comm.CRCGenerator

Generate a CRC-8 checksum for the example shown in 802.11™-2016[1], section 21.3.10.3 and compare with the expected CRC.

Create a CRC Generator System object™. To align with the CRC calculation in 802.11-20016, the System object sets the generator polynomial as $$z^8+z^2+z+1$$, initial states to 1, direct method, and final XOR to 1.

crc8 = comm.CRCGenerator('Polynomial','z^8 + z^2 + z + 1', ...
    'InitialConditions',1,'DirectMethod',true,'FinalXOR',1)

crc8 = 
  comm.CRCGenerator with properties:

           Polynomial: 'z^8 + z^2 + z + 1'
    InitialConditions: 1
         DirectMethod: true
    ReflectInputBytes: false
     ReflectChecksums: false
             FinalXOR: 1
    ChecksumsPerFrame: 1

Process one input frame according to the example from the 802.11-2016 standard in section 21.3.10.3. In the example, the input bit stream {m0, … m22} is {1 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1} and the expected CRC checksum {c7, … c0} is {0 0 0 1 1 1 0 0}.

x = [1 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1]';
expectedChecksum = [0 0 0 1 1 1 0 0]';
checksumLength = length(expectedChecksum);

The generated CRC checksum is compared to the expected checksum.

codeword = crc8(x);
checksum = codeword(end-checksumLength+1:end);
isequal(checksum,expectedChecksum)

ans = logical
   1

Pass binary data through a CRC generator, introduce a bit error, and detect the error using a CRC detector.

Create a random binary vector.

x = randi([0 1],12,1);

Encode the input message frame using a CRC generator with the ChecksumsPerFrame property set to 2. This subdivides the incoming frame into two equal-length subframes.

crcgenerator = comm.CRCGenerator([1 0 0 1],'ChecksumsPerFrame',2);
codeword = crcgenerator(x);

Decode the codeword and verify that there are no errors in either subframe.

crcdetector = comm.CRCDetector([1 0 0 1],'ChecksumsPerFrame',2);
[~, err] = crcdetector(codeword)

err = 2×1

     0
     0

Introduce an error in the second subframe by inverting the last element of subframe 2. Pass the corrupted codeword through the CRC detector and verify that the error is detected in the second subframe.

codeword(end) = not(codeword(end));
[~,err] = crcdetector(codeword)

err = 2×1

     0
     1

Use a CRC code to detect frame errors in a noisy BPSK signal.

Create a CRC generator and detector pair using a standard CRC-4 polynomial, $$z^4+z^3+z^2+z+1$$.

poly = 'z4+z3+z2+z+1';
crcgenerator = comm.CRCGenerator(poly);
crcdetector = comm.CRCDetector(poly);

Generate 12-bit frames of binary data and append the CRC bits. Based on the degree of the polynomial, 4 bits are appended to each frame. Apply BPSK modulation and pass the signal through an AWGN channel. Demodulate and use the CRC detector to determine if the frame is in error.

numFrames = 20;
frmError = zeros(numFrames,1);

for k = 1:numFrames
    data = randi([0 1],12,1);                 % Generate binary data
    encData = crcgenerator(data);                   % Append CRC bits
    modData = pskmod(encData,2);              % BPSK modulate
    rxSig = awgn(modData,5);                  % AWGN channel, SNR = 5 dB
    demodData = pskdemod(rxSig,2);            % BPSK demodulate
    [~,frmError(k)] = crcdetector(demodData); % Detect CRC errors
end

Identify the frames in which CRC code bit errors are detected.

find(frmError)

ans =

  0x1 empty double column vector

Create a CRC-16-CCITT generator as described in Section 2.2.7.4 of ITU-T Recommendation X-25[1] using the input data and expected frame check sequence (FCS) from Example 2 in Appendix I, I.1.

Create an unnumbered acknowledgement (UA) response frame where address = B and F = 1.

Address = [1 0 0 0 0 0 0 0];
UA = [1 1 0 0 1 1 1 0];
input = [Address UA]';
expectedChecksum = [1 1 0 0 0 0 0 1 1 1 1 0 1 0 1 0]'; % Expected FCS
checksumLength = 16;

crcGen = comm.CRCGenerator(...
    'Polynomial','X^16 + X^12 + X^5 + 1',...
    'InitialConditions',1,...
    'DirectMethod',true,...
    'FinalXOR',1);
crcSeq = crcGen(input);
checkSum =  crcSeq(end-checksumLength+1:end);

Compare calculated checksum with the expected checksum.

isequal(expectedChecksum,checkSum)

ans = logical
   1

Create a CRC-32 code for the frame check sequence (FCS) field for Ethernet as described in Section 3.2.9 of the IEEE Standard for Ethernet[1].

rng(1865);  % Seed for repeatable results

Initialize a message with random data to represent the protected fields of the MAC frame, specifically the destination address, source address, length or type field, MAC client data, and padding.

data = randi([0,1],100,1);

Specify the CRC-32 generating polynomial used for encoding Ethernet messages.

poly = [32,26,23,22,16,12,11,10,8,7,5,4,2,1,0];

Calculate the CRC by following the steps specified in the standard and using the nondirect method to generate the CRC code.

% Section 3.2.9 step a) and b)
dataN = [not(data(1:32));data(33:end)];
crcGen1 = comm.CRCGenerator(...
    'Polynomial',poly, ...
    'InitialConditions',0, ...
    'DirectMethod',false, ...
    'FinalXOR',1);
% Section 3.2.9 step c), d) and e)
seq = crcGen1(dataN);
csNondirect = seq(end-31:end);

Calculate the CRC by following the steps specified in the standard and using the direct method to generate the CRC code.

crcGen2 = comm.CRCGenerator( ...
    'Polynomial',poly, ...
    'InitialConditions',1, ...
    'DirectMethod',true, ...
    'FinalXOR',1);
txSeq = crcGen2(data);
csDirect = txSeq(end-31:end);

Compare the generated CRC codes by using the nondirect and direct methods.

disp([csNondirect';csDirect']);

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

isequal(csNondirect,csDirect)

ans = logical
   1

rng('default');  % Reset the random number generator