function rop_fec = interp_fec_cross(rops, ber, fec_thr)
    if all(~isfinite(ber))
        rop_fec = NaN; return;
    end
    idx = find(ber < fec_thr, 1, 'first');
    if isempty(idx) || idx == 1
        rop_fec = NaN; return; % no crossing
    end
    % linear interpolation between the two nearest points
    x1 = rops(idx-1); x2 = rops(idx);
    y1 = ber(idx-1);  y2 = ber(idx);
    rop_fec = interp1([y1 y2], [x1 x2], fec_thr, 'linear', NaN);
end