New MPI mitigation schemes // Duobinary // Start of FTN schemes

projects/standard_system/testcode_duobinary.m

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+% Define parameters
+n = 1;  % Define the memory length n+1 (e.g., 1 for duobinary, 2 for tribinary, 3 for tetrabinary)
+M = 4;  % Modulation order (e.g., 4 for QPSK)
+d = randi([0 M-1], 1, 100);  % Example input sequence d(k)
+
+% Pre-coding: bPR(k) = (d(k) - bPR(k-1)) mod M
+bPR = zeros(size(d));
+%bPR(1) = d(1);  % Initial condition for pre-coding
+
+for k = 1:numel(d)-1
+    bPR(k+1) = mod( d(k) - bPR(k), M );
+end
+
+% Polybinary coding: Convolution with (1 + z^-1)^n
+% Generate coefficients for the polybinary filter (1 + z^-1)^n
+coeff = ones(1, n+1);  % Initialize coefficients with ones
+
+for i = 2:n+1
+    coeff(i) = nchoosek(n, i-1);  % Binomial coefficient for expansion
+end
+
+% Apply convolution to get the polybinary coded sequence
+polybinary_data = conv(bPR, coeff, "same");
+
+% Modulo operation for decoding to stay within M levels
+d_reconstructed = mod(polybinary_data, M);
+
+% Check if reconstruction is correct
+reconstruction_success = isequal(d, d_reconstructed);
+
+figure(111)
+hold on
+stairs(d_reconstructed)
+stairs(d)
+
+disp(['Reconstruction success: ', num2str(reconstruction_success)]);