CRC32 VHDL block

Computation (example with crc4 and data width=4)

For a CRC4 and data width=4 a generator matrix needs to be 4x8.

Poly Matrix

Starting from a given polynomyal, the poly_matrix is computed by right shifting the polynomyal by 1 for each row.
poly = $x^4+x^2+x^1+1$
Or in binary format: 10111
The poly_matrix is the following:

1 0 1 1 1 0 0 0 
0 1 0 1 1 1 0 0 
0 0 1 0 1 1 1 0 
0 0 0 1 0 1 1 1 

Generator Matrix

The generator_matrix should have an identity matrix on the far left block:

1 0 0 0 - - - - 
0 1 0 0 - - - - 
0 0 1 0 - - - -
0 0 0 1 - - - - 

To achieve this we start from the first row and XOR the next if 1 is in its position: e.g. row 0 we XOR row 0 with row 2: 10111000 xor 00101110 = 10010110, now we XOR the result with row 3 and so on for all the rows. The result will be:

1 0 0 0 0 0 0 1	
0 1 0 0 1 0 1 1 
0 0 1 0 1 1 1 0 
0 0 0 1 0 1 1 1

Check Matrix

The check_matrix can be generated directly from the generator matrix. We have to take the far rigth block of the genrator matrix and transpose it:

0 0 0 1     0 1 1 0 
1 0 1 1 --> 0 0 1 1  
1 1 1 0 --> 0 1 1 1  
0 1 1 1     1 1 0 1 

CRC computation

Now with the matrix computed we are able to compute the CRC value for a given data:
$CRC4 = [M] \times D + CRC_{init}$
Where:

• CRC4 is the result
• [M] is the check matrix
• D is the data in
• CRC_init is the CRC initial value, e.g. 0xF for the first data in

0 1 1 0    D[0]   D[1] xor D[2] 
0 0 1 1  X D[1] = D[2] xor D[3]
0 1 1 1  X D[2] = D[1] xor D[2] xor D[3]
1 1 0 1    D[3]   D[0] xor D[1] xor D[3]

For example with DATA=0110 we obatin 0101

VHDL block

Coming soon

The complete explanation can be found here