44 lines
1.4 KiB
Matlab
44 lines
1.4 KiB
Matlab
% estimate_entropies.m
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clear; rng(0);
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%% 1) Parameters
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M = 1e5; % number of Monte-Carlo samples
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EbNo_dB = 0; % SNR per bit in dB
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EbNo = 10^(EbNo_dB/10);
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sigma2 = 1/(2*EbNo); % noise variance per real dimension
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% 4-QAM constellation (row vector)
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X = [1+1j, 1-1j, -1+1j, -1-1j];
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N = numel(X);
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PX = ones(1,N)/N; % uniform PMF
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%% 2) Generate transmit symbols and AWGN
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idx = randi(N,1,M); % 1×M random symbol indices
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s = X(idx); % 1×M transmitted symbols
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n = sqrt(sigma2)*(randn(1,M) + 1j*randn(1,M));
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y = s + n; % 1×M received samples
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%% 3) Compute p_{Y|X}(y|x) for each constellation point
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% Create an N×M matrix where row n is |y - X(n)|^2
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d2 = abs(bsxfun(@minus, X(:), y)).^2; % N×M
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pYgX = (1/(pi*sigma2)) * exp(-d2 / sigma2); % N×M
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%% 4) Estimate H(Y) = -E[ log2 p_Y(Y) ]
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% Mixture density p_Y(y_m) = sum_n PX(n)*pYgX(n,m)
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pY = PX * pYgX; % 1×M
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HY = -mean(log2(pY)); % bits
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%% 5) Estimate H(Y|X) = -E[ log2 p(Y|X) ]
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% For each m, pick the row corresponding to the true idx(m)
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linearIdx = sub2ind([N, M], idx, 1:M);
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pYgX_true = pYgX(linearIdx); % 1×M
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HYgX = -mean(log2(pYgX_true)); % bits
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%% 6) Mutual information
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I = HY - HYgX;
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%% 7) Display
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fprintf('Estimated H(Y) = %.4f bits\n', HY);
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fprintf('Estimated H(Y|X) = %.4f bits\n', HYgX);
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fprintf('Estimated I(X;Y) = %.4f bits\n', I);
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