CRC16并行計(jì)算的Matlab推導(dǎo)

1、CRC16并行計(jì)算的Matlab推導(dǎo)本文使用的CRC16的生成多項(xiàng)式為：x16 + x15 + x2 + 1其對(duì)應(yīng)的串行編碼圖如以下圖所示。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In put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CRC16計(jì)算模塊，于是I0輸入后各個(gè)存放 器的狀態(tài)變化如下：D15 = D14 + D15 + I0D14= D13fD13= D12D12 = D11D11 = D10fD10 = D9D9= DgD8 = D7D7= D6D6 = D5D5 = D4D4= D3D3 = D2D2 =

2、 D15 + D 1 + I0D1 = D0D0 = D15 + I0可以將以上表達(dá)式組成矩陣乘法的形式，那么有：D T?D S?I01其中，D為DoDi5構(gòu)成的列向量，用轉(zhuǎn)置矩陣的形式表示為：T D D0 D1 D2 D3 D4 D5 D6 D7 D8 D9 D10 D11 D12 D13 D14 D15同理，D是D0Di5構(gòu)成的列向量，用轉(zhuǎn)置矩陣的形式表示為：T DD0D1D2D3D4D5D6D7D8D9D10D11D12D13D14D15表達(dá)式 1中的矩陣T，表示為00000000000000011000000000000000010000000000000100100000000000

3、000001000000000000000010000000000000000100000000000000001000000000T00000001000000000000000010000000000000000100000000000000001000000000000000010000000000000000100000000000000001000000000000000011表達(dá)式 1中的矩陣 S 也是一個(gè)列向量，表示為：TS 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1T當(dāng) I1 輸入后各個(gè)存放器的狀態(tài)為：D 2 T ?D S?I1 T T?D S?I0 S?I

4、0 T2?D T ?S?I0 S?I1以此類推，當(dāng) I7 輸入后各存放器的狀態(tài)為：D(8) T8 ?D T7?S?I0 T6?S?I1 T5 ?S?I2 T4?S?I3 T3?S?I4 T2?S?I5 T1?S?I6 T0?S?I7上式中T7?S?I0 T6?S?I1 T5?S?I2 T4?S?I3 T3?S?I 4 T2?S?I5 T1?S?I6 T0?S?I7可以看成兩個(gè)矩陣A和B的相乘A*B,其中A = T7S T6S T5S T4S T3S T2S T1S T0SI000000000I100000000I200000000I30000B0000I400000000I500000000I

5、600000000I7于是 D(8) 可以簡(jiǎn)化為D(8) T8 ?D A?B而此時(shí)各個(gè)存放器中的值就是最后要求的CRC16的值。對(duì)應(yīng)的 matlab 程序如下：T8二mod(D8),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 二mod(D7),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);T0 =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)

6、;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 =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豪IiT11111110e90A90nA9AeQflQa1ARnn90000&0e0Q00100090nfliaARa0annt1nnnfl09aaDQ00ea90i00uftnaRD0QQaaRA1R01D09Q9B

7、0QDog9a1011anG0Q00a0aahn1I91iQ000G00aaa9Qa101GGG0aa&aeaElGg0a1100e0aa0aCa0a11QGaa9a0GHsuUU11Uu00HaUU0Qi0BEl611G003a001111111tiunu0HUUi1111II1100e000c 1111111100000Q(I0U000u0cI00Q000Q)c000000CI0U000u0cI01Q0009(I611008S(I0011Q00(I00Q1100EIe000110(I0U00a1TfI00Q000T16000Q0S111111111011111111所以將T8和C帶入D(8

8、) T8?D A?B，就能得到各個(gè)存放器中最后的值，這也就是CRC16的并行計(jì)算實(shí)現(xiàn)，最后用 Verilog寫(xiě)出CRC16并行計(jì)算的代碼:auEign npi(r_crr_e(yL ii assign next_crc_reg1 jGEign npxt_crc_reg2j hssIijii _i：n：_rpij3 jssiqn next crc reg it atfLgn next_crc_rpg5 design next_crt_reg6 dHmiqn next crc rpg|；7 Rzlgn npm crr_rpgR next crc ireq91 (rrr lnLinj (nrc rp

9、gilbj; -(*crc_ini: * (*crc_rea15;?)!=crc_inZj Cri:_lnft -crc in乍 crc_iniij =crc_in3 -crc imCS =crc_lnl -crc inGcrc_in6亠 crcZlREi * crc_inf *i crc_ln(aj crcZin23 * crc in1 crc21nOj * crc req門(mén)刃crc_rtg9Jcrc_rc 叭創(chuàng) 1 crc_regl2 crc_rcg13crc_rsg0J; i:fR_rpy9； crc rrq1; crc_rQgH ;crc_reg1 E;crc F?q門(mén)片D crc reql31;crc r* crc_rpg 14J 亠 crc_req|11;crr_rpgO;jfsign ne?ttcrc_rpgLlii