Cyclic Redundancy Check (CRC) implementation in Software

using C

Physics Department Indian Institute of Technology Delhi

Ajay Singh (2014JOP2558)Manoj Falaswal (2014JOP2489)

Contents:-

1. Why Error Detection And Correction?2. Type Of Errors3. Error Detection Techniques

Parity Check Two Dimensional Parity Check Checksum Cyclic Redundancy Check

4. CRC Implementation Modulo-2 Arithmetic Digital circuit for polynomial division Implementation and Code for CRC in C Performance of CRC

Why error detection and correction

• Because of attenuation, distortion, noise andinterference, error during transmission areinevitable, leading to corruption transmittedbits.

• Longer the frame size and higher theprobability of single bit error ,lower is theprobability receiving a frame without error.

Types of error

• Single-bit error: only one bit get corruptedCommon in parallel transmission.

• Burst errormore than one bit get corruptedVery common in serial transmission of dataOccurs when the duration of noise is larger thanthe duration of one bit.

Error detection techniques

• Use of redundancy: additional bits are added to facilitate detection and correction of error.

• Popular techniques:

Parity Check

Two Dimensional Parity Check

Checksum

Cyclic Redundancy Check

• CRC is one of the most powerful and commonlyused error detecting technique.

Cyclic redundancy check (CRC)

• Basic approach: a m-bit block of bit sequence,the sender generate an n-bit sequence, knownas frame check sequence (FCS) , so that theresulting frame, consisting of m+n bits, isexactly divisible by same pre determinednumber.

• The receiver divides the incoming frame bythat number and, if there is no remainder,assumes there are no error.

Cyclic redundancy check (CRC)

Data 000….0

Divisor

CRC

Data CRC

m n

(n+1) bits

N-bits

Divisor

(n+1) bits

CRCReminder

Data 000….0

m n

zeroRejected Accept

YN

Sender Receiver

Data: 1010Divisor: 1011

1001 Quotient

1 0 1 0 0 0 01 0 1 1

0 0 1 00 0 0 0

0 1 0 0 0 0 0 0

1 0 0 01 0 1 1

0 1 1 Reminder

1 0 1 1

Modulo-2 Arithmetic

Data to be sent:1 0 1 0 0 1 1Data CRC

Received Data: 1010011Divisor: 1011

1001 Quotient1 0 1 0 0 1 11 0 1 1

0 0 1 00 0 0 0

0 1 0 1 0 0 0 0

1 0 1 11 0 1 1

0 0 0 Reminder

1 0 1 1

Modulo-2 Arithmetic

No error

Polynomials

• All the value can be expressed as polynomial of a dummy variable X. P=11001 => X4+X3+1

• CRC process can be expressed as:

Xn*M(X)/P(X)=Q(X)+R(X)/P(X)

• Commonly used divisor polynomial:

(1) CRC-16 = X16+X15+X2+1

(2) CRC-CCITT = X16+X12+X5+1

Digital circuit for polynomial division

• The CRC process can be vary easilyimplemented in hardware using LinearFeedback shift register (LFSR).

• The LFSR divides a message polynomial bysuitably chosen divisor polynomial; thereminder constitutes the FCS.

Implementation

C2 C1 C0 ++

clock

Input 1 0 1 0 0 0 0

Initial C2 C1 C0 C2(+)C0 C2(+)input input0 0 0 0 1 1

Step 1 0 0 1 1 0 0

Step 2 0 1 0 0 1 1

Step 3 1 0 1 0 1 0

Step 4 0 0 1 1 0 0

Step 5 0 1 0 0 0 0

Step 6 1 0 0 1 1 0

Step 7 0 1 1 1 0 -

Data to be sent:1010011

Code for CRC in C

#include <stdio.h>#include <string.h>void main(){int i,j,keylen,msglen;char input[100], key[30],temp[30],quot[100],rem[30],key1[30];clrscr();printf("Enter Data: ");gets(input);printf("Enter Key: ");gets(key);keylen=strlen(key);msglen=strlen(input);strcpy(key1,key);for(i=0;i<keylen-1;i++){input[msglen+i]='0';}

1

for(i=0;i<keylen;i++)temp[i]=input[i];for(i=0;i<msglen;i++){quot[i]=temp[0];if(quot[i]=='0')for(j=0;j<keylen;j++)key[j]='0';elsefor(j=0;j<keylen;j++)key[j]=key1[j];for(j=keylen-1;j>0;j--){if(temp[j]==key[j])rem[j-1]='0';elserem[j-1]='1';}

rem[keylen-1]=input[i+keylen];strcpy(temp,rem);}strcpy(rem,temp);printf("\nQuotient is ");for(i=0;i<msglen;i++)printf("%c",quot[i]);printf("\nRemainder is ");for(i=0;i<keylen-1;i++)printf("%c",rem[i]);printf("\nFinal data is: ");for(i=0;i<msglen;i++)printf("%c",input[i]);for(i=0;i<keylen-1;i++)printf("%c",rem[i]);}

#include<stdio.h>#include<string.h>#define N strlen(g)

char t[28],cs[28],g[]="1011";int a,e,c;

void xor(){for(c = 1;c < N; c++)cs[c] = (( cs[c] == g[c])?'0':'1');

}

void crc(){for(e=0;e<N;e++)

cs[e]=t[e];do{

if(cs[0]=='1')xor();

for(c=0;c<N-1;c++)cs[c]=cs[c+1];

cs[c]=t[e++];}

while(e<=a+N-1);}int main()

{printf("\nEnter data : ");scanf("%s",t);printf("\n-------------------------------------

---");printf("\nGeneratng polynomial :

%s",g);a=strlen(t);for(e=a;e<a+N-1;e++)

t[e]='0';printf("\n-------------------------------------

---");printf("\nModified data is : %s",t);

2

printf("\n----------------------------------------");

crc();printf("\nCRC is : %s",cs);for(e=a;e<a+N-1;e++)

t[e]=cs[e-a];printf("\n--------------------------------

--------");printf("\nFinal codeword is :

%s",t);printf("\n--------------------------------

--------");printf("\nTest error detection

0(yes) 1(no)? : ");scanf("%d",&e);if(e==0){

do{printf("\nEnter the position

where error is to be inserted : ");

scanf("%d",&e);}while(e==0 || e>a+N-1);t[e-1]=(t[e-1]=='0')?'1':'0';

printf("\n----------------------------------------");

printf("\nErroneous data : %s\n",t);

}crc();for(e=0;(e<N-1) &&

(cs[e]!='1');e++);if(e<N-1)

printf("\nErrordetected\n\n");

elseprintf("\nNo error

detected\n\n");printf("\n---------------------------

-------------\n");return 0;

}

Performance of CRC

• CRC can detect all single bit errors

• CRC can detect all double-bit error(three 1’s)

• CRC can detect any odd number of error (X+1)

• CRC can detect all burst error of less than the

degree of the polynomial.

• CRC detects most of the larger burst errorswith a high probability.

• For example CRC-12 detects 99.97% of error

Reference Links:

http://en.wikipedia.org/wiki/Computation_of_cyclic_redundancy_checkshttp://www.barrgroup.com/Embedded-Systems/How-To/CRC-Calculation-C-Codehttp://stackoverflow.com/questions/18974220/how-to-implement-crc-using-c-languagehttp://www.ccodechamp.com/c-program-to-implement-cyclic-redundancy-check-crc/http://getprogramcode.com/2013/03/c-program-to-implement-crc-cyclic-redundancy-code/http://www.barrgroup.com/Embedded-Systems/How-To/CRC-Calculation-C-Code

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