes, with the analysis based on representing the n/spl times/m/spl times/m arrays as vectors over certain algebras on m/spl times/m matrices. |
| doi_str_mv | 10.1109/TIT.2005.850042 |
| format | Article |
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Two specific cases are studied. In the first case, referred to as a singly-intersecting coding scheme, the user data is mapped into n/spl times/(2m-1) arrays over an alphabet F, such that the n/spl times/m subarray that consists of the left (respectively, right) m columns forms a codeword of a prescribed code of length n over F/sup m/; in particular, the center column is shared by the left and right subarrays. Bounds are obtained on the achievable redundancy region of singly-intersecting coding schemes, and constructions are presented that approach-and sometimes meet-these bounds. It is shown that singly-intersecting coding schemes can be applied in a certain model of broadcast channels to guarantee reliable communication. The second setting, referred to as a fully-intersecting coding scheme, maps the user data into n/spl times/m/spl times/m three-dimensional arrays in which parallel n/spl times/m subarrays are all codewords of the same prescribed code over F/sup m/. Bounds and constructions are presented for these codes, with the analysis based on representing the n/spl times/m/spl times/m arrays as vectors over certain algebras on m/spl times/m matrices.</description><identifier>ISSN: 0018-9448</identifier><identifier>EISSN: 1557-9654</identifier><identifier>DOI: 10.1109/TIT.2005.850042</identifier><identifier>CODEN: IETTAW</identifier><language>eng</language><publisher>New York, NY: IEEE</publisher><subject>Achievable region ; Algebra ; Alphabets ; Applied sciences ; Arrays ; broadcast channels ; Broadcasting ; Case studies ; Channels ; Cities and towns ; Codes ; codes over rings ; Coding ; Coding, codes ; Communication channels ; Computer science ; Construction ; Exact sciences and technology ; Information theory ; Information, signal and communications theory ; Kronecker sum of matrices ; Laboratories ; Mathematical analysis ; Matrices ; Redundancy ; Reed-Solomon (RS) codes ; Signal and communications theory ; subfield subcodes ; Telecommunications and information theory ; Vectors (mathematics)</subject><ispartof>IEEE transactions on information theory, 2005-07, Vol.51 (7), p.2266-2281</ispartof><rights>2005 INIST-CNRS</rights><rights>Copyright Institute of Electrical and Electronics Engineers, Inc. (IEEE) Jul 2005</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c381t-835538cfc48f81cffc9d186db81ceb6479c0f312be718548cfcbfbd0571b15fe3</citedby><cites>FETCH-LOGICAL-c381t-835538cfc48f81cffc9d186db81ceb6479c0f312be718548cfcbfbd0571b15fe3</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktohtml>$$Uhttps://ieeexplore.ieee.org/document/1459043$$EHTML$$P50$$Gieee$$H</linktohtml><link.rule.ids>314,776,780,792,27903,27904,54737</link.rule.ids><linktorsrc>$$Uhttps://ieeexplore.ieee.org/document/1459043$$EView_record_in_IEEE$$FView_record_in_$$GIEEE</linktorsrc><backlink>$$Uhttp://pascal-francis.inist.fr/vibad/index.php?action=getRecordDetail&idt=16926204$$DView record in Pascal Francis$$Hfree_for_read</backlink></links><search><creatorcontrib>Roth, R.M.</creatorcontrib><creatorcontrib>Seroussi, G.</creatorcontrib><title>Symbol-intersecting codes</title><title>IEEE transactions on information theory</title><addtitle>TIT</addtitle><description>We consider codes consisting of arrays over an alphabet F, in which certain intersecting subsets of n/spl times/m coordinates are required to form codewords of length n in prescribed codes over the alphabet F/sup m/. Two specific cases are studied. In the first case, referred to as a singly-intersecting coding scheme, the user data is mapped into n/spl times/(2m-1) arrays over an alphabet F, such that the n/spl times/m subarray that consists of the left (respectively, right) m columns forms a codeword of a prescribed code of length n over F/sup m/; in particular, the center column is shared by the left and right subarrays. Bounds are obtained on the achievable redundancy region of singly-intersecting coding schemes, and constructions are presented that approach-and sometimes meet-these bounds. It is shown that singly-intersecting coding schemes can be applied in a certain model of broadcast channels to guarantee reliable communication. The second setting, referred to as a fully-intersecting coding scheme, maps the user data into n/spl times/m/spl times/m three-dimensional arrays in which parallel n/spl times/m subarrays are all codewords of the same prescribed code over F/sup m/. Bounds and constructions are presented for these codes, with the analysis based on representing the n/spl times/m/spl times/m arrays as vectors over certain algebras on m/spl times/m matrices.</description><subject>Achievable region</subject><subject>Algebra</subject><subject>Alphabets</subject><subject>Applied sciences</subject><subject>Arrays</subject><subject>broadcast channels</subject><subject>Broadcasting</subject><subject>Case studies</subject><subject>Channels</subject><subject>Cities and towns</subject><subject>Codes</subject><subject>codes over rings</subject><subject>Coding</subject><subject>Coding, codes</subject><subject>Communication channels</subject><subject>Computer science</subject><subject>Construction</subject><subject>Exact sciences and technology</subject><subject>Information theory</subject><subject>Information, signal and communications theory</subject><subject>Kronecker sum of matrices</subject><subject>Laboratories</subject><subject>Mathematical analysis</subject><subject>Matrices</subject><subject>Redundancy</subject><subject>Reed-Solomon (RS) codes</subject><subject>Signal and communications theory</subject><subject>subfield subcodes</subject><subject>Telecommunications and information theory</subject><subject>Vectors (mathematics)</subject><issn>0018-9448</issn><issn>1557-9654</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2005</creationdate><recordtype>article</recordtype><sourceid>RIE</sourceid><recordid>eNp90M9LwzAUB_AgCs7pWcSLCOqp3Xv50SZHGf4YDDw4z6FNE-no2pl0h_33pnQw8OApPPJ57_G-hFwjpIigZqvFKqUAIpUCgNMTMkEh8kRlgp-SCQDKRHEuz8lFCOtYcoF0Qm4-95uya5K67a0P1vR1-31nusqGS3LmiibYq8M7JV-vL6v5e7L8eFvMn5eJYRL7RDIhmDTOcOkkGueMqlBmVRkLW2Y8VwYcQ1raHKXggyxdWYHIsUThLJuSp3Hu1nc_Oxt6vamDsU1TtLbbBa2QxxMYQJSP_0oqEWQOeYT3f-C62_k2XqFRCQU0ywc0G5HxXQjeOr319abwe42gh0R1TFQPieox0djxcBhbBFM0zhetqcOxLVM0o8Cjux1dba09fvO4mTP2C_btfGk</recordid><startdate>20050701</startdate><enddate>20050701</enddate><creator>Roth, R.M.</creator><creator>Seroussi, G.</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><scope>F28</scope><scope>FR3</scope></search><sort><creationdate>20050701</creationdate><title>Symbol-intersecting codes</title><author>Roth, R.M. ; Seroussi, G.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c381t-835538cfc48f81cffc9d186db81ceb6479c0f312be718548cfcbfbd0571b15fe3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2005</creationdate><topic>Achievable region</topic><topic>Algebra</topic><topic>Alphabets</topic><topic>Applied sciences</topic><topic>Arrays</topic><topic>broadcast channels</topic><topic>Broadcasting</topic><topic>Case studies</topic><topic>Channels</topic><topic>Cities and towns</topic><topic>Codes</topic><topic>codes over rings</topic><topic>Coding</topic><topic>Coding, codes</topic><topic>Communication channels</topic><topic>Computer science</topic><topic>Construction</topic><topic>Exact sciences and technology</topic><topic>Information theory</topic><topic>Information, signal and communications theory</topic><topic>Kronecker sum of matrices</topic><topic>Laboratories</topic><topic>Mathematical analysis</topic><topic>Matrices</topic><topic>Redundancy</topic><topic>Reed-Solomon (RS) codes</topic><topic>Signal and communications theory</topic><topic>subfield subcodes</topic><topic>Telecommunications and information theory</topic><topic>Vectors (mathematics)</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Roth, R.M.</creatorcontrib><creatorcontrib>Seroussi, G.</creatorcontrib><collection>IEEE All-Society Periodicals Package (ASPP) 2005-present</collection><collection>IEEE All-Society Periodicals Package (ASPP) 1998-Present</collection><collection>IEEE 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><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>Roth, R.M.</au><au>Seroussi, G.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Symbol-intersecting codes</atitle><jtitle>IEEE transactions on information theory</jtitle><stitle>TIT</stitle><date>2005-07-01</date><risdate>2005</risdate><volume>51</volume><issue>7</issue><spage>2266</spage><epage>2281</epage><pages>2266-2281</pages><issn>0018-9448</issn><eissn>1557-9654</eissn><coden>IETTAW</coden><abstract>We consider codes consisting of arrays over an alphabet F, in which certain intersecting subsets of n/spl times/m coordinates are required to form codewords of length n in prescribed codes over the alphabet F/sup m/. Two specific cases are studied. In the first case, referred to as a singly-intersecting coding scheme, the user data is mapped into n/spl times/(2m-1) arrays over an alphabet F, such that the n/spl times/m subarray that consists of the left (respectively, right) m columns forms a codeword of a prescribed code of length n over F/sup m/; in particular, the center column is shared by the left and right subarrays. Bounds are obtained on the achievable redundancy region of singly-intersecting coding schemes, and constructions are presented that approach-and sometimes meet-these bounds. It is shown that singly-intersecting coding schemes can be applied in a certain model of broadcast channels to guarantee reliable communication. The second setting, referred to as a fully-intersecting coding scheme, maps the user data into n/spl times/m/spl times/m three-dimensional arrays in which parallel n/spl times/m subarrays are all codewords of the same prescribed code over F/sup m/. Bounds and constructions are presented for these codes, with the analysis based on representing the n/spl times/m/spl times/m arrays as vectors over certain algebras on m/spl times/m matrices.</abstract><cop>New York, NY</cop><pub>IEEE</pub><doi>10.1109/TIT.2005.850042</doi><tpages>16</tpages></addata></record> |
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| subjects | Achievable region Algebra Alphabets Applied sciences Arrays broadcast channels Broadcasting Case studies Channels Cities and towns Codes codes over rings Coding Coding, codes Communication channels Computer science Construction Exact sciences and technology Information theory Information, signal and communications theory Kronecker sum of matrices Laboratories Mathematical analysis Matrices Redundancy Reed-Solomon (RS) codes Signal and communications theory subfield subcodes Telecommunications and information theory Vectors (mathematics) |
| title | Symbol-intersecting codes |
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