% 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)]);