- 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
ASCII/HAMMING DECODER
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Branislav Gabco
el 24 de Feb. de 2023
Comentada: Branislav Gabco
el 25 de Feb. de 2023
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?
![](https://www.mathworks.com/matlabcentral/answers/uploaded_files/1305940/image.jpeg)
% 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)
1 comentario
Voss
el 25 de Feb. de 2023
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
Now, length returns the size of the largest dimension, so length(binaryMsg) is:
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.
Respuesta aceptada
Voss
el 24 de Feb. de 2023
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]);
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