Codes approaching the Shannon limit with polynomial complexity per information bit
We consider codes for channels with extreme noise that emerge in various low-power applications. Simple LDPC-type codes with parity checks of weight 3 are first studied for any dimension $m\rightarrow\infty.$ These codes form modulation schemes: they improve the original channel output for any $SNR&...
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| creator | Dumer, Ilya Gharavi, Navid |
| description | We consider codes for channels with extreme noise that emerge in various
low-power applications. Simple LDPC-type codes with parity checks of weight 3
are first studied for any dimension $m\rightarrow\infty.$ These codes form
modulation schemes: they improve the original channel output for any $SNR>$
$-6$ dB (per information bit) and gain $3$ dB over uncoded modulation as $SNR$
grows. However, they also have a floor on the output bit error rate (BER)
irrespective of their length. Tight lower and upper bounds, which are virtually
identical to simulation results, are then obtained for BER at any SNR. We also
study a combined scheme that splits $m$ information bits into $b$ blocks and
protects each with some polar code. Decoding moves back and forth between polar
and LDPC codes, every time using a polar code of a higher rate. For a
sufficiently large constant $b$ and $m\rightarrow\infty$, this design yields a
vanishing BER at any SNR that is arbitrarily close to the Shannon limit of
-1.59 dB. Unlike other existing designs, this scheme has polynomial complexity
of order $m\ln m$ per information bit. |
| doi_str_mv | 10.48550/arxiv.2101.10145 |
| format | Article |
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low-power applications. Simple LDPC-type codes with parity checks of weight 3
are first studied for any dimension $m\rightarrow\infty.$ These codes form
modulation schemes: they improve the original channel output for any $SNR>$
$-6$ dB (per information bit) and gain $3$ dB over uncoded modulation as $SNR$
grows. However, they also have a floor on the output bit error rate (BER)
irrespective of their length. Tight lower and upper bounds, which are virtually
identical to simulation results, are then obtained for BER at any SNR. We also
study a combined scheme that splits $m$ information bits into $b$ blocks and
protects each with some polar code. Decoding moves back and forth between polar
and LDPC codes, every time using a polar code of a higher rate. For a
sufficiently large constant $b$ and $m\rightarrow\infty$, this design yields a
vanishing BER at any SNR that is arbitrarily close to the Shannon limit of
-1.59 dB. Unlike other existing designs, this scheme has polynomial complexity
of order $m\ln m$ per information bit.</description><identifier>DOI: 10.48550/arxiv.2101.10145</identifier><language>eng</language><subject>Computer Science - Information Theory ; Mathematics - Information Theory</subject><creationdate>2021-01</creationdate><rights>http://creativecommons.org/licenses/by-nc-sa/4.0</rights><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>228,230,776,881</link.rule.ids><linktorsrc>$$Uhttps://arxiv.org/abs/2101.10145$$EView_record_in_Cornell_University$$FView_record_in_$$GCornell_University$$Hfree_for_read</linktorsrc><backlink>$$Uhttps://doi.org/10.48550/arXiv.2101.10145$$DView paper in arXiv$$Hfree_for_read</backlink></links><search><creatorcontrib>Dumer, Ilya</creatorcontrib><creatorcontrib>Gharavi, Navid</creatorcontrib><title>Codes approaching the Shannon limit with polynomial complexity per information bit</title><description>We consider codes for channels with extreme noise that emerge in various
low-power applications. Simple LDPC-type codes with parity checks of weight 3
are first studied for any dimension $m\rightarrow\infty.$ These codes form
modulation schemes: they improve the original channel output for any $SNR>$
$-6$ dB (per information bit) and gain $3$ dB over uncoded modulation as $SNR$
grows. However, they also have a floor on the output bit error rate (BER)
irrespective of their length. Tight lower and upper bounds, which are virtually
identical to simulation results, are then obtained for BER at any SNR. We also
study a combined scheme that splits $m$ information bits into $b$ blocks and
protects each with some polar code. Decoding moves back and forth between polar
and LDPC codes, every time using a polar code of a higher rate. For a
sufficiently large constant $b$ and $m\rightarrow\infty$, this design yields a
vanishing BER at any SNR that is arbitrarily close to the Shannon limit of
-1.59 dB. Unlike other existing designs, this scheme has polynomial complexity
of order $m\ln m$ per information bit.</description><subject>Computer Science - Information Theory</subject><subject>Mathematics - Information Theory</subject><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2021</creationdate><recordtype>article</recordtype><sourceid>GOX</sourceid><recordid>eNotj81OhDAUhbtxYUYfwJV9AbAUCmVpiH_JJCYz7skt3MpNoG06jQ5vL44uzjmr7yQfY3eFyCutlHiAeKavXBaiyLdU6podOj_iiUMI0cMwkfvkaUJ-nMA57_hMCyX-TWniwc-r8wvBzAe_hBnPlFYeMHJy1scFEm2AoXTDrizMJ7z93x07Pj99dK_Z_v3lrXvcZ1A3KtOocJRC1dYIU6lRYYONFkOxtR1kW0toBepKtoNBUGNdWGNLjVpqKaUqd-z-7_Xi1IdIC8S1_3XrL27lD07sSwI</recordid><startdate>20210125</startdate><enddate>20210125</enddate><creator>Dumer, Ilya</creator><creator>Gharavi, Navid</creator><scope>AKY</scope><scope>AKZ</scope><scope>GOX</scope></search><sort><creationdate>20210125</creationdate><title>Codes approaching the Shannon limit with polynomial complexity per information bit</title><author>Dumer, Ilya ; Gharavi, Navid</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-a675-8e5ed2056fb0b45d5e7e780c1e78fc2962a90e8429cbea5d61fbf38e82822253</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2021</creationdate><topic>Computer Science - Information Theory</topic><topic>Mathematics - Information Theory</topic><toplevel>online_resources</toplevel><creatorcontrib>Dumer, Ilya</creatorcontrib><creatorcontrib>Gharavi, Navid</creatorcontrib><collection>arXiv Computer Science</collection><collection>arXiv Mathematics</collection><collection>arXiv.org</collection></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext_linktorsrc</fulltext></delivery><addata><au>Dumer, Ilya</au><au>Gharavi, Navid</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Codes approaching the Shannon limit with polynomial complexity per information bit</atitle><date>2021-01-25</date><risdate>2021</risdate><abstract>We consider codes for channels with extreme noise that emerge in various
low-power applications. Simple LDPC-type codes with parity checks of weight 3
are first studied for any dimension $m\rightarrow\infty.$ These codes form
modulation schemes: they improve the original channel output for any $SNR>$
$-6$ dB (per information bit) and gain $3$ dB over uncoded modulation as $SNR$
grows. However, they also have a floor on the output bit error rate (BER)
irrespective of their length. Tight lower and upper bounds, which are virtually
identical to simulation results, are then obtained for BER at any SNR. We also
study a combined scheme that splits $m$ information bits into $b$ blocks and
protects each with some polar code. Decoding moves back and forth between polar
and LDPC codes, every time using a polar code of a higher rate. For a
sufficiently large constant $b$ and $m\rightarrow\infty$, this design yields a
vanishing BER at any SNR that is arbitrarily close to the Shannon limit of
-1.59 dB. Unlike other existing designs, this scheme has polynomial complexity
of order $m\ln m$ per information bit.</abstract><doi>10.48550/arxiv.2101.10145</doi><oa>free_for_read</oa></addata></record> |
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| subjects | Computer Science - Information Theory Mathematics - Information Theory |
| title | Codes approaching the Shannon limit with polynomial complexity per information bit |
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