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D.10.2.13 decode
Procedure from library decodegb.lib (see decodegb_lib).
- Usage:
- decode(check, rec, t); check, rec matrix, t int
| | - check is the check matrix of the code,
- rec is a received word,
- t is an upper bound for the number of errors one wants to correct
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- Note:
- The method described in Decoding method based on quadratic equations
is used for decoding.
- Assume:
- Errors in rec should be correctable, otherwise the output is
unpredictable
- Return:
- a codeword that is closest to rec
Example:
| | LIB "decodegb.lib";
//correct 1 error in [15,7] binary code
int t=1; int q=16; int n=15; int redun=10;
ring r=(q,a),x,dp;
//generate random check matrix
matrix h=randomCheck(redun,n,1);
matrix g=dual_code(h);
matrix x[1][n-redun]=0,0,1,0,1,0,1;
matrix y[1][n]=encode(x,g);
print(y);
==> 1,0,1,0,1,0,1,1,1,1,0,0,1,0,1
// find out the minimum distance of the code
list l=mindist(h);
//disturb with errors
"Correct ",(l[1]-1) div 2," errors";
==> Correct 1 errors
matrix rec[1][n]=errorRand(y,(l[1]-1) div 2,1);
print(rec);
==> 1,0,1,0,1,0,1,1,1,0,0,0,1,0,1
//let us decode
matrix dec_word=decode(h,rec);
print(dec_word);
==> 1,0,1,0,1,0,1,1,1,1,0,0,1,0,1
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