I m working on 2 dimensional parity model in forward error correction. Most probably it refers to product systematic codes, where interleaving is arranged by rows and columns and parity is calculated for each row and each column. For example
000 | 0
001 | 1
010 | 1
---------
011 | 0
When one bit is received with error, you can find that bit and correct it, because the row and the column of that bit have wrong parities.
What will be matlab code for this 2 dimensional parity model in forward error correction? Any ideal of this?
Hello Shahid, Please go through this this may helpful to you i think so
Use a Decoding Table in MATLAB.
The script below shows how to use a Hamming decoding table to correct an error in a received message. The hammgen function produces the parity-check matrix, while the syndtable function produces the decoding table. The transpose of the parity-check matrix is multiplied on the left by the received codeword, yielding the syndrome. The decoding table helps determine the correction vector. The corrected codeword is the sum (modulo 2) of the correction vector and the received codeword.
% Use a [7,4] Hamming code.
m = 3; n = 2^m-1; k = n-m;
parmat = hammgen(m); % Produce parity-check matrix.
trt = syndtable(parmat); % Produce decoding table.
recd = [1 0 0 1 1 1 1] % Suppose this is the received vector.
syndrome = rem(recd * parmat',2);
syndrome_de = bi2de(syndrome,'left-msb'); % Convert to decimal.
disp(['Syndrome = ',num2str(syndrome_de),...
' (decimal), ',num2str(syndrome),' (binary)'])
corrvect = trt(1+syndrome_de,:) % Correction vector
% Now compute the corrected codeword.
correctedcode = rem(corrvect+recd,2)
The output is below.
recd =
1 0 0 1 1 1 1
Syndrome = 3 (decimal), 0 1 1 (binary)
corrvect =
0 0 0 0 1 0 0
correctedcode =
1 0 0 1 0 1 1
Create and Decode Linear Block Codes
The functions for encoding and decoding cyclic, Hamming, and generic linear block codes are encode and decode. This section discusses how to use these functions to create and decode generic linear block codes, cyclic codes, and Hamming codes.
Generic Linear Block Codes. Encoding a message using a generic linear block code requires a generator matrix. If you have defined variables msg, n, k, and genmat, either of the commands
code = encode(msg,n,k,'linear',genmat);
code = encode(msg,n,k,'linear/decimal',genmat);
encodes the information in msg using the [n,k] code that the generator matrix genmat determines. The /decimal option, suitable when 2^n and 2^k are not very large, indicates that msg contains nonnegative decimal integers rather than their binary representations. See Represent Words for Linear Block Codes or the reference page for encode for a description of the formats of msg and code.
Decoding the code requires the generator matrix and possibly a decoding table. If you have defined variables code, n, k, genmat, and possibly also trt, then the commands
newmsg = decode(code,n,k,'linear',genmat);
newmsg = decode(code,n,k,'linear/decimal',genmat);
newmsg = decode(code,n,k,'linear',genmat,trt);
newmsg = decode(code,n,k,'linear/decimal',genmat,trt);
decode the information in code, using the [n,k] code that the generator matrix genmat determines. decode also corrects errors according to instructions in the decoding table that trt represents.
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