Algorithm 5 Decoding at legitimate Receiver 2

Require:${{\rm Y}}_{(2)}^{(V)}$, ${\Phi }_{(2),1:L}^{(V)}$, ${\kappa }_{\Theta }^{(V)}$ and ${\kappa }_{\Gamma }^{(V)}$, and ${\tilde{Y}}_{(2),1:L}^n$.

1: ${\widehat{A}}_L^n\leftarrow \left({{\rm Y}}_{(2)}^{(V)},{\Phi }_{(2),L}^{(V)},{\tilde{Y}}_{(2),L}^n\right)$  2: ${\widehat{\Lambda }}_{1:L-1}^{(V)}\leftarrow {\widehat{A}}_L\left[{\mathcal{R}}_{\Lambda }^{(n)}\right]$  3:for$i=L$ to 2 do  4:    ${\widehat{\overline{\Theta }}}_i^{(V)}\leftarrow {\widehat{A}}_i[{\mathcal{C}}_1^{(n)}]\oplus {\kappa }_{\Theta }^{(V)}$  5:    ${\widehat{\overline{\Gamma }}}_i^{(V)}\leftarrow {\widehat{A}}_i[{\mathcal{C}}_{1,2}^{(n)}]\oplus {\kappa }_{\Gamma }^{(V)}$  6:    ${\widehat{\Psi }}_{i-1}^{(V)}\leftarrow \left({\widehat{A}}_i[{\mathcal{R}}_2^{(n)}],{\widehat{A}}_i[{\mathcal{R}}_{1,2}^{\prime (n)}]\oplus {\widehat{\overline{\Theta }}}_{2,i+1}^{(V)}\right)$  7:    ${\widehat{\Gamma }}_{i-1}^{(V)}\leftarrow \left({\widehat{A}}_i[{\mathcal{R}}_{1,2}^{(n)}]\oplus {\widehat{\overline{\Gamma }}}_{1,i+1}^{(V)},{\widehat{A}}_i[{\mathcal{R}}_2^{\prime (n)}]\right)$  8:    ${\widehat{\Pi }}_{i-1}^{(V)}\leftarrow {\widehat{A}}_i[{\mathcal{R}}_{\mathrm{S}}^{(n)}]$  9:    ${{\rm Y}}_{(2),i-1}^{\prime (V)}\leftarrow \left({\widehat{\overline{\Theta }}}_{1,i}^{(V)},{\widehat{\overline{\Gamma }}}_{2,i}^{(V)},{\widehat{\Psi }}_{i-1}^{(V)},{\widehat{\Gamma }}_{i-1}^{(V)},{\widehat{\Pi }}_{i-1}^{(V)},{\widehat{\Lambda }}_{i-1}^{(V)}\right)$ 10:    ${\widehat{A}}_{i-1}^n\leftarrow \left({{\rm Y}}_{(2),i-1}^{\prime (V)},{\Phi }_{(2),i-1}^{(V)},{\tilde{Y}}_{(2),i-1}^n\right)$ 11: end for