## 6 Simulation Results and Discussions
### TT-NOMS and TT-NSMS  
First, the performance of the proposed TT-NOMS, TT-NSMS algorithms with the NOMS [22] and NSMS algorithms are obtained, in which we use five iterations. As shown in Figure 3, when the decoding network has 12 layers in five iterations, the bit error rate (BER) and frame error rate (FER) performances of TT-NOMS, TT-NSMS algorithms and NOMS, NSMS algorithms are basically the same for the Hamming(7,3) code. However, TT-NOMS and TT-NSMS algorithms only use 1.5% the number of parameters in NOMS and NSMS algorithm while the multiplication of TT-NSMS is reduced 222 times, as listed in Table 2. TT-NOMS adds low-rank multiplication to reduce the number of parameters. \begin{table}
\begin{tabular}{c c} \hline \hline
**Parameters** & **Content** \\ \hline Code & \(LDPC\), \(BCH\), \(Hamming\) \\ \hline Min frame error & 100 \\ \hline Max frame & 100,000 \\ \hline Learning rate & 0.01 \\ \hline Batch size & 120 \\ \hline Optimizer & \(Adam\) \\ \hline \(E_{b}/N_{0}\) & 1–8 (dB) \\ \hline Number of iterations & \(5,15\) \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Parameters of simulation. As shown in Figures 4 and 5, when the decoding network has 12 layers, there is not much difference in BER performance between TT-NOMS, TT-NSMS algorithm, NOMS and NSMS algorithms for BCH(63,45) and BCH(127,106) codes. However, TT-NOMS algorithm only uses 0.12% and 0.7% number of parameters in NOMS algorithm, while at the same time, the multiplication of TT-NSMS is reduced rapidly, as listed in Table 2. \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Code**} & \multirow{2}{*}{**Algorithm**} & **Number of** & **Parameter** & **Number of** \\  & & **Parameters** & **Reduction** & **Multiplications** \\ \hline \multirow{4}{*}{LDPC(576,432)} & NOMS & 1,224,000 & 100\% & 0 \\  & NSMS & 2,448,000 & 100\% & 146,880,000 \\  & TT-NOMS & 474 & 0.03\% & 25,780 \\  & TR-NOMS & 474 & 0.03\% & 25,780 \\  & TT-NSMS & 948 & 0.03\% & 88,700 \\  & TR-NSMS & 948 & 0.03\% & 88,700 \\  & NOMS & 604,800 & 100\% & 0 \\ BCH(127,106) & NSMS & 1,209,600 & 100\% & 72,576,000 \\  & TT-NOMS & 430 & 0.70\% & 19,692 \\  & TT-NOMS & 430 & 0.70\% & 19,692 \\  & TT-NSMS & 860 & 0.70\% & 67,812 \\  & TR-NSMS & 860 & 0.70\% & 67,812 \\  & NOMS & 259,200 & 100\% & 0 \\ BCH(63,45) & NSMS & 518,400 & 100\% & 31,104,000 \\  & TT-NOMS & 316 & 0.12\% & 7584 \\  & TT-NOMS & 632 & 0.12\% & 21,264 \\  & TR-NSMS & 632 & 0.12\% & 21,264 \\  & NOMS & 7200 & 100\% & 0 \\ Hamming(7,3) & NSMS & 14,400 & 100\% & 864,000 \\  & TT-NOMS & 108 & 1.5\% & 1008 \\  & TR-NOMS & 108 & 1.5\% & 1008 \\  & TT-NSMS & 216 & 1.5\% & 3888 \\  & TR-NSMS & 216 & 1.5\% & 3888 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Comparison of parameters and multiplication in NOMS [22], NSMS, TR-NOMS and TR-NSMS algorithms. Figure 3: BER performance of TT-NOMS, TT-NSMS, NOMS [22] and NSMS algorithms for Hamming(7,3) code. As shown in Figure 6, the BER performances of the TT-NOMS algorithm and NOMS algorithm are basically the same for LDPC(576,432) code. However, TT-NOMS algorithm only uses 0.03% the number of parameters in NOMS algorithm while the multiplication of TT-NSMS is reduced from 14,688 W to 8.9 W as listed in Table 2.  
Figure 4: BER performance of TT-NOMS, TT-NSMS, NOMS [22] and NSMS algorithms for BCH(63,45) code. Figure 5: BER performance of TT-NOMS, TT-NSMS, NOMS [22] and NSMS algorithms for BCH(127,106) code. Figure 6: BER performance of TT-NOMS, TT-NSMS, NOMS [22] and NSMS algorithms for LDPC(576,432) code. As shown in Figure 10, performance in TR-NOMS algorithm and NOMS algorithm are basically the same for LDPC(576,432) code. However, TR-NOMS algorithm only uses 0.03% the number of parameters in NOMS algorithm and the same saving is achieved by TT-NOMS for the two algorithms have the same rank while the multiplication of TR-NSMS is reduced rapidly, as listed in Table 2. Figure 11 shows algorithms with 5 and 15 iterations, in which the decomposed network has continuous stability. Figure 12 shows TR-NOMS algorithm for LDPC with different ranks.