function [GMI,NGMI] = calc_gmi_bitwise(test_signal,reference_signal,options)
%  https://cioffi-group.stanford.edu/doc/book/AppendixG.pdf

arguments(Input)
    test_signal;
    reference_signal;
    options.skip_front = 0;
    options.skip_end = 0;
    options.returnErrorLocation = 0;
end

options.skip_end = abs(options.skip_end);
options.skip_front = abs(options.skip_front);

assert((options.skip_end+options.skip_front)<length(test_signal),"You can not skip more bits than overall length of data! Set skip_front or skip_end to lower value or check data_in");

if isa(reference_signal,'Signal')
    reference_signal = reference_signal.signal;
end

if isa(test_signal,'Signal')
    test_signal = test_signal.signal;
end

% TRIM
[test_signal,reference_signal]=trimseq(test_signal,reference_signal,options.skip_front,options.skip_end);

% CALC AIR
%%% new implementation of AIR
% Precompute
N       = length(test_signal);
M       = numel(unique(reference_signal));
nBits   = log2(M);
levels  = PAMmapper(M,0).levels / PAMmapper(M,0).scaling;
grayBits= PAMmapper(M,0).showBitMapping;
priors  = ones(1,M)/M;

noise   = test_signal-reference_signal;
sigma2  = var(noise);

% Allocate
LLR     = zeros(N, nBits);
rxBits  = zeros(N, nBits);

for n = 1:N
    y       = test_signal(n);
    ll_table= -((y - levels).^2)/(2*sigma2) + log(priors);  % M×1

    % Per‐bit LLR
    for b = 1:nBits
        idx0 = grayBits(:,b)==0;
        idx1 = grayBits(:,b)==1;
        L0   = logsumexp(ll_table(idx0));
        L1   = logsumexp(ll_table(idx1));
        LLR(n,b) = L1 - L0;
    end
end

tx_bits = PAMmapper(M,0,"eth_style",0).demap(reference_signal);

% Compute GMI (bit‐wise MI averaged over all symbols)
MI_bits = zeros(1,nBits);
for b = 1:nBits
    r0 = LLR(tx_bits(:,b)==0,b);
    r1 = LLR(tx_bits(:,b)==1,b);
    I0 = mean( log2(1 + exp(r0)) );
    I1 = mean( log2(1 + exp( -r1)) );
    MI_bits(b) = 1 - 0.5*(I0 + I1);
end

GMI = sum(MI_bits);            % in bits per symbol
NGMI = GMI / nBits;        % normalized per bit

% Auxiliary nested helper for numerically stable log-sum-exp
    function s = logsumexp(a)
        % LOGSUMEXP   Compute log(sum(exp(a))) in a numerically stable way
        m = max(a);
        s = m + log(sum(exp(a - m)));
    end


    function [data_,reference_]=trimseq(data,reference,skipstart,skip_end)

        data_  =  data(skipstart+1:end-skip_end,:);

        delta_bits = length(reference) - length(data);

        skip_end = delta_bits + skip_end;

        reference_ = reference(skipstart+1:end-skip_end,:);

    end

end