Loading…
Least Squares Superposition Codes With Bernoulli Dictionary are Still Reliable at Rates up to Capacity
For the additive white Gaussian noise channel with average power constraint, sparse superposition codes with least squares decoding are proposed by Barron and Joseph in 2010. The codewords are designed by using a dictionary each entry of which is drawn from a Gaussian distribution. The error probabi...
Saved in:
| Published in: | IEEE transactions on information theory 2014-05, Vol.60 (5), p.2737-2750 |
|---|---|
| Main Authors: | , , |
| Format: | Article |
| Language: | English |
| Subjects: | |
| Citations: | Items that this one cites Items that cite this one |
| Online Access: | Get full text |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| cited_by | cdi_FETCH-LOGICAL-c354t-46cce660566fdcb875a4c9cf43a581525473660a654dfce9e4cac0c4a648c3ae3 |
|---|---|
| cites | cdi_FETCH-LOGICAL-c354t-46cce660566fdcb875a4c9cf43a581525473660a654dfce9e4cac0c4a648c3ae3 |
| container_end_page | 2750 |
| container_issue | 5 |
| container_start_page | 2737 |
| container_title | IEEE transactions on information theory |
| container_volume | 60 |
| creator | Takeishi, Yoshinari Kawakita, Masanori Takeuchi, Jun'ichi |
| description | For the additive white Gaussian noise channel with average power constraint, sparse superposition codes with least squares decoding are proposed by Barron and Joseph in 2010. The codewords are designed by using a dictionary each entry of which is drawn from a Gaussian distribution. The error probability is shown to be exponentially small for all rates up to the capacity. This paper proves that when each entry of the dictionary is drawn from a Bernoulli distribution, the error probability is also exponentially small for all rates up to the capacity. The proof is via a central limit theorem-type inequality, which we show for this analysis. |
| doi_str_mv | 10.1109/TIT.2014.2312728 |
| format | article |
| fullrecord | <record><control><sourceid>proquest_ieee_</sourceid><recordid>TN_cdi_proquest_miscellaneous_1620103307</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><ieee_id>6776455</ieee_id><sourcerecordid>3291694591</sourcerecordid><originalsourceid>FETCH-LOGICAL-c354t-46cce660566fdcb875a4c9cf43a581525473660a654dfce9e4cac0c4a648c3ae3</originalsourceid><addsrcrecordid>eNpdkEFrGzEQhUVpIW7ae6AXQSn0sq60Gml3j62btAFDIXbpUUzkWaqgrDaS9pB_XxmbHHoaNO97M5rH2JUUaynF8GV_u1-3QsK6VbLt2v4VW0mtu2YwGl6zlRCybwaA_oK9zfmhPkHLdsXGLWEufPe0YKLMd8tMaY7ZFx8nvomH2vvjy1_-jdIUlxA8_-7dUcT0zKuF74oPgd9R8HgfiGPhd1iqa5l5iXyDMzpfnt-xNyOGTO_P9ZL9vrneb342218_bjdft41TGkoDxjkyRmhjxoO77zuN4AY3gkLdS91q6FSVsd50GB0NBA6dcIAGeqeQ1CX7fJo7p_i0UC720WdHIeBEcclWmpqRUEp0Ff34H_oQlzTV39m6SUArRC8rJU6USzHnRKOdk3-sx1sp7DF4W4O3x-DtOfhq-XQejNlhGBNOzucXX9vDYAQMlftw4jwRvcim6wxorf4B37OLeQ</addsrcrecordid><sourcetype>Aggregation Database</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype><pqid>1520420081</pqid></control><display><type>article</type><title>Least Squares Superposition Codes With Bernoulli Dictionary are Still Reliable at Rates up to Capacity</title><source>IEEE Electronic Library (IEL) Journals</source><creator>Takeishi, Yoshinari ; Kawakita, Masanori ; Takeuchi, Jun'ichi</creator><creatorcontrib>Takeishi, Yoshinari ; Kawakita, Masanori ; Takeuchi, Jun'ichi</creatorcontrib><description>For the additive white Gaussian noise channel with average power constraint, sparse superposition codes with least squares decoding are proposed by Barron and Joseph in 2010. The codewords are designed by using a dictionary each entry of which is drawn from a Gaussian distribution. The error probability is shown to be exponentially small for all rates up to the capacity. This paper proves that when each entry of the dictionary is drawn from a Bernoulli distribution, the error probability is also exponentially small for all rates up to the capacity. The proof is via a central limit theorem-type inequality, which we show for this analysis.</description><identifier>ISSN: 0018-9448</identifier><identifier>EISSN: 1557-9654</identifier><identifier>DOI: 10.1109/TIT.2014.2312728</identifier><identifier>CODEN: IETTAW</identifier><language>eng</language><publisher>New York, NY: IEEE</publisher><subject>Applied sciences ; AWGN channels ; Channels ; Codes ; Coding, codes ; Decoding ; Dictionaries ; Error probability ; Errors ; Exact sciences and technology ; Gaussian ; Gaussian distribution ; Inequalities ; Information theory ; Information, signal and communications theory ; Least squares method ; Noise ; Normal distribution ; Random variables ; Signal and communications theory ; Telecommunications and information theory ; Vectors</subject><ispartof>IEEE transactions on information theory, 2014-05, Vol.60 (5), p.2737-2750</ispartof><rights>2015 INIST-CNRS</rights><rights>Copyright The Institute of Electrical and Electronics Engineers, Inc. (IEEE) May 2014</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c354t-46cce660566fdcb875a4c9cf43a581525473660a654dfce9e4cac0c4a648c3ae3</citedby><cites>FETCH-LOGICAL-c354t-46cce660566fdcb875a4c9cf43a581525473660a654dfce9e4cac0c4a648c3ae3</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktohtml>$$Uhttps://ieeexplore.ieee.org/document/6776455$$EHTML$$P50$$Gieee$$H</linktohtml><link.rule.ids>314,780,784,27924,27925,54796</link.rule.ids><backlink>$$Uhttp://pascal-francis.inist.fr/vibad/index.php?action=getRecordDetail&idt=28496049$$DView record in Pascal Francis$$Hfree_for_read</backlink></links><search><creatorcontrib>Takeishi, Yoshinari</creatorcontrib><creatorcontrib>Kawakita, Masanori</creatorcontrib><creatorcontrib>Takeuchi, Jun'ichi</creatorcontrib><title>Least Squares Superposition Codes With Bernoulli Dictionary are Still Reliable at Rates up to Capacity</title><title>IEEE transactions on information theory</title><addtitle>TIT</addtitle><description>For the additive white Gaussian noise channel with average power constraint, sparse superposition codes with least squares decoding are proposed by Barron and Joseph in 2010. The codewords are designed by using a dictionary each entry of which is drawn from a Gaussian distribution. The error probability is shown to be exponentially small for all rates up to the capacity. This paper proves that when each entry of the dictionary is drawn from a Bernoulli distribution, the error probability is also exponentially small for all rates up to the capacity. The proof is via a central limit theorem-type inequality, which we show for this analysis.</description><subject>Applied sciences</subject><subject>AWGN channels</subject><subject>Channels</subject><subject>Codes</subject><subject>Coding, codes</subject><subject>Decoding</subject><subject>Dictionaries</subject><subject>Error probability</subject><subject>Errors</subject><subject>Exact sciences and technology</subject><subject>Gaussian</subject><subject>Gaussian distribution</subject><subject>Inequalities</subject><subject>Information theory</subject><subject>Information, signal and communications theory</subject><subject>Least squares method</subject><subject>Noise</subject><subject>Normal distribution</subject><subject>Random variables</subject><subject>Signal and communications theory</subject><subject>Telecommunications and information theory</subject><subject>Vectors</subject><issn>0018-9448</issn><issn>1557-9654</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2014</creationdate><recordtype>article</recordtype><recordid>eNpdkEFrGzEQhUVpIW7ae6AXQSn0sq60Gml3j62btAFDIXbpUUzkWaqgrDaS9pB_XxmbHHoaNO97M5rH2JUUaynF8GV_u1-3QsK6VbLt2v4VW0mtu2YwGl6zlRCybwaA_oK9zfmhPkHLdsXGLWEufPe0YKLMd8tMaY7ZFx8nvomH2vvjy1_-jdIUlxA8_-7dUcT0zKuF74oPgd9R8HgfiGPhd1iqa5l5iXyDMzpfnt-xNyOGTO_P9ZL9vrneb342218_bjdft41TGkoDxjkyRmhjxoO77zuN4AY3gkLdS91q6FSVsd50GB0NBA6dcIAGeqeQ1CX7fJo7p_i0UC720WdHIeBEcclWmpqRUEp0Ff34H_oQlzTV39m6SUArRC8rJU6USzHnRKOdk3-sx1sp7DF4W4O3x-DtOfhq-XQejNlhGBNOzucXX9vDYAQMlftw4jwRvcim6wxorf4B37OLeQ</recordid><startdate>20140501</startdate><enddate>20140501</enddate><creator>Takeishi, Yoshinari</creator><creator>Kawakita, Masanori</creator><creator>Takeuchi, Jun'ichi</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>20140501</creationdate><title>Least Squares Superposition Codes With Bernoulli Dictionary are Still Reliable at Rates up to Capacity</title><author>Takeishi, Yoshinari ; Kawakita, Masanori ; Takeuchi, Jun'ichi</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c354t-46cce660566fdcb875a4c9cf43a581525473660a654dfce9e4cac0c4a648c3ae3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2014</creationdate><topic>Applied sciences</topic><topic>AWGN channels</topic><topic>Channels</topic><topic>Codes</topic><topic>Coding, codes</topic><topic>Decoding</topic><topic>Dictionaries</topic><topic>Error probability</topic><topic>Errors</topic><topic>Exact sciences and technology</topic><topic>Gaussian</topic><topic>Gaussian distribution</topic><topic>Inequalities</topic><topic>Information theory</topic><topic>Information, signal and communications theory</topic><topic>Least squares method</topic><topic>Noise</topic><topic>Normal distribution</topic><topic>Random variables</topic><topic>Signal and communications theory</topic><topic>Telecommunications and information theory</topic><topic>Vectors</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Takeishi, Yoshinari</creatorcontrib><creatorcontrib>Kawakita, Masanori</creatorcontrib><creatorcontrib>Takeuchi, Jun'ichi</creatorcontrib><collection>IEEE All-Society Periodicals Package (ASPP) 2005-present</collection><collection>IEEE All-Society Periodicals Package (ASPP) Online</collection><collection>IEEE/IET Electronic Library</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</fulltext></delivery><addata><au>Takeishi, Yoshinari</au><au>Kawakita, Masanori</au><au>Takeuchi, Jun'ichi</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Least Squares Superposition Codes With Bernoulli Dictionary are Still Reliable at Rates up to Capacity</atitle><jtitle>IEEE transactions on information theory</jtitle><stitle>TIT</stitle><date>2014-05-01</date><risdate>2014</risdate><volume>60</volume><issue>5</issue><spage>2737</spage><epage>2750</epage><pages>2737-2750</pages><issn>0018-9448</issn><eissn>1557-9654</eissn><coden>IETTAW</coden><abstract>For the additive white Gaussian noise channel with average power constraint, sparse superposition codes with least squares decoding are proposed by Barron and Joseph in 2010. The codewords are designed by using a dictionary each entry of which is drawn from a Gaussian distribution. The error probability is shown to be exponentially small for all rates up to the capacity. This paper proves that when each entry of the dictionary is drawn from a Bernoulli distribution, the error probability is also exponentially small for all rates up to the capacity. The proof is via a central limit theorem-type inequality, which we show for this analysis.</abstract><cop>New York, NY</cop><pub>IEEE</pub><doi>10.1109/TIT.2014.2312728</doi><tpages>14</tpages></addata></record> |
| fulltext | fulltext |
| identifier | ISSN: 0018-9448 |
| ispartof | IEEE transactions on information theory, 2014-05, Vol.60 (5), p.2737-2750 |
| issn | 0018-9448 1557-9654 |
| language | eng |
| recordid | cdi_proquest_miscellaneous_1620103307 |
| source | IEEE Electronic Library (IEL) Journals |
| subjects | Applied sciences AWGN channels Channels Codes Coding, codes Decoding Dictionaries Error probability Errors Exact sciences and technology Gaussian Gaussian distribution Inequalities Information theory Information, signal and communications theory Least squares method Noise Normal distribution Random variables Signal and communications theory Telecommunications and information theory Vectors |
| title | Least Squares Superposition Codes With Bernoulli Dictionary are Still Reliable at Rates up to Capacity |
| url | http://sfxeu10.hosted.exlibrisgroup.com/loughborough?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2025-01-06T03%3A46%3A20IST&url_ver=Z39.88-2004&url_ctx_fmt=infofi/fmt:kev:mtx:ctx&rfr_id=info:sid/primo.exlibrisgroup.com:primo3-Article-proquest_ieee_&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.genre=article&rft.atitle=Least%20Squares%20Superposition%20Codes%20With%20Bernoulli%20Dictionary%20are%20Still%20Reliable%20at%20Rates%20up%20to%20Capacity&rft.jtitle=IEEE%20transactions%20on%20information%20theory&rft.au=Takeishi,%20Yoshinari&rft.date=2014-05-01&rft.volume=60&rft.issue=5&rft.spage=2737&rft.epage=2750&rft.pages=2737-2750&rft.issn=0018-9448&rft.eissn=1557-9654&rft.coden=IETTAW&rft_id=info:doi/10.1109/TIT.2014.2312728&rft_dat=%3Cproquest_ieee_%3E3291694591%3C/proquest_ieee_%3E%3Cgrp_id%3Ecdi_FETCH-LOGICAL-c354t-46cce660566fdcb875a4c9cf43a581525473660a654dfce9e4cac0c4a648c3ae3%3C/grp_id%3E%3Coa%3E%3C/oa%3E%3Curl%3E%3C/url%3E&rft_id=info:oai/&rft_pqid=1520420081&rft_id=info:pmid/&rft_ieee_id=6776455&rfr_iscdi=true |