% Reed-Solomon FEC Performance
%
% Using Equation 8.7, in section 8.1.1 Reed-Solomon Error Probability from 
% Digital Communications, 2nd edition, by Bernard Sklar

clear all;
close all;
m = 8;		% bits per symbol
n = 204;		% codeword length (symbols)
k = 188;		% no. input symbols
erasure = 0;	
min_SER = 10^-3;
max_SER = 0.1;
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

input_SER = [min_SER:min_SER:max_SER];

if erasure == 0
   t = floor((n-k)/2)
else
   t = n - k
end

for j=(t+1:2^m-1)
   combination(j,1) = nchoosek(2^m-1,j);  % n! / (k! * (n-k)!) combination function
end

output_SER = zeros(length(input_SER),1);

for i=1:length(input_SER)
   for j=(t+1:2^m-1)
      output_SER(i) = output_SER(i) + j * combination(j,1) ...
      * (input_SER(i))^j * (1 - input_SER(i))^(2^m-1-j);
   end
end

output_SER = (1/(2^m-1)) * output_SER;

if erasure == 1
   string = 'Using Erasures';
else
   string = 'No Erasures';
end

loglog(input_SER,output_SER)
title(['Reed-Solomon Code Performance - (', num2str(n), ', ', num2str(k), ', ',...
   num2str(t), ') ', string]);

xlabel('Input SER')
ylabel('Output SER')