Generating parity check equations for bounded-distance iterative erasure decoding
A generic (r,m)-erasure correcting set is a collection of vectors in F 2 r which can be used to generate, for each binary linear code of codimension r, a collection of parity check equations that enables iterative decoding of all correctable erasure patterns of size at most m. That is to say, the on...
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| creator | Hollmann, H.D.L. Tolhuizen, L.M.G.M. |
| description | A generic (r,m)-erasure correcting set is a collection of vectors in F 2 r which can be used to generate, for each binary linear code of codimension r, a collection of parity check equations that enables iterative decoding of all correctable erasure patterns of size at most m. That is to say, the only stopping sets of size at most m for the generated parity check equations are the erasure patterns for which there is more than one manner to fill in the erasures to obtain a codeword. We give an explicit construction of generic (r,m)-erasure correcting sets of cardinality Sigma i=0 m-1 ( i r-1 ). Using a random-coding-like argument, we show that for fixed m, the minimum size of a generic (r,m)-erasure correcting set is linear in r |
| doi_str_mv | 10.1109/ISIT.2006.261769 |
| format | Conference Proceeding |
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Using a random-coding-like argument, we show that for fixed m, the minimum size of a generic (r,m)-erasure correcting set is linear in r</description><subject>binary erasure channel</subject><subject>Differential equations</subject><subject>Iterative algorithms</subject><subject>Iterative decoding</subject><subject>Laboratories</subject><subject>Linear code</subject><subject>Parity check codes</subject><subject>stopping set</subject><issn>2157-8095</issn><issn>2157-8117</issn><isbn>142440505X</isbn><isbn>9781424405053</isbn><isbn>1424405041</isbn><isbn>9781424405046</isbn><fulltext>true</fulltext><rsrctype>conference_proceeding</rsrctype><creationdate>2006</creationdate><recordtype>conference_proceeding</recordtype><sourceid>6IE</sourceid><sourceid>RIE</sourceid><recordid>eNpFj0lLA0EUhNsNjDF3wUv_gYmv9-mjBI0DAREjeAu9vNF2mYk9M0L-vYML1qWgPqqgCDljMGcM7EV1X63nHEDPuWZG2z1ywiSXEhRItk8mnClTlIyZg3-gHg__AFh1TGZd9wKjpJLc6gm5W2KD2fWpeaJbl1O_o-EZwyvFj2FM26ajdZupb4cmYixi6nrXBKSp_259Ih29GzLSiKGN48wpOardW4ezX5-Sh-ur9eKmWN0uq8Xlqkicmb4wtQVvy9I7Hy0or2UpbEAXjRK8jsJGLUNEgcJ6Pr43qlROSRUCYO05F1Ny_rObEHGzzend5d1GgtDAlPgC_LxUnA</recordid><startdate>20060101</startdate><enddate>20060101</enddate><creator>Hollmann, H.D.L.</creator><creator>Tolhuizen, L.M.G.M.</creator><general>IEEE</general><scope>6IE</scope><scope>6IH</scope><scope>CBEJK</scope><scope>RIE</scope><scope>RIO</scope></search><sort><creationdate>20060101</creationdate><title>Generating parity check equations for bounded-distance iterative erasure decoding</title><author>Hollmann, H.D.L. ; Tolhuizen, L.M.G.M.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-i217t-7f90b988babd905b64839cead7532fd39d64cde3e39b21097585a545cc0efb223</frbrgroupid><rsrctype>conference_proceedings</rsrctype><prefilter>conference_proceedings</prefilter><language>eng</language><creationdate>2006</creationdate><topic>binary erasure channel</topic><topic>Differential equations</topic><topic>Iterative algorithms</topic><topic>Iterative decoding</topic><topic>Laboratories</topic><topic>Linear code</topic><topic>Parity check codes</topic><topic>stopping set</topic><toplevel>online_resources</toplevel><creatorcontrib>Hollmann, H.D.L.</creatorcontrib><creatorcontrib>Tolhuizen, L.M.G.M.</creatorcontrib><collection>IEEE Electronic Library (IEL) Conference Proceedings</collection><collection>IEEE Proceedings Order Plan (POP) 1998-present by volume</collection><collection>IEEE Xplore All Conference Proceedings</collection><collection>IEEE Electronic Library (IEL)</collection><collection>IEEE Proceedings Order Plans (POP) 1998-present</collection></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext_linktorsrc</fulltext></delivery><addata><au>Hollmann, H.D.L.</au><au>Tolhuizen, L.M.G.M.</au><format>book</format><genre>proceeding</genre><ristype>CONF</ristype><atitle>Generating parity check equations for bounded-distance iterative erasure decoding</atitle><btitle>2006 IEEE International Symposium on Information Theory</btitle><stitle>ISIT</stitle><date>2006-01-01</date><risdate>2006</risdate><spage>514</spage><epage>517</epage><pages>514-517</pages><issn>2157-8095</issn><eissn>2157-8117</eissn><isbn>142440505X</isbn><isbn>9781424405053</isbn><eisbn>1424405041</eisbn><eisbn>9781424405046</eisbn><abstract>A generic (r,m)-erasure correcting set is a collection of vectors in F 2 r which can be used to generate, for each binary linear code of codimension r, a collection of parity check equations that enables iterative decoding of all correctable erasure patterns of size at most m. That is to say, the only stopping sets of size at most m for the generated parity check equations are the erasure patterns for which there is more than one manner to fill in the erasures to obtain a codeword. We give an explicit construction of generic (r,m)-erasure correcting sets of cardinality Sigma i=0 m-1 ( i r-1 ). Using a random-coding-like argument, we show that for fixed m, the minimum size of a generic (r,m)-erasure correcting set is linear in r</abstract><pub>IEEE</pub><doi>10.1109/ISIT.2006.261769</doi><tpages>4</tpages><oa>free_for_read</oa></addata></record> |
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| language | eng |
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| source | IEEE Electronic Library (IEL) Conference Proceedings |
| subjects | binary erasure channel Differential equations Iterative algorithms Iterative decoding Laboratories Linear code Parity check codes stopping set |
| title | Generating parity check equations for bounded-distance iterative erasure decoding |
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