Given the following system function $$ H(z) =\frac{1}{1+\frac{2}{3}z^{-1}+\frac{5}{8}z^{-2}+\frac{2}{3}z^{-3}+z^{-4}} \tag{1} $$ We have to draw lattice structure for above system function
The denominator polynomial of the transfer function at lattice stage number $m=4$ is assumed as $A_m$ and now $A_{m-1}$ can be found with
$$\begin{align} A_{m-1}(z)&=\frac{A_{m}(z)-k_mB_{m}(z)}{1-k_m^{2}}\\ \text{with}\quad B_m(z)&=z^{-m}A_m(1/z)\\ \text{and}\quad A_0(z)&=B_0(z)=1\end{align}\tag{2}$$
where $k_m$ is the $m^{th}$ reflection coefficient. But since the $k_m$ value is 1 equation (2) becomes zero in denominator and hence cannot be solved.
I couldn't find the solution to this particular problem in some of my book or other site. How can I get the lattice coefficient for above system function?