Create a simulation of the entire contents of the LDPC code through MATLAB based on the contents of the picture.

1. a theoretical explanation

2. Note 1. Example of results (This created based on code other than LDPC code)

3. Note 2. Please refer to this

74 CHAPTER 4. DECODING LINEAR BLOCK CODES Figure 4.4: Comparison of ML decoding and the union bound for the (5,3) code of Example 4.8. function syndromeDecodingExample (p, Nstop) G=[%Generatormatrix 10110; H=[01011]; \%Parity-check matrix 10100; 11010; 01001]; [k,n]=size(G); Phi =[%Syndromedecodertable 00000; 00100; 00010; 10000; 00001; 00101; 01000; 01100]] numberOfBitErrors =0; numberOfWordErrors =0; Nframes =0; while Nframes u=randi([01],1,k); c=mod(uG,2); \%channel e=rand(1,n)

0); Nframes = Nframes +1 ; end WER = numberOfWordErrors / Nframes; BER = numberOfBitErrors / (n * Nframes ); fprintf('Nerr =%d, WER =%G,BER=%G , numberOfWordErrors, WER, BER) ; save decoding-data \%change filename to avoid overwrite \%another .m file loads and plots Figure 4.6: Matlab source code implementing simulation using syndrome decoding. 74 CHAPTER 4. DECODING LINEAR BLOCK CODES Figure 4.4: Comparison of ML decoding and the union bound for the (5,3) code of Example 4.8. function syndromeDecodingExample (p, Nstop) G=[%Generatormatrix 10110; H=[01011]; \%Parity-check matrix 10100; 11010; 01001]; [k,n]=size(G); Phi =[%Syndromedecodertable 00000; 00100; 00010; 10000; 00001; 00101; 01000; 01100]] numberOfBitErrors =0; numberOfWordErrors =0; Nframes =0; while Nframes u=randi([01],1,k); c=mod(uG,2); \%channel e=rand(1,n)

0); Nframes = Nframes +1 ; end WER = numberOfWordErrors / Nframes; BER = numberOfBitErrors / (n * Nframes ); fprintf('Nerr =%d, WER =%G,BER=%G , numberOfWordErrors, WER, BER) ; save decoding-data \%change filename to avoid overwrite \%another .m file loads and plots Figure 4.6: Matlab source code implementing simulation using syndrome decoding