%% Target source entropy for PS-PAM8
clear; clc;

M = 8;
a = -(M-1):2:(M-1);      % PAM-8 amplitude levels: [-7 -5 -3 -1 1 3 5 7]
H_target = 2.79;          % desired entropy [bits/symbol]

% Objective: find nu such that H(PA) = H_target
f = @(nu) entropy_MB(a,nu) - H_target;
nu_opt = fzero(f, [0, 2]);   % search ν in reasonable range

% Compute final distribution
P = exp(-nu_opt*a.^2);
P = P/sum(P);
H = -sum(P .* log2(P));

fprintf('Shaping parameter ν = %.4f\n', nu_opt);
fprintf('Entropy H(A) = %.3f bits/symbol\n', H);
disp('Probability vector (P_A):');
disp(P.');

%% Helper: entropy function
function H = entropy_MB(a,nu)
    P = exp(-nu*a.^2);
    P = P/sum(P);
    H = -sum(P .* log2(P));
end