Algorithm 1 Improved statistical model for the simulation of soft responses based on the model proposed in [20].

1:Input: K, ${\mu }_{count}^u$, ${\sigma }_{count}^u$, ${\mu }_{LLR}^u$, ${\sigma }_{LLR}^u$, ${\mu }_{count}^e$, ${\sigma }_{count}^e$, ${\mu }_{LLR}^e$, ${\sigma }_{LLR}^e$, $L_{max}$   2:Output: $L_{ref}$, $L_{res}$   3:$R\leftarrow$ create zero vector of length K                                                                                     ▷Variable initialization   4:$R_{ref}\leftarrow$ create zero vector of length K   5:$U\leftarrow$ random sample using ${\mu }_{count}^u,{\sigma }_{count}^{u2}$                                 ▷ Sample number of unstable bits and bit errors   6:$E\leftarrow$ random sample using ${\mu }_{count}^e,{\sigma }_{count}^{e2}$   7:$U_{\mathrm{vec}}\leftarrow$ select U random indices from R                           ▷ Determine positions of unstable bits and bit errors   8:$E_{\mathrm{vec}}\leftarrow$ select E random indices from R   9:for each index i in $U_{\mathrm{vec}}$ do                                                                                                   ▷ Simulate unstable bits 10:    $tmpVar\leftarrow$ random sample using ${\mu }_{LLR}^u,{\sigma }_{LLR}^{u2}$                                                                        ▷ Sample LLR value 11:    if $\mathrm{abs}\left(tmpVar\right)>L_{max}$ then                                                                              ▷ Generate simulated response 12:        $R\left[i\right]\leftarrow \mathrm{sign}\left(tmpVar\right)·L_{max}$ 13:    else 14:        $R\left[i\right]\leftarrow tmpVar$ 15:    end if 16:    if $R\left[i\right]>0$ then                                                                                                      ▷ Generate reference response 17:        $R_{ref}\left[i\right]\leftarrow L_{\max }$ 18:    else if $R\left[i\right]<0$ then 19:        $R_{ref}\left[i\right]\leftarrow -L_{\max }$ 20:    else 21:        $R_{ref}\left[i\right]\leftarrow \mathrm{rand}\{-1,+1\}·L_{max}$ 22:    end if 23:end for 24:for each index j in $E_{\mathrm{vec}}$ do                                                                                                     ▷ Simulate bit errors 25:    $tmpVar\leftarrow$ random sample using ${\mu }_{LLR}^e,{\sigma }_{LLR}^{e2}$                                                                   ▷ Sample LLR value 26:    if $\mathrm{abs}\left(tmpVar\right)>L_{max}$ then                                                                            ▷ Generate simulated response 27:        $R\left[j\right]\leftarrow \mathrm{sign}\left(tmpVar\right)·L_{max}$ 28:    else 29:        $R\left[j\right]\leftarrow tmpVar$ 30:    end if 31:    if $R\left[j\right]>0$ then                                                                                                  ▷ Generate reference response 32:        $R_{ref}\left[j\right]\leftarrow -L_{\max }$ 33:    else if $R\left[j\right]<0$ then 34:        $R_{ref}\left[j\right]\leftarrow L_{\max }$ 35:    else 36:        $R_{ref}\left[j\right]\leftarrow \mathrm{rand}\{-1,+1\}·L_{max}$ 37:    end if 38:end for 39:for each remaining index k in R not in $(U_{\mathrm{vec}}\cup E_{\mathrm{vec}})$ do                                          ▷ Generate stable response 40:    $R\left[k\right]\leftarrow \mathrm{rand}\{-1,+1\}·L_{max}$ 41:    $R_{ref}\left[k\right]\leftarrow R\left[k\right]$ 42:end for 43:$L_{ref}\leftarrow R_{ref}$ 44:$L_{res}\leftarrow R$ 45:return $L_{ref}$, $L_{res}$