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105 lines
2.3 KiB
Matlab
105 lines
2.3 KiB
Matlab
% Reed-Solomon Errors and Erasures Decoding
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% Decoding is based on the Massey-Berlekamp decoder. Based on the notes of Adina Matache: http://www.ee.ucla.edu/~matache/rsc/slide.html
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% This program was written by Jaco Versfeld. For any questions or remarks email Jaco at jaco.versfeld@gmail.com.
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% This code is provided as is and Jaco Versfeld accepts no liability what so ever.
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% Feel free to use and modify this code for whatever purpose.
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clear
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clc
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%**************************
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%*** RS code Parameters ***
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%**************************
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% Here we specify the parameters of the (n,k) Reed-Solomon code
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m = 4 %Determine the Galois Field, GF(2^m)
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n = 2^m - 1 %This is fixed for a Reed-Solomon, the length of the codeword
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k = 3 %The number of data symbols, can be anything between 1 to n - 1
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h = n-k
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t = h/2
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%**************************
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%*** Generate the Galois Field and Generator polynomial ***
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% This step is neccessary for Matlab. Here we create the Galois Field which is used for
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% computations of the Reed-Solomon code
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field = gftuple([-1:2^m-2]', m, 2);
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%Generator Polynomial:
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%Lin + Costello, p.171
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%The Generator polynomial is one way of encoding Reed-Solomon codes
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%Construct the generator polynomial
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c = [1 0];
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p(1) = c(1);
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for i = 1:h-1
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p(1) = gfmul(p(1),1,field);
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p(2) = 0;
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c = gfconv(c,p,field);
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end
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g = c;
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%**************************
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%*** RS Encode ***
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%Generate Random Data
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DATA_IN = randint(1,k,[-1 n-1]);
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%RS encoding
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parity = RS_ENC4(DATA_IN,n,k,g,field);
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RS_CODE = [parity DATA_IN];
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%********************************
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%*** Channel ***
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RECEIVED = RS_CODE
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%I introduce the errors manually here, but any channel can be used here, like an AWGN.
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% A maximum of 2*t + e <= (n-k) errors and erasures can be corrected, where t is the number of
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% errors and e the number of erasures
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%Introduce some errors
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RECEIVED(3) = gfadd(RECEIVED(3),randint(1,1,[-1 n-1]),field);
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RECEIVED(5) = gfadd(RECEIVED(3),randint(1,1,[-1 n-1]),field);
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%Introduce some erasures
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erasures = [1 7 9]; %This polynomial contains the positions of the erasures
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RECEIVED(1) = -2
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RECEIVED(7) = -2
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RECEIVED(9) = -2
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%****************
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%*** Decoding ***
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DECODED = RS_E_E_DEC(RECEIVED, erasures,n,k,t,h,g,field);
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%****************
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if all(DECODED == RS_CODE)
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disp('Decoding Success')
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else
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disp('Decoding Failure')
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end |