Algorithm 2 Hi-DM decoding.

1:Data: Received amplitude sequence ${\mathbf{d}}^{\left(1\right)}=(d_1,\dots ,d_N)$ 2:Result: The k decoded bits $\mathbf{b}$ 3:for$\ell =1,\dots ,L$do 4: Divide ${\mathbf{d}}^{(\ell )}$ into $T_{\ell }$ sequences of length $N_{\ell }$${\mathbf{d}}^{(\ell )}=({\mathbf{a}}_1,\dots ,{\mathbf{a}}_{T_{\ell }})$ 5: for $h=1,\dots ,T_{\ell }$ do 6:  Find j such that ${\mathbf{a}}_h$ is produced by ${\mathcal{D}}_j^{(\ell )}$. 7:  Decode ${\mathbf{a}}_h$ using ${\mathcal{D}}_j^{(\ell )}$ and obtain $k_{\ell }$ bits ${\mathbf{b}}_t$. 8:  Append the bits $\mathbf{b}=({\mathbf{b}}_t,\mathbf{b})$ 9:  If $\ell <L$, append the sequence of DM ${\mathbf{d}}^{(\ell +1)}=({\mathbf{d}}^{(\ell +1)},{\mathcal{D}}_j^{(\ell )})$ 10: end for 11:end for