CRC16并行計(jì)算的Matlab推導(dǎo)

1、CRC1拼行計(jì)算的Matlab推導(dǎo)本文使用的CRC1啪生成多項(xiàng)式為：x16+x15+x2+1其對(duì)應(yīng)的串行編碼圖如下列圖所示。msDM鳥Dfl0)千)DC壬*假設(shè)輸入數(shù)據(jù)的位寬為8比特，即17,16,15,14,13,12,11,10,I為Input的首字母。I0表示最低比特位，I7表示最高比特位。在串行模式下，I0先輸入CRC1辯算模塊，于是I0輸入后各個(gè)寄存器的狀態(tài)變化如下：D15=D14+Di5+I0D14=D13.D13=D12D12=D11D11=D10D10-。9D9=D8D8=D7D7=。6D6=D5D5=D4D4=D3D3=D2D2=D15+D1+I0Di=D0Do=D15+I0

2、可以將以上表達(dá)式組成矩陣乘法的形式，則有：-DT?DS?I01其中，D為DDi5構(gòu)成的列向量，用轉(zhuǎn)置矩陣的形式表示為：TDD0DiD2D3D4D5D6D7D8D9D10D11D12D13D14D15同理，D是D0D15構(gòu)成的列向量，用轉(zhuǎn)置矩陣的形式表示為：TDD0D1D2D3D4D5D6D7D8D9D10D11D12D13D14D15表達(dá)式1中的矩陣T,表示為：0000000000000001100000000000000001000000000000010010000000000000000100000000000000001000000000000000010000000000000000

3、1000000000T00000001000000000000000010000000000000000100000000000000001000000000000000010000000000000000100000000000000001000000000000000011表達(dá)式1中的矩陣S也是一個(gè)列向量，表示為:TS1010000000000001當(dāng)I1輸入后各個(gè)寄存器的狀態(tài)為：D2T?DS?I1TT?DS?I0S?I0T2?DT?S?I0S?I1以此類推，當(dāng)I7輸入后各寄存器的狀態(tài)為：D(8)T8?DT7?S?I0T6?S?I1T5?S?I2T4?S?I3T3?S?I4T2?S?I5T

4、1?S?I6T0?S?I7上式中T7CCCICT6CCCI4T5CCCICT4CCCICT3CCCIaT2CCCI片T1CCCICT0CCCir?S?10T?S?11T?S?12T?S?I3T?S?I4T?S?I5T?S?I6T?S?I7可以看成兩個(gè)矩陣A和B的相乘A*B,其中A=T7ST6ST5ST4STST2ST1ST0SI000000000I100000000I2000000B00I300000000I400000000I500000000I600000000I7于是D(8)可以簡化為D(8)T8?DA?B而此時(shí)各個(gè)寄存器中的值就是最后要求的CRC16的值。對(duì)應(yīng)的matlab程序如下：T

5、8=mod(TA8),2);%計(jì)算結(jié)果對(duì)2取模，是因?yàn)槲覀儓?zhí)行的是二進(jìn)制%加減運(yùn)算T7=mod(TA7),2);T6=mod(TA6),2);T5=mod(TA5),2);T4=mod(TA4),2);T3=mod(TA3),2);T2=mod(TA2),2);T1=mod(TA1),2);TO=mod(TA0),2);S=1,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1;T7S=mod(T7*S),2);T6S=mod(T6*S),2);T5S=mod(T5*S),2);T4S=mod(T4*S),2);T3S=mod(T3*S),2);T2S=mod(T2*S),2);T1S

6、=mod(T1*S),2);T0S=mod(T0*S),2);A=T7S,T6S,T5S,T4S,T3S,T2S,T1S,T0S;B=eye(8);C=A*B;運(yùn)算結(jié)果:TS-1i11111111090A90nA0AeflQa1Rnn9fl000&0e0Q00100090nnaARa00ant1nnnn00aUD;CcrcZieg15:9J);ii(crT_injasslipnext_crc_reg1-(*crc_ir*6:fljGEignnpxt_crc_reg2jhssIijiiot*xl_i：n：_rpij3jssiqnnextcrcregitatfLgnnext_crc_rpg5des

7、ignnext_crt_reg6a”iqnnextcrcrpg|；7npmcrr_rpgRnextcrcreq91=crc_inZjCri:_lnft-crcin5crc_iniij=crc_in3=crcii2=crc_lnl-crcinGcrc_in6j好clK5crc_inf*icrc_ln(ajcrcZin23crcin1l*n(njcrcreq15crc_rcg9JCri:_r*ij1P*crc_rcQ11crc_regl2crc_reg13*crccrc_r*9lF|姓crc_req|11;crc_rsg0J;i:fR_rpy9；crcrcq19crc_rQgHtrc_reg12crc_reg13lcrirfpgfii*jcrrrpgO;jfsignne?ttcrc_rpgLlii:1WJ=c-c_reg|if