Algorithm 1 Encode b into c

Input:  $\alpha$, L, $\mathit{b}=(b_0,b_1,\dots ,b_{k-1})$, $b_t\in \{0,1\}$

Output:  $\mathit{c}=(c_0,c_1,\dots ,c_{L-1})$, $c_t\in \{0,1\}$

1:  ${\displaystyle B\leftarrow \sum _{t=0}^{k-1}{b}_t{2}^t}$;

2:  $\mathcal{l}\leftarrow \alpha$;

3:  for  $t=0$ to  $L-1$  do

4:    if ${\displaystyle B\ge \left(\genfrac{}{}{0pt}{}{L-t-1}{\mathcal{l}}\right)}$ then

5:     $c_{L-t-1}=1$;

6:     ${\displaystyle B\leftarrow B-\left(\genfrac{}{}{0pt}{}{L-t-1}{\mathcal{l}}\right)}$;

7:     $\mathcal{l}\leftarrow \mathcal{l}-1$;

8:   else

9:     $c_{L-t-1}=0$;

10:   end if

11: end for