Soft Error Detection and Correction for FFT Based ... - IEEE Xplore

2 downloads 0 Views 195KB Size Report
AbstractE The structure of radix 2 Fast Fourier Transforms of length 2n where n is an integer is used to propose a new soft error detection and correction scheme ...


6RIW(UURU'HWHFWLRQDQG&RUUHFWLRQIRU))7 %DVHG&RQYROXWLRQXVLQJ'LIIHUHQW%ORFN /HQJWKV 3HGUR5HYLULHJR-XDQ$QWRQLR0DHVWUR$QQH2¶'RQQHOODQG&KULV-%OHDNOH\  

$EVWUDFW² 7KHVWUXFWXUHRIUDGL[)DVW)RXULHU7UDQVIRUPVRI

OHQJWKQZKHUHQLVDQLQWHJHULVXVHGWRSURSRVHDQHZVRIWHUURU GHWHFWLRQDQGFRUUHFWLRQVFKHPHIRUWUDQVIRUPEDVHGFRQYROXWLRQ 7KH VFKHPH FDQ SURYLGH XS WR GHWHFWLRQ DQG FRUUHFWLRQRI LVRODWHGVRIW HUURUV IRULQ PDQ\FDVHV DSSUR[LPDWHO\ GRXEOHWKH RULJLQDO V\VWHP FRVW LQ WHUPV RI DUHD DQGRU FRPSXWDWLRQDO FRPSOH[LW\ 7KLV LV D VXEVWDQWLDO UHGXFWLRQ ZKHQ FRPSDUHG ZLWK FRQYHQWLRQDO 7ULSOH 0RGXODU 5HGXQGDQF\ 7KH PHWKRG FDQ EH XVHG IRU ERWK KDUGZDUH DQG VRIWZDUH LPSOHPHQWDWLRQV RI WUDQVIRUPEDVHGFRQYROXWLRQ 

,QGH[ 7HUPV² 6RIW (UURU ))7 7UDQVIRUPEDVHG &RQYROXWLRQ 6LJQDO3URFHVVLQJ 

, ,1752'8&7,21

7

 +( GHWHFWLRQ DQG FRUUHFWLRQ RI VRIW HUURUV LV DQ

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

7KLV ZRUN ZDV VXSSRUWHG E\ WKH 6SDQLVK 0LQLVWU\ RI 6FLHQFH DQG (GXFDWLRQXQGHU*UDQW(63 35HYLULHJRDQG-$0DHVWURDUHZLWK8QLYHUVLGDG$QWRQLRGH1HEULMD& 3LULQHRV   (  0DGULG 6SDLQ  SKRQH  ID[  HPDLO^SUHYLULHMPDHVWUR`#QHEULMDHV  $2¶'RQQHOODQG&-%OHDNOH\DUHZLWK8QLYHUVLW\&ROOHJH'XEOLQ%HOILHOG 'XEOLQ  ,UHODQG SKRQH  ID[  HPDLO DQQHRGRQQHOO#HLUFRPQHWFKULVEOHDNOH\#XFGLH  

c 2009 IEEE 978-1-4244-4595-0/09/$25.00 

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

138

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

,,, 75$16)250%$6('&2192/87,21 'LUHFW FRPSXWDWLRQ RI FLUFXODU FRQYROXWLRQ LV D YHU\ FRPSXWDWLRQDOO\ H[SHQVLYH RSHUDWLRQ LQYROYLQJ 1 PXOWLSOLFDWLRQV ZKHUH 1 LV WKH OHQJWK RI WKH VHTXHQFHV WR EH FRQYROYHG7KHRSHUDWLRQFDQEHIRUPXODWHGDV 1 −

\ ( Q PRG 1 ) =  K ( N ) [ ( ( Q − N ) PRG 1 )

N =              ZKHUH \ Q  LV WKH FLUFXODU FRQYROXWLRQ RI WKH VHTXHQFHV K Q  DQG[ Q 







)LJ&LUFXODUFRQYROXWLRQXVLQJ))7V



7KHFRQYROXWLRQWKHRUHPIRUWKH'LVFUHWH)RXULHU7UDQVIRUP ')7  LQGLFDWHV WKDW WKH FLUFXODU FRQYROXWLRQ RI WZR ILQLWH VHTXHQFHV FDQ EH REWDLQHG DV WKH LQYHUVH WUDQVIRUP RI WKH SURGXFWRIWKHWUDQVIRUPVRIWKHVHTXHQFHV>@

(

\ ( Q PRG 1 ) = ) − ) ( K ( Q ) ) ) ( [ ( Q ) )

)

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ω N 



\ = [ − [ω N                   

)RU HIILFLHQF\ WKH EXWWHUIO\ LV LPSOHPHQWHG DV D WZLGGOH IDFWRUPXOWLSOLFDWLRQ[ωNIROORZHGE\DFURVVRYHU ±  ,Q PDQ\ SUDFWLFDO OLQHDU ILOWHULQJ DSSOLFDWLRQV RQH RI WKH FRQYROXWLRQLQSXWVHTXHQFHVLVYHU\ORQJDQGWKHRWKHUZKLFK LV W\SLFDOO\ WKH LPSXOVH UHVSRQVH RI D ILOWHU LV FRPSDUDWLYHO\ VKRUW DQG IL[HG :KHQ XVLQJ WUDQVIRUPEDVHG PHWKRGV WKH ORQJ VHTXHQFH LV VHJPHQWHG LQWR IL[HG VL]H EORFNV SULRU WR SURFHVVLQJ7KHLQSXWVDQGRXWSXWVRIWKHFLUFXODUFRQYROXWLRQ PXVWEH]HURSDGGHGDQGRYHUODSSHGWRDOORZIRUWKHIDFWWKDW WKH GHVLUHG FRQYROXWLRQ LV OLQHDU 7KHUH DUH WZR FRPPRQ PHWKRGV  2YHUODS 6DYH DQG 2YHUODS $GG ,Q WKLV ZRUN WKH 2YHUODS$GGPHWKRGLVXVHG>@,QWKLVWKHORQJVHTXHQFHLV EURNHQLQWREORFNVRIOHQJWK/7KHVHEORFNVDUHSDGGHGZLWK 0 ]HURHV ZKHUH 0 LV WKH OHQJWK RI WKH ILOWHU LPSXOVH UHVSRQVH 7KH YDOXH RI / LV FKRVHQ VXFK WKDW WKH WUDQVIRUP OHQJWK 1 /0 7KH RXWSXWV RI VXFFHVVLYH FLUFXODU FRQYROXWLRQV DUH RYHUODSSHG E\ 0 VDPSOHV DQG WKH OLQHDU

2009 15th IEEE International On-Line Testing Symposium (IOLTS 2009)

139

 FRQYROXWLRQLVFDOFXODWHGE\DGGLQJWKHVDPSOHVLQWKHRYHUODS HOHPHQWZLVH 8VHRIWKH))7WRUHDOLVHWKHWUDQVIRUPFDQUHVXOWLQURXQG RII HUURU DW WKH RXWSXW RI WKH FRQYROXWLRQ 7KH GHVLJQ KDV WR HQVXUHWKDWWKHPDJQLWXGHRIWKRVHHUURUVLVVPDOO>@

 

,9 352326('6&+(0(

+HUHLQ ZH SURSRVH WKDW WKH FRQYROXWLRQ LV SHUIRUPHG E\ WZRPRGXOHVRSHUDWLQJLQSDUDOOHORQWKHVDPHLQSXWGDWD7KLV LV VLPLODU WR '05 +RZHYHU ZH SURSRVH WKDW WZR GLIIHUHQW ))7OHQJWKVDUHXVHGLQHDFKPRGXOH:HUHIHUWRWKLVDV))7 OHQJWK'057KHRYHUDOODSSURDFKLVLOOXVWUDWHGLQ)LJ7KH WZR PRGXOHV VKDOO EH UHIHUUHG WR DV EDVLF DQG UHGXQGDQW PRGXOHV DQG WKH\ ZLOO SHUIRUP LQGHSHQGHQW FRPSXWDWLRQV RI WKH FRQYROXWLRQ XVLQJ GLIIHUHQW WUDQVIRUP OHQJWKV 1E DQG 1U UHVSHFWLYHO\  ,QSXWV



%DVLF 0RGXOH

1E

5HGXQGDQW 0RGXOH

1U

2YHUODS $GG 2YHUODS $GG

(UURU 'HWHFWLRQ DQG &RUUHFWLRQ

HUURU SURSDJDWHV WR WKH RXWSXWV RI WKH WUDQVIRUP DV VKRZQ LQ )LJ  ,Q WKLV FDVH HUURUV RQ ;  ;  ;   DQG ;   ZLOO EH REVHUYHG DWWKH))7RXWSXW DQG WKHQWKURXJK WKHRYHUODS DGG VHFWLRQ7KHIRXUHUURUVZLWKDVHSDUDWLRQRIWZRZLOOUHDFKWKH RXWSXWRIWKHEDVLFPRGXOHDVLOOXVWUDWHGLQ)LJRQWKHXSSHU SDUW DJDLQ WKH VDPSOHV IRU ZKLFK D GLIIHUHQFH RFFXUV DUH VKRZQ LQ UHG LQ ERWK FKDQQHOV DQG HUURUV DUH PDUNHG ZLWK D FURVV)RUWKHUHGXQGDQWPRGXOHIRXUHUURUVZLOORFFXUZKHQJ VXFKWKDWU 1UJ ,QWKLVFDVHV DVVKRZQLQWKH ORZHU SDUWRI)LJ DQGWKHUHIRUHWKHVHSDUDWLRQRIWKHHUURUV FDQ EH XVHG WR GHWHFW WKH PRGXOH LQ HUURU &RUUHFWLRQ LV WKHQ GRQHE\VHOHFWLQJWKHRXWSXWIURPWKHRWKHUPRGXOH 

&RQYROXWLRQ RXWSXW



)LJ%ORFN'LDJUDPRIWKHSURSRVHGDSSURDFK 

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

140





)LJ  SRLQW UDGL[ ))7 VKRZLQJ SDWK RI HUURU DW WKH LQSXW WR VWDJH  



)LJ ([DPSOHV RIRXWSXW (UURUVSDWWHUQVIRUHUURUVRQWKHIRUZDUG ))7RUPXOWLSOLFDWLRQVWDJHIRUWKHEDVLF WRS DQGUHGXQGDQWFKDQQHO ERWWRP 



2009 15th IEEE International On-Line Testing Symposium (IOLTS 2009)

 1E 1U 0  %ORFNZLWK (UURUV 2YHUODS $GG

2YHUODS $GG

2YHUODS $GG

2YHUODS $GG (UURURQEDVLF&KDQQHO

2YHUODS $GG

2YHUODS $GG

2YHUODS $GG

2YHUODS $GG

%ORFNZLWK (UURUV



(UURURQ5HGXQGDQW&KDQQHO

 )LJ  ([DPSOHVRIRXWSXW(UURUVSDWWHUQVIRUHUURUVRQWKH,))7RI WKHEDVLF VWDJH DQGUHGXQGDQWFKDQQHO VWDJH 



VRIWHUURU

[  [ 



Ȧ



[ 

;  Ȧ

[  

Ȧ







Ȧ

;  

[ 

Ȧ







Ȧ Ȧ

[  [ 

;  Ȧ

[  

Ȧ



; 

Ȧ

 



; 



; 

Ȧ



Ȧ



; 

%DVLF 0RGXOH

'HOD\/LQH

5HGXQGDQW 0RGXOH

'HOD\/LQH

1EVDPSOHV

1EVDPSOHV

&RPSDUH

; 

6HOHFW 2XWSXWIRU EORFN

&RPSDUH



)LJ([DPSOHRIVRIWHUURUDWWKHODVWVWDJHRIWKH,))7



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η>@6LQFHWKHPRGXOHVRSHUDWHRQ GLIIHUHQW GDWD EORFNV WKH URXQGRII HUURU ZLOO EH GLIIHUHQW LQ FRUUHVSRQGLQJ PRGXOH RXWSXWV 7KXV D PLVPDWFK LV RQO\ GHHPHG WR KDYH RFFXUUHG LQ FDVHV ZKHUH WKH GLIIHUHQFH EHWZHHQ FRUUHVSRQGLQJ RXWSXWV LV JUHDWHU WKDQ  η 7KHVH URXQGRIIHUURUVPD\PDVNVRPHRIWKHHUURUVSURGXFHGE\VRIW HUURUV,WLVOLNHO\WKDWLQPRVWFDVHVVXFKPDVNLQJRFFXUVRQO\ IRU VPDOO HUURUV DQG WKHUHIRUH ZLWK OLWWOH LPSDFW RQ SHUIRUPDQFH ,I HUURU PDVNLQJ EHFRPHV DQ LVVXH WKHQ PRUH UREXVWWHFKQLTXHVFDQEHXVHGWRORFDWHWKHPRGXOHLQHUURUE\ XVLQJ DOO REVHUYHG RXWSXW HUURUV LQ WKH SURFHVV 7KDW ZRXOG LQWURGXFHDGGLWLRQDOFRPSOH[LW\LQWKHFRUUHFWLRQORJLF 

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

 )LJ,PSOHPHQWDWLRQRIWKHSURSRVHGFRUUHFWLRQVFKHPH





 

9 &203/(;,7@ 

%DXPDQQ56RIWHUURUVLQDGYDQFHGFRPSXWHUV\VWHPV,((('HVLJQ 7HVWRI&RPSXWHUVYRO,VVXH0D\-XQHSS±

>@ >@ >@ >@ >@ >@

>@

>@ >@ >@ >@ >@ >@

1LFRODLGLV0µ'HVLJQIRUVRIWHUURUPLWLJDWLRQ¶,(((7UDQVDFWLRQVRQ 'HYLFHDQG0DWHULDOV5HOLDELOLW\YROLVVXH6HSWSS±  3URDNLV -. DQG 0DQRODNLV '* µ'LJLWDO 6LJQDO 3URFHVVLQJ 3ULQFLSOHV $OJRULWKPV DQG $SSOLFDWLRQV¶ UG (GLWLRQ 3UHQWLFH +DOO  5HGG\ $ DQG %DQDUMHH 3 µ$OJRULWKPEDVHG IDXOW GHWHFWLRQ IRU VLJQDO SURFHVVLQJ DSSOLFDWLRQV¶ ,((( 7UDQVDFWLRQV RQ &RPSXWHUV  YRO  LVVXH2FWSS± -RX - DQG $EUDKDP -$ µ)DXOWWROHUDQW ))7 QHWZRUNV¶ &RPSXWHUV ,(((7UDQVDFWLRQVRQYROLVVXH0D\ 5HGLQER *5 ¶6\VWHP OHYHO UHOLDELOLW\ LQ FRQYROXWLRQ FRPSXWDWLRQV¶ ,(((7UDQVDFWLRQVRQ$FRXVWLFV6SHHFKDQG6LJQDO3URFHVVLQJYRO LVVXH$XJSS± %HFNPDQQ 3( DQG 0XVLFXV % 5 µ)DVW IDXOWWROHUDQW GLJLWDO FRQYROXWLRQ XVLQJ D SRO\QRPLDO UHVLGXH QXPEHU V\VWHP¶ ,((( 7UDQVDFWLRQVRQ6LJQDO3URFHVVLQJYROLVVXH-XO\SS±  6XQGDUDP 6 DQG +DGMLFRVWLV &1 ¶)DXOW7ROHUDQW &RQYROXWLRQ 9LD &KLQHVH 5HPDLQGHU &RGHV &RQVWUXFWHG )URP 1RQ&RSULPH 0RGXOL¶ ,((( 7UDQVDFWLRQV RQ 6LJQDO 3URFHVVLQJ YRO  LVVXH  6HSW  SS± &RQZD\5µ0RGLILHG2YHUODS7HFKQLTXH8VLQJ)HUPDWDQG0HUVHQQH 7UDQVIRUPV¶ ,((( 7UDQVDFWLRQV RQ &LUFXLWV DQG 6\VWHPV ,, ([SUHVV %ULHIVYRO,VVXH$XJSS 7DKLU -0 'OD\ 66 1DJXLE 51* DQG +LQWRQ 25 µ6HOI FKHFNLQJDUFKLWHFWXUHVIRUIDVW+DUWOH\WUDQVIRUP¶(XURSHDQ'HVLJQDQG 7HVW&RQIHUHQFH0DUFKSS± &KRRQJ * 2 +HH