Design and analysis of codes with distance 4 and 6 minimizing the probability of decoder error
The problem of minimization of the decoder error probability is considered for shortened codes of dimension 2 m with distance 4 and 6. We prove that shortened Panchenko codes with distance 4 achieve the minimal probability of decoder error under special form of shortening. This shows that Hamming co...
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| Veröffentlicht in: | Journal of communications technology & electronics 2016-12, Vol.61 (12), p.1440-1455 |
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| creator | Afanassiev, V. B. Davydov, A. A. Zigangirov, D. K. |
| description | The problem of minimization of the decoder error probability is considered for shortened codes of dimension 2
m
with distance 4 and 6. We prove that shortened Panchenko codes with distance 4 achieve the minimal probability of decoder error under special form of shortening. This shows that Hamming codes are not the best. In the paper, the rules for shortening Panchenko codes are defined and a combinatorial method to minimize the number of words of weight 4 and 5 is developed. There are obtained exact lower bounds on the probability of decoder error and the full solution of the problem of minimization of the decoder error probability for [39,32,4] and [72,64,4] codes. For shortened BCH codes with distance 6, upper and lower bounds on the number of minimal weight codewords are derived. There are constructed [45,32,6] and [79,64,6] BCH codes with the number of weight 6 codewords close to the lower bound and the decoder error probabilities are calculated for these codes. The results are intended for use in memory devices. |
| doi_str_mv | 10.1134/S1064226916120020 |
| format | Article |
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m
with distance 4 and 6. We prove that shortened Panchenko codes with distance 4 achieve the minimal probability of decoder error under special form of shortening. This shows that Hamming codes are not the best. In the paper, the rules for shortening Panchenko codes are defined and a combinatorial method to minimize the number of words of weight 4 and 5 is developed. There are obtained exact lower bounds on the probability of decoder error and the full solution of the problem of minimization of the decoder error probability for [39,32,4] and [72,64,4] codes. For shortened BCH codes with distance 6, upper and lower bounds on the number of minimal weight codewords are derived. There are constructed [45,32,6] and [79,64,6] BCH codes with the number of weight 6 codewords close to the lower bound and the decoder error probabilities are calculated for these codes. The results are intended for use in memory devices.</description><identifier>ISSN: 1064-2269</identifier><identifier>EISSN: 1555-6557</identifier><identifier>DOI: 10.1134/S1064226916120020</identifier><language>eng</language><publisher>Moscow: Pleiades Publishing</publisher><subject>Algorithms ; Analysis ; BCH codes ; Codes ; Coding theory ; Communications Engineering ; Computer memory ; Computer programming ; Data storage ; Decoders ; Engineering ; Error correction & detection ; Errors ; Linear codes ; Lower bounds ; Memory devices ; Minimization ; Networks ; Optimization ; Probability ; Random access memory ; Studies ; Theory and Methods of Information Processing</subject><ispartof>Journal of communications technology & electronics, 2016-12, Vol.61 (12), p.1440-1455</ispartof><rights>Pleiades Publishing, Inc. 2016</rights><rights>COPYRIGHT 2016 Springer</rights><rights>Journal of Communications Technology and Electronics is a copyright of Springer, 2016.</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c459t-e5218ac20005fa466e3d029f5e614592f8ca42b4a22e848e4ce52cf518547e963</citedby><cites>FETCH-LOGICAL-c459t-e5218ac20005fa466e3d029f5e614592f8ca42b4a22e848e4ce52cf518547e963</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://link.springer.com/content/pdf/10.1134/S1064226916120020$$EPDF$$P50$$Gspringer$$H</linktopdf><linktohtml>$$Uhttps://link.springer.com/10.1134/S1064226916120020$$EHTML$$P50$$Gspringer$$H</linktohtml><link.rule.ids>314,776,780,27901,27902,41464,42533,51294</link.rule.ids></links><search><creatorcontrib>Afanassiev, V. B.</creatorcontrib><creatorcontrib>Davydov, A. A.</creatorcontrib><creatorcontrib>Zigangirov, D. K.</creatorcontrib><title>Design and analysis of codes with distance 4 and 6 minimizing the probability of decoder error</title><title>Journal of communications technology & electronics</title><addtitle>J. Commun. Technol. Electron</addtitle><description>The problem of minimization of the decoder error probability is considered for shortened codes of dimension 2
m
with distance 4 and 6. We prove that shortened Panchenko codes with distance 4 achieve the minimal probability of decoder error under special form of shortening. This shows that Hamming codes are not the best. In the paper, the rules for shortening Panchenko codes are defined and a combinatorial method to minimize the number of words of weight 4 and 5 is developed. There are obtained exact lower bounds on the probability of decoder error and the full solution of the problem of minimization of the decoder error probability for [39,32,4] and [72,64,4] codes. For shortened BCH codes with distance 6, upper and lower bounds on the number of minimal weight codewords are derived. There are constructed [45,32,6] and [79,64,6] BCH codes with the number of weight 6 codewords close to the lower bound and the decoder error probabilities are calculated for these codes. The results are intended for use in memory devices.</description><subject>Algorithms</subject><subject>Analysis</subject><subject>BCH codes</subject><subject>Codes</subject><subject>Coding theory</subject><subject>Communications Engineering</subject><subject>Computer memory</subject><subject>Computer programming</subject><subject>Data storage</subject><subject>Decoders</subject><subject>Engineering</subject><subject>Error correction & detection</subject><subject>Errors</subject><subject>Linear codes</subject><subject>Lower bounds</subject><subject>Memory devices</subject><subject>Minimization</subject><subject>Networks</subject><subject>Optimization</subject><subject>Probability</subject><subject>Random access memory</subject><subject>Studies</subject><subject>Theory and Methods of Information Processing</subject><issn>1064-2269</issn><issn>1555-6557</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2016</creationdate><recordtype>article</recordtype><sourceid>N95</sourceid><sourceid>BENPR</sourceid><recordid>eNp1kd9r1TAUgIs4cG7-Ab4FfFFYZ5Imue3j2KYOBoLTV0tuetqb0SYzJ0Wvf72n1oddRUJ-kHzf4Zycongp-LkQlXp7J7hRUppGGCE5l_xJcSy01qXRevOUzvRcLu_PiueI95xXjeHVcfH1CtAPgdnQ0bTjHj2y2DMXO0D23ecd6zxmGxww9ZsybPLBT_6nDwPLO2APKW7t1o8-7xezg8VNDFKK6bQ46u2I8OLPflJ8eXf9-fJDefvx_c3lxW3plG5yCVqK2jpKnOveKmOg6rhseg1GECD72lklt8pKCbWqQTkyXK9FrdUGGlOdFK_XuJTMtxkwt5NHB-NoA8QZW1HX9ClNJQWhr_5C7-OcqPSF0kpvuFSKqPOVGuwIrQ99zMk6Gh1M3sUAvaf7C9UYbWohlrBvDgRiMvzIg50R25u7T4fs2SN2O6MPgLRQJ3YZV-UAFyvuUkRM0LcPyU827VvB26X77T_dJ0euDhIbBkiPqvyv9AvEsq1n</recordid><startdate>20161201</startdate><enddate>20161201</enddate><creator>Afanassiev, V. 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B.</au><au>Davydov, A. A.</au><au>Zigangirov, D. K.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Design and analysis of codes with distance 4 and 6 minimizing the probability of decoder error</atitle><jtitle>Journal of communications technology & electronics</jtitle><stitle>J. Commun. Technol. Electron</stitle><date>2016-12-01</date><risdate>2016</risdate><volume>61</volume><issue>12</issue><spage>1440</spage><epage>1455</epage><pages>1440-1455</pages><issn>1064-2269</issn><eissn>1555-6557</eissn><abstract>The problem of minimization of the decoder error probability is considered for shortened codes of dimension 2
m
with distance 4 and 6. We prove that shortened Panchenko codes with distance 4 achieve the minimal probability of decoder error under special form of shortening. This shows that Hamming codes are not the best. In the paper, the rules for shortening Panchenko codes are defined and a combinatorial method to minimize the number of words of weight 4 and 5 is developed. There are obtained exact lower bounds on the probability of decoder error and the full solution of the problem of minimization of the decoder error probability for [39,32,4] and [72,64,4] codes. For shortened BCH codes with distance 6, upper and lower bounds on the number of minimal weight codewords are derived. There are constructed [45,32,6] and [79,64,6] BCH codes with the number of weight 6 codewords close to the lower bound and the decoder error probabilities are calculated for these codes. The results are intended for use in memory devices.</abstract><cop>Moscow</cop><pub>Pleiades Publishing</pub><doi>10.1134/S1064226916120020</doi><tpages>16</tpages></addata></record> |
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| subjects | Algorithms Analysis BCH codes Codes Coding theory Communications Engineering Computer memory Computer programming Data storage Decoders Engineering Error correction & detection Errors Linear codes Lower bounds Memory devices Minimization Networks Optimization Probability Random access memory Studies Theory and Methods of Information Processing |
| title | Design and analysis of codes with distance 4 and 6 minimizing the probability of decoder error |
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