  In \cite{butman1976} the linear coding scheme is applied, $X_t
=g_t\Big(\Theta - {\bf E}\Big\{\Theta\Big|Y^{t-1}, V_0=v_0\Big\}\Big)$,
$t=2,\ldots,n$, $X_1=g_1\Theta$, with $\Theta: \Omega \to {\mathbb R}$, a
Gaussian random variable, to derive a lower bound on the feedback rate, for
additive Gaussian noise (AGN) channels, $Y_t=X_t+V_t, t=1, \ldots, n$, where
$V_t$ is a Gaussian autoregressive (AR) noise, and $\kappa \in [0,\infty)$ is
the total transmitter power. For the unit memory AR noise, with parameters $(c,
K_W)$, where $c\in [-1,1]$ is the pole and $K_W$ is the variance of the
Gaussian noise, the lower bound is $C^{L,B} =\frac{1}{2} \log \chi^2$, where
$\chi =\lim_{n\longrightarrow \infty} \chi_n$ is the positive root of
$\chi^2=1+\Big(1+ \frac{|c|}{\chi}\Big)^2 \frac{\kappa}{K_W}$, and the sequence
$\chi_n \triangleq \Big|\frac{g_n}{g_{n-1}}\Big|, n=2, 3, \ldots,$ satisfies a
certain recursion, and conjectured that $C^{L,B}$ is the feedback capacity.
  In this correspondence, it is observed that the nontrivial lower bound
$C^{L,B}=\frac{1}{2} \log \chi^2$ such that $\chi >1$, necessarily implies the
scaling coefficients of the feedback code, $g_n$, $n=1,2, \ldots$, grow
unbounded, in the sense that, $\lim_{n\longrightarrow\infty}|g_n| =+\infty$.
The unbounded behaviour of $g_n$ follows from the ratio limit theorem of a
sequence of real numbers, and it is verified by simulations. It is then
concluded that such linear codes are not practical, and fragile with respect to
a mismatch between the statistics of the mathematical model of the channel and
the real statistics of the channel. In particular, if the error is perturbed by
$\epsilon_n>0$ no matter how small, then $X_n =g_t\Big(\Theta - {\bf
E}\Big\{\Theta\Big|Y^{t-1}, V_0=v_0\Big\}\Big)+g_n \epsilon_n$, and
$|g_n|\epsilon_n \longrightarrow \infty$, as $n \longrightarrow \infty$.
