ASCII/HAMMING DECODER

Hi guys. I work on encoding and decoding ASCII binary characters with hamming code 7.4 although the v code runs without stopping on an error, but the decoding output is incorrect. It only works for some letters like: e,l,o,c,i the rest of the letters don't work properly. Can you please advise me what is wrong with the code?

% Define the generator matrix for Hamming code 7.4
G = [1 0 0 0 1 1 0;
     0 1 0 0 1 0 1;
     0 0 1 0 1 1 1;
     0 0 0 1 0 1 1];

% Define the parity check matrix for Hamming code 7.4
H = [1 1 1 0 1 0 0;
     1 0 1 1 0 1 0;
     1 1 0 1 0 0 1];

% Ask the user to input a text message
msg = input("Enter a text message: ", 's');

% Convert the message to ASCII codes
asciiMsg = uint8(msg);

% Convert the ASCII codes to binary and concatenate them into a single vector
binaryMsg = dec2bin(asciiMsg, 8) - '0';
binaryMsg = binaryMsg.';

% Pad the binary message with zeros if its length is not a multiple of 4
numPaddingZeros = mod(-length(binaryMsg), 4);
binaryMsg = [zeros(1, numPaddingZeros), binaryMsg(:).'].';

% Reshape the binary message into 4-bit blocks
binaryMsg = reshape(binaryMsg, 4, []).';

% Encode each 4-bit block using Hamming code 7.4
encodedMsg = mod(binaryMsg * G, 2);

% Convert the encoded message to a string of characters
encodedMsgStr = reshape(char(encodedMsg.'+'0'), 1, []);

% Print the encoded message
disp("Encoded message: " + encodedMsgStr)


% Convert the encoded message to binary
encodedMsg = encodedMsgStr - '0';

% Reshape the binary message into 7-bit blocks
encodedMsg = reshape(encodedMsg, 7, []).';

% Calculate the syndrome for each 7-bit block
syndrome = mod(encodedMsg * H.', 2);

% Determine the error correction vector
errorVector = zeros(size(syndrome, 1), 7);
for i = 1:size(syndrome, 1)
    for j = 1:size(H, 2)
        if H(:, j).' == syndrome(i, :)
            errorVector(i, j) = 1;
        end
    end
end

% Correct the errors in the encoded message
decodedEncodedMsg = mod(encodedMsg + errorVector, 2);

% Remove the parity bits to retrieve the original message
decodedMsg = decodedEncodedMsg(:, [1, 2, 3, 5]);

% Convert the binary message to decimal and then to ASCII
decodedMsg = decodedMsg.';
decodedMsg = decodedMsg(:);
decodedMsg = reshape(decodedMsg, 8, []).';
decodedMsg = bin2dec(num2str(decodedMsg, '%d'));
decodedMsg = char(decodedMsg).';

% Print the decoded message
disp("Decoded message: " + decodedMsg)

[Voss]

Notice that, at the point where you do the zero-padding, binaryMsg is an 8-by-M matrix, where M is the number of characters in the original message:

msg = 'message'; % 7 characters long

% Convert the message to ASCII codes
asciiMsg = uint8(msg);

% Convert the ASCII codes to binary and concatenate them into a single vector
binaryMsg = dec2bin(asciiMsg, 8) - '0';
binaryMsg = binaryMsg.' % 8-by-7 after transposing

binaryMsg = 8×7

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

Now, length returns the size of the largest dimension, so length(binaryMsg) is:

• the length of the message, if the message is 8 or more characters long, or
• 8, if the message is 8 or fewer characters long

What I think you meant, instead of length(binaryMsg), is size(binaryMsg,2) or numel(asciiMsg).

However, that's not going to work either because this

binaryMsg = [zeros(1, numPaddingZeros), binaryMsg(:).'].';

is only padding numPaddingZeros zeros, instead of 8*numPaddingZeros zeros (i.e., a column's worth of zeros for each "missing" column of binaryMsg), so you'll get an error using reshape on the next line any time the message length is more than 8 and not a multiple of 4.

Instead of padding binaryMsg with zeros, you could more easily pad asciiMsg with numPaddingZeros zeros, before binaryMsg is created.

However, I don't think you need any zero-padding at all because the purpose of zero-padding in this case is to make sure the number of elements in binaryMsg (not the number of columns) is a multple of 4 (so that you can encode each sequence of 4 bits by multiplying with G to get 7 encoded bits), and since you are expressing each character as 8 bits when you do

binaryMsg = dec2bin(asciiMsg, 8) - '0';
%                             ^ eight bits specified

you are guaranteeing that numel(binaryMsg) is a multiple of 8 (and therefore a multiple of 4); no zero-padding is necessary.

Answer 1

[Voss]

It's been awhile since I studied error-correcting codes, but I believe that with this generator matrix:

G = [1 0 0 0 1 1 0;
     0 1 0 0 1 0 1;
     0 0 1 0 1 1 1;
     0 0 0 1 0 1 1];

the message bits are bits 1-4 and the parity bits are bits 5-7. (Notice G(:,1:4) is the identity matrix - that's how you can tell which are message bits - and the parity bits always have more than one 1 in their columns.)

So use the following to retrieve the original message

% Remove the parity bits to retrieve the original message
decodedMsg = decodedEncodedMsg(:, [1, 2, 3, 4]);

[Branislav Gabco]

Thank you very much for explanation and solving my problem with code. After running the code. Code has correct output.

>> encod_decod

Enter a text message: message

Encoded message: 01100101101000011001001011100111001001110001110010011100011001000010110110010011100101100100101110

Decoded message: message