cyclic code encoder/decoder problem

I keep getting errors when running, but I don't know where the problem is.

% Decoder for Systematic (N,K) Cyclic Codes

function M = CyclicDecoder(R, P, T)

% Define N, K, DegPoly

K = length(R); % K is the length of Received Code

N = length(P); % N is length of Polynomial

DegPoly = N - 1;

LFSR = zeros(1, N - K);

for i = 1:K

feedback = R(i); % compute feedback

disp(['Input message: ', num2str(R(i)), ', Current LFSR: ', num2str(LFSR), ', feedback: ', num2str(feedback)]);

for j = DegPoly:-1:2

if (P(j) == 1)

LFSR(j) = rem((LFSR(j - 1) + feedback), 2);

else

LFSR(j) = LFSR(j - 1);

end

end

LFSR(1) = feedback;

disp(['Next LFSR: ', num2str(LFSR)]);

end

SYN = mod(conv(R, P), 2); % compute syndrome using convolution

index = bi2de(SYN, 'left-msb'); % get index value from binary syndrome

ErrorPattern = T(index + 1, :);

Uhat = mod(R + ErrorPattern, 2); % Correct R using ErrorPattern

M = Uhat(1:K); % Extract the message part from corrected Codeword

end

M = [1 0 1 1];

P = [1 1 0 1];

C = [1 0 0 1 0 1 0];

T = syndtable(cyclgen(length(ReceivedCodeword), P, 'system'));

Answer 1

[Sudarsanan A K]

Hello Dohyung,

It is my understanding that you are trying to implement a decoder for systematic (N, K) cyclic code using the provided code snippet. The code aims to correct errors in a received codeword by utilizing the generator polynomial "P" and the syndrome table "T".

To help you resolve the errors, it would be helpful if you can provide the specific error messages you are encountering. However, I have noticed some issues in the code you provided:

• Check Variable Names: In your code, you have used the variable name "ReceivedCodeword" in the "syndtable()" function, but it is not defined anywhere. Make sure you are using the correct variable names throughout your code.
• Calculation of Syndrome: Check the syndrome calculation. For an (N, K) cyclic code, the syndrome should be of length (N - K) and it would be the content in the syndrome register (LFSR). The LFSR content is unused in your code.

Additionally, I have attached below, a simplified approach for the detection of cyclic code by using the parity check matrix.

n = 7; % Codeword length
k = 4; % Message length
data = [1 0 1 1];
P = [1 1 0 1];
parmat = cyclgen(n,P);
T = syndtable(parmat);
encData = encode(data,n,k,'cyclic/binary',P);
disp(['Transmitted codeword: ', num2str(encData)]);

Transmitted codeword: 1  0  0  1  0  1  1

encData(3) = ~encData(3); % Error in 3rd bit
disp(['Received codeword: ', num2str(encData)]);

Received codeword: 1  0  1  1  0  1  1

syndrome = mod(encData*parmat', 2);
disp(['Syndrome: ', num2str(syndrome)]);

Syndrome: 0  0  1

errorPattern = T(bi2de(syndrome, 'left-msb') + 1, :);
disp(['Error pattern: ', num2str(errorPattern)]);

Error pattern: 0  0  1  0  0  0  0

corData = mod(encData + errorPattern, 2);
disp(['Corrected codeword: ', num2str(corData)]);

Corrected codeword: 1  0  0  1  0  1  1

Further, you can refer to the MathWorks documentation with example on "Encode and Decode Message with Cyclic Block Code" in the link:

https://mathworks.com/help/comm/ref/encode.html#mw_d43b9977-394d-4a28-a04b-026eebe693be

Hope this helps you to get the decoding of cyclic codes with minimum effort