标题: CRC???é?÷??ר?ù-5 ???é?????í
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CRC???é?÷??ר?ù-5 ???é?????í

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×???????8-2??8????×??à????×???????bit?????ì???ò??????????????????????????±?????????????????????????×????????ú???ì?é????????????????1001???ó????1011???????ú????·??ú?????????í???ò??1011??????????×??¨±í???????????????????í????±??????????¨???????????????í???????·??×???????1001??1111??0011?ò1010?????????????·?¨???????×????4????×??????????????????????? ?????????????????????¨2?ò4?????í????·¨·?????

?????????????????ì?é?????????????í??????×????à??±??????????°3?±??×????à????3?±???ò???????????í???ò???ì?????í???????????±???????í???ì?????í??±à?????????í???ì?í?????????????á???è??????????????×?????×????à???? ??8-3??±í???¨??×????à????1??7?????????í???ì?í??????



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???à???ó?????í???????????????????à?????ó????±à???§?????????ù???????????à???????????¨??????????????×????????è????±???????????·??ú???í???????????????????í??×??????í?????ò????????ר????????????????????????

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????=a0¨’a1¨’a2¨’??¨’an  

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??????×?0??????ASCII???¨0110000?????????????????ó??±??????????í??0±???1??????????????????????·¨???ú??0110001?¨??×?1??ASCII??????????×?×ó±????????????é????±à??±???10110000???????????ó??±??????????í???ò±???10110001??1??????±?????????????????·¨???????é?????????????????¨???è????1??2???????í??±???10110011??1????????5????????????????????????????????·¨???ú???¨??×?3??ASCII???????ù?????????é????·?????

???????é?????????????·?¨?ì?ò?????ò?í???ú?ú??

?????é?? an =a0¨’a1¨’a2¨’??¨’an-1?? ?????é?? an =NOT?¨a0¨’a1¨’a2¨’??¨’an-1????

???????????????????????????°????????·??ú?÷°????????é??????????×???????????????????×????????ú??±??ì???? ???????????????·????????????????????±ê?¨???í?ó??????????????°??í?ó??×??×???ò?????ó??·???

???????¤×÷????????????×??á???????é???????é????±à??????--·?×é???????é????

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??????4??????·?×é???????é?????????ì???í?à???????í?ó???????????¨?????ò?????ú?ú???????í?ó?±???????????í?ó??????????

?????????ò?±???????¨???????????????ò?±????????????????×??á???????é??????????°???·¨?????????ù???????????ò?????????????ê???????·?¨???????¨?ò???????????é?????????é???????è?????????????????????é?¨???????è??·????·????????×??ê?ó?????????é?¤???????ó?????????????????????ò?????ù?????é?????·?¨?????????????ù????×????????????ó???ù??????????




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??????2001?ê???????ò?±????

?? 6 ??×?·??? 7 ?? ASCII ±à?????????????????????±???????é?????????????ó?¨×??ó?????????????????é????×??ó?????????±???????é????:




?ò X1 X2 X3 X4 ????±???·?±??? __(36)__ ??

  X5 X6 X7 X8 ????±???·?±??? ____ ??

  X9 X10 XI1 X12 ????±???·?±??? __(38)__ ??Y1 ?? Y2 ????×?·?·?±??? __(39)__ ?? __(40)__ ??

[??]

??ASCII??×ó????5?????????±???????é???ò??

????1??????X4=0??????3???????????????????é??

????2??????X3=1??????7??????X8=0??????8??????X12=1??

????7??????X11=1??????6??????X10=0??????6??????X9=1??????2??????X1=1??

????1??????X2=1??????3??????X5=1??????4??????X6=0??

????4???¨?ò??5????????X7=0?????í??????

(36) X1X2X3X4 = 1110

(37) X5X6X7X8 = 1000

(38) X9X10X11X12 = 1011

(39) ??×?·?Y1??ASCII??1001001=49H??????Y1?????°I?±?¨???°D?±??ASCII????1000100=44H??????

(40) ??×?·?Y2??ASCII??0110111=37H??????Y2?????°7?±?¨???°3?±??ASCII????0110011=33H??????

??????????×??°0?±??ASCII????0110000=30H???°A?±??ASCII????1000001=41H???ò?????????ü·?±?????




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???????÷???é

???????°????????????????????×??????????í?ó???ù?è??×????à????3????????????????·?·¨?????????÷????

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2k-1??m+k

??×?????

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??5??????m=4??k=3?±?????????????é????·????é????





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???é?????·?¨

k?????é?????¨????m+k????????×????????????é???·?¨????

??????P1?????????é???÷??????1??3??5??7?????¨P1??D1??D2??D4???????????¨°ü?¨P1×?????

P2???????é???÷??????2??3??6??7?????¨P2??D1??D3??D4???????????¨°ü?¨P2×?????

P3???????é???÷??????4??5??6??7?????¨P3??D2??D3??D4???????????¨°ü?¨P3×?????

??m=4??k=3???????é????×??????????????????????????????????¨??A??B??C±í????????6?ù???÷????????????????




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?ò???????????????é·????°?·?¨???é??????????????

A=B1¨’B3¨’B5¨’B7=0 ??P1=D1¨’D2¨’D4

B=B2¨’B3¨’B6¨’B7=0 ??P2=D1¨’D3¨’D4

C=B4¨’B5¨’B6¨’B7=0 ??P3=D2¨’D3¨’D4

??????????????1001???????????????????ó?????????é??P1??P2??P3?????????÷????????7?ò±í????????????1001?±?????÷??±à?????????é????????8???ò??????????16???????¨D1D2D3D4=0000??1111???????÷????




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??????·???·??????í

??????·????????ù???????????é·????????????????????????ù????????????

A=B1¨’B3¨’B5¨’B7=0??

B=B2¨’B3¨’B6¨’B7=0??

C=B4¨’B5¨’B5¨’B7=0??

?????????é·?????????,??·???????±???????0???ò???÷?????í????????????·???????±???????0?????÷???í????????·???????±????????????????????????í??????????????3????×?·??????òC=0(??·???????B3????A=B=1?¨??????·?????B3????????????????CBA????A??×??????§?????ò?í?ó?????????ò????????????CBA=011??????

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???????·???à???é??

???????????¨???????¨??????????·????????·???à???é???¨CRC????CRC???????????????????????é??????????????±à???????????à???é?í???í??????

CRC???í????????????°??é?????é???????ú???à?????ó???????é????·?·¨???ì?í???????ú???à???????????????ù???é?????á????????

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???é?????????ú?????????????è·??????????????à????C(X)±í??????C(x)×ó??R?????ò??±í????C(x)*2R?????ùC(x)????±????á????R?????????????é???????????¨??C(x)*2R?????ú???à????G(x)???????à?????????é????

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?à????°ü?¨?ú???à????G(x)???????à????C(x)??

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??·????????? 1111????×??????????à??????C(x)=x3+x2+x+1??

2???ú???à????

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3????2???¨°???????

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a??????????±?????×???????×???2?????????è????

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1011????????

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1111000-----±?????

1101???????? ????

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010000

1101

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01010

1101

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1001-------??

------------------------

1010000

1011----------????

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1000

1011

------------

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1010000

+       011

------------------

1010011

CRC???????í

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???????·???????????í????G(x)×÷??2????????????????0???à???????????à????0??????????????????·??????????¤???á?????÷???à????°???10???ò???·???????????????í???à??????001????0?ó?????¨??0?ó??×???????1???ò??????×???2?????à????×???????0???ò??×???3???????à?????????????????à????010?????ó??????0×÷??2?????????????à????100??0ll????·??????·?????????°???·???±?????????????????????????????????????????????ó???à??????0?ó????±????à????0????×???2???????±??±??ì???????é??×????·×ó??????10???÷???±?????à??(101)?±?????í????????A7?????????¨???ì?ò?????ü?????ó?????????????±????A1?????ù????????±??????÷???é???ù?????????·?????????á?????????????±???????à?±?????·?????é?????§???????????ú?????????ü??????·????????÷?????ò??

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?¨????????????????CRC

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??°??é??????r???ú???à?????ú?ú??CRC?????ì?????ù???????í?????????í????·??¤??????????r????·??í???°?¨1-2-(r-1)??????·??¤????r+1????·??í???¨1-2-r??????·??¤???ó??r+1????·??í??????????????r=16???é?????????ì?????ù????·??¤??????????16????·??í???°99??997%????·??¤????17????·??í??99??998%????·??¤???ó??17????·??í???ù??CRC?????ì?í????????????????????????·??í?ó??????????????·??ú???????í????·??¤?????????????í?????????????í??×??ó???????¤??(?????????????????¨?????????í)??

????1???????·???à???¨CRC?????ú???à???? G(x)??x3+x2+1???????ú???à?????ú?ú?????à???????????????ó???? CRC ??????·????????? 1111 ?? 1100 ?ò?ü?? CRC ??·?±?????A??????B???????????????ò????????????????°????????????????????í?? CRC ??????????×???C??????D????????E?????¨1998?ê????11??
??????????°?

A???? lllll00 ?? 1111101 ?? 1111110 ?? 1111111
B???? 1100100 ?? 1100101 ?? 1100110 ?? 1100111
C??E???? 0000000 ?? 0001100 ?? 0010111  
     ?? 1000110 ?? 1001111 ?? 1010001 ?à 1011000

????

A??G(x)??1101??C(x)??1111 C(x)*23??G(x)??1111000??1101??1011?à111

??????CRC????1111111

B??G(x)??1101??C(x)??1100 C(x)*23??G(x)??1100000??1101??1001?à101

??????CRC????1100101

C??E??

·?±???G(x)??1101???????à ×÷??2??: ?? 0000000??1101 ?à000  ?? 1111101??1101 ?à001

?? 0010111??1101 ?à000  ?? 0011010??1101 ?à000  ?? 1000110??1101 ?à000

?? 1001111??1101 ?à100  ?? 1010001??1101 ?à000  ?à 1011000??1101 ?à100

?ù????C??????D??????E??????°????????????à

????2???????ú?????????????ì?í????CRC???? _A_ ??????????±à?????????????? _B_ ?????????è???????ú???à?????? G(X)=X4+X3+X+1?? ????±¨????11001010101???ò±à???ó??±¨???? _C_ ??CRC?? _D_ ????·¨?????·????

?????????¨???????????ü???¨??×??¤??7????????????×?????????3???°1?±??????????±à???§????_E_??

??????????°???

A???? ???????±???????é                        ?? ???·?ó??                        ?? ???·???à                        ????±???

B???? ??2??·¨                        ???¨??????????·¨                        ??????????????·¨                        ?????·????·¨

C???? 1100101010111                        ?? 110010101010011                 

?? 110010101011100                        ?? 110010101010101

D???? ?????????????í                                                ?????ì???ù?????????í

?? ???ì???ù?????????é???¤??????·??í                  ?????ì???ù???????????????é???¤??????·??í

E???? 3/7       ?? 4/7       ?? log23/log27     ?? (log235)/7

???????°??????CRC????????????????  A???? ???·???à  B???? ??2??·¨

C??G(x)??11011??C(x)??11001010101??C(x)*24??G(x)??110010101010000??11011 ?à0011

??????CRC?????? 110010101010011

D?????°???????¨????????????????CRC?????????????????? ???ì???ù???????????????é???¤??????·??í

E???¨±????????¨???????????????é???????????¨±????????????ò??????????±?????±?????????????????????????×???1??×????????¨???????????????????¨±??????ó?????????é???????à???????????????????????????é???????ü?à???ì?í??????

?ù??7????3?¨±???????????????×??¤????7????????1?????????¨??3???ù??128??7???ú???¨0000000??1111111????????1?????????¨??3??????????·¨??×??????????ó×é?????????ó??????·¨??×???????C73??7!/(3!*(7-3)!)??7*6*5/(1*2*3)??35

±à???§??????·¨??×??ù?è????/??×?×???????(log235)/7




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