Sum Codes with Fixed Values of Multiplicities for Detectable Unidirectional and Asymmetrical Errors for Technical Diagnostics of Discrete Systems
We introduce the concept of sum codes with fixed values of the multiplicities of unidirectional and asymmetrical errors in data vectors. We show that such codes can be constructed on the basis of weighing one of the data vector's bits by a natural number w = 2 and then calculating the total wei...
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| Veröffentlicht in: | Automation and remote control 2019-06, Vol.80 (6), p.1082-1097 |
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| creator | Efanov, D. V. Sapozhnikov, V. V. Sapozhnikov, Vl. V. |
| description | We introduce the concept of sum codes with fixed values of the multiplicities of unidirectional and asymmetrical errors in data vectors. We show that such codes can be constructed on the basis of weighing one of the data vector's bits by a natural number
w =
2 and then calculating the total weight of the data vector modulo the Berger code (
M
= 2[
log
2
(
m
+1)]
). We establish the basic characteristics of the new class of sum codes. Compared with the Berger code, the proposed codes have the advantage of detecting symmetrical errors while maintaining the property of detecting any unidirectional and asymmetrical errors up to fixed multiplicities. Such codes can be effectively used in the construction of concurrent error-detection systems for combinational logic devices and, especially, in the construction of systems with the detection of all single faults in the controlled device. |
| doi_str_mv | 10.1134/S0005117919060079 |
| format | Article |
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w =
2 and then calculating the total weight of the data vector modulo the Berger code (
M
= 2[
log
2
(
m
+1)]
). We establish the basic characteristics of the new class of sum codes. Compared with the Berger code, the proposed codes have the advantage of detecting symmetrical errors while maintaining the property of detecting any unidirectional and asymmetrical errors up to fixed multiplicities. Such codes can be effectively used in the construction of concurrent error-detection systems for combinational logic devices and, especially, in the construction of systems with the detection of all single faults in the controlled device.</description><identifier>ISSN: 0005-1179</identifier><identifier>EISSN: 1608-3032</identifier><identifier>DOI: 10.1134/S0005117919060079</identifier><language>eng</language><publisher>Moscow: Pleiades Publishing</publisher><subject>Asymmetry ; CAE) and Design ; Calculus of Variations and Optimal Control; Optimization ; Codes ; Computer-Aided Engineering (CAD ; Control ; Control in Technical Systems ; Discrete systems ; Error detection ; Fault detection ; Mathematics ; Mathematics and Statistics ; Mechanical Engineering ; Mechatronics ; Robotics ; System effectiveness ; Systems Theory</subject><ispartof>Automation and remote control, 2019-06, Vol.80 (6), p.1082-1097</ispartof><rights>Pleiades Publishing, Ltd. 2019</rights><rights>Copyright Springer Nature B.V. 2019</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c316t-109fa0f2e3fc41a20eb4f0efacf06817be20923bec0384dba2cc3d6855ff280d3</citedby><cites>FETCH-LOGICAL-c316t-109fa0f2e3fc41a20eb4f0efacf06817be20923bec0384dba2cc3d6855ff280d3</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/S0005117919060079$$EPDF$$P50$$Gspringer$$H</linktopdf><linktohtml>$$Uhttps://link.springer.com/10.1134/S0005117919060079$$EHTML$$P50$$Gspringer$$H</linktohtml><link.rule.ids>314,777,781,27905,27906,41469,42538,51300</link.rule.ids></links><search><creatorcontrib>Efanov, D. V.</creatorcontrib><creatorcontrib>Sapozhnikov, V. V.</creatorcontrib><creatorcontrib>Sapozhnikov, Vl. V.</creatorcontrib><title>Sum Codes with Fixed Values of Multiplicities for Detectable Unidirectional and Asymmetrical Errors for Technical Diagnostics of Discrete Systems</title><title>Automation and remote control</title><addtitle>Autom Remote Control</addtitle><description>We introduce the concept of sum codes with fixed values of the multiplicities of unidirectional and asymmetrical errors in data vectors. We show that such codes can be constructed on the basis of weighing one of the data vector's bits by a natural number
w =
2 and then calculating the total weight of the data vector modulo the Berger code (
M
= 2[
log
2
(
m
+1)]
). We establish the basic characteristics of the new class of sum codes. Compared with the Berger code, the proposed codes have the advantage of detecting symmetrical errors while maintaining the property of detecting any unidirectional and asymmetrical errors up to fixed multiplicities. Such codes can be effectively used in the construction of concurrent error-detection systems for combinational logic devices and, especially, in the construction of systems with the detection of all single faults in the controlled device.</description><subject>Asymmetry</subject><subject>CAE) and Design</subject><subject>Calculus of Variations and Optimal Control; Optimization</subject><subject>Codes</subject><subject>Computer-Aided Engineering (CAD</subject><subject>Control</subject><subject>Control in Technical Systems</subject><subject>Discrete systems</subject><subject>Error detection</subject><subject>Fault detection</subject><subject>Mathematics</subject><subject>Mathematics and Statistics</subject><subject>Mechanical Engineering</subject><subject>Mechatronics</subject><subject>Robotics</subject><subject>System effectiveness</subject><subject>Systems Theory</subject><issn>0005-1179</issn><issn>1608-3032</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2019</creationdate><recordtype>article</recordtype><recordid>eNp1UEtOwzAQtRBIlMIB2FliHRjbaZosq34AqYhFC9vIccbgKomL7Qp6DG6MS5BYIFajeb_RPEIuGVwzJtKbFQCMGBsXrIAMYFwckQHLIE8ECH5MBgc6OfCn5Mz7DQBjwMWAfK52LZ3aGj19N-GVLswH1vRZNruIWE0fdk0w28YoE0xEtHV0hgFVkFWD9KkztXFxM7aTDZVdTSd-37YYnFERmDtnXe9ao3rtvsGZkS-d9cGo7wsz45WLkXS19wFbf05OtGw8XvzMIXlazNfTu2T5eHs_nSwTJVgWEgaFlqA5Cq1SJjlglWpALZWGLGfjCjkUXFSoQORpXUmulKizfDTSmudQiyG56nO3zr7Fb0O5sTsX3_Al5yIHnsaOoor1KuWs9w51uXWmlW5fMigPzZd_mo8e3nt81HYv6H6T_zd9ARWuh-M</recordid><startdate>20190601</startdate><enddate>20190601</enddate><creator>Efanov, D. V.</creator><creator>Sapozhnikov, V. V.</creator><creator>Sapozhnikov, Vl. V.</creator><general>Pleiades Publishing</general><general>Springer Nature B.V</general><scope>AAYXX</scope><scope>CITATION</scope></search><sort><creationdate>20190601</creationdate><title>Sum Codes with Fixed Values of Multiplicities for Detectable Unidirectional and Asymmetrical Errors for Technical Diagnostics of Discrete Systems</title><author>Efanov, D. V. ; Sapozhnikov, V. V. ; Sapozhnikov, Vl. V.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c316t-109fa0f2e3fc41a20eb4f0efacf06817be20923bec0384dba2cc3d6855ff280d3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2019</creationdate><topic>Asymmetry</topic><topic>CAE) and Design</topic><topic>Calculus of Variations and Optimal Control; Optimization</topic><topic>Codes</topic><topic>Computer-Aided Engineering (CAD</topic><topic>Control</topic><topic>Control in Technical Systems</topic><topic>Discrete systems</topic><topic>Error detection</topic><topic>Fault detection</topic><topic>Mathematics</topic><topic>Mathematics and Statistics</topic><topic>Mechanical Engineering</topic><topic>Mechatronics</topic><topic>Robotics</topic><topic>System effectiveness</topic><topic>Systems Theory</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Efanov, D. V.</creatorcontrib><creatorcontrib>Sapozhnikov, V. V.</creatorcontrib><creatorcontrib>Sapozhnikov, Vl. V.</creatorcontrib><collection>CrossRef</collection><jtitle>Automation and remote control</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Efanov, D. V.</au><au>Sapozhnikov, V. V.</au><au>Sapozhnikov, Vl. V.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Sum Codes with Fixed Values of Multiplicities for Detectable Unidirectional and Asymmetrical Errors for Technical Diagnostics of Discrete Systems</atitle><jtitle>Automation and remote control</jtitle><stitle>Autom Remote Control</stitle><date>2019-06-01</date><risdate>2019</risdate><volume>80</volume><issue>6</issue><spage>1082</spage><epage>1097</epage><pages>1082-1097</pages><issn>0005-1179</issn><eissn>1608-3032</eissn><abstract>We introduce the concept of sum codes with fixed values of the multiplicities of unidirectional and asymmetrical errors in data vectors. We show that such codes can be constructed on the basis of weighing one of the data vector's bits by a natural number
w =
2 and then calculating the total weight of the data vector modulo the Berger code (
M
= 2[
log
2
(
m
+1)]
). We establish the basic characteristics of the new class of sum codes. Compared with the Berger code, the proposed codes have the advantage of detecting symmetrical errors while maintaining the property of detecting any unidirectional and asymmetrical errors up to fixed multiplicities. Such codes can be effectively used in the construction of concurrent error-detection systems for combinational logic devices and, especially, in the construction of systems with the detection of all single faults in the controlled device.</abstract><cop>Moscow</cop><pub>Pleiades Publishing</pub><doi>10.1134/S0005117919060079</doi><tpages>16</tpages></addata></record> |
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| ispartof | Automation and remote control, 2019-06, Vol.80 (6), p.1082-1097 |
| issn | 0005-1179 1608-3032 |
| language | eng |
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| source | SpringerLink Journals |
| subjects | Asymmetry CAE) and Design Calculus of Variations and Optimal Control Optimization Codes Computer-Aided Engineering (CAD Control Control in Technical Systems Discrete systems Error detection Fault detection Mathematics Mathematics and Statistics Mechanical Engineering Mechatronics Robotics System effectiveness Systems Theory |
| title | Sum Codes with Fixed Values of Multiplicities for Detectable Unidirectional and Asymmetrical Errors for Technical Diagnostics of Discrete Systems |
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