# Low Power QC-LDPC Decoder Based on Token Ring Architecture
## 4 Experimental Results
\begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline \multicolumn{2}{c}{**Parity Check Matrix H**} & \multicolumn{4}{c}{**Without “Token Ring”**} & \multicolumn{4}{c}{**With “Token Ring”**} & \multicolumn{2}{c}{**Differences**} \\ \hline
**Type** & \(M\times N\) & \(P\) & \(Z\) & \(P_{d}\) **[mW]** & **ALM** & **Mem** & \(P_{d}\) **[mW]** & **ALM** & **Mem** & \(P_{d}\) **[\%]** & **ALM [\%]** \\ \hline \(I\) & \(336\times 672\) & 42 & 2184 & 201.95 & 7568 & 24,424 & 119.92 & 7928 & 24,424 & \(-\)40.619 & 4.7569 \\ \(I\) & \(512\times 1024\) & 64 & 3072 & 289.63 & 11,336 & 34,064 & 178.24 & 11,868 & 34,064 & \(-\)38.4594 & 4.693 \\ \(I\) & \(512\times 1024\) & 64 & 3200 & 301.8 & 12,906 & 35,264 & 196.55 & 13,425 & 35,264 & \(-\)34.8741 & 4.0214 \\ \(I\) & \(512\times 1024\) & 64 & 3264 & 312.1 & 13,531 & 35,864 & 201.04 & 14,065 & 35,864 & \(-\)35.5847 & 3.9465 \\ \(I\) & \(1152\times 2304\) & 69 & 7296 & 445.67 & 19,227 & 79,528 & 261.08 & 20,006 & 79,528 & \(-\)41.4185 & 4.0516 \\ \(R\) & \(256\times 512\) & 64 & 1536 & 122.37 & 6997 & 16,912 & 64 & 8169 & 16,912 & \(-\)47.8615 & 16.75 \\ \(R\) & \(384\times 768\) & 32 & 2304 & 120.17 & 3724 & 26,304 & 67.8 & 3994 & 26,304 & \(-\)43.5799 & 7.2503 \\ \(R\) & \(416\times 832\) & 32 & 2496 & 122.37 & 3716 & 28,496 & 72.43 & 3978 & 28,496 & \(-\)40.8107 & 7.0506 \\ \(R\) & \(448\times 896\) & 32 & 2688 & 118.68 & 3723 & 30,688 & 73.8 & 3988 & 30,688 & \(-\)37.816 & 7.1179 \\ \(R\) & \(480\times 960\) & 32 & 2880 & 118.22 & 3732 & 32,880 & 74.04 & 3991 & 32,880 & \(-\)37.371 & 6.94 \\ \(R\) & \(512\times 1024\) & 8 & 3072 & 22.95 & 887 & 41,984 & 15.88 & 1092 & 41,984 & \(-\)30.8061 & 23.1116 \\ \(R\) & \(512\times 1024\) & 64 & 3072 & 114.34 & 7029 & 33,920 & 66.41 & 8199 & 33,920 & \(-\)41.9188 & 16.6453 \\ \(R\) & \(544\times 1088\) & 32 & 3264 & 116.7 & 3641 & 37,264 & 68.52 & 3972 & 37,264 & \(-\)41.2853 & 9.0909 \\ \(R\) & \(608\times 1216\) & 32 & 3648 & 116.71 & 3641 & 41,648 & 69.12 & 3972 & 41,648 & \(-\)40.7763 & 9.0909 \\ \(R\) & \(576\times 1152\) & 4 & 3456 & 40.99 & 598 & 57,600 & 28.41 & 712 & 57,600 & \(-\)30.6904 & 19.0635 \\ \(R\) & \(576\times 1152\) & 8 & 3456 & 44.84 & 979 & 47,232 & 27.64 & 1119 & 47,232 & \(-\)38.3586 & 14.3003 \\ \(R\) & \(576\times 1152\) & 18 & 3456 & 91.05 & 2183 & 41,856 & 44.37 & 2359 & 41,856 & \(-\)51.2685 & 8.0623 \\ \(R\) & \(576\times 1152\) & 24 & 3456 & 101.43 & 2837 & 40,608 & 55.59 & 3054 & 40,608 & \(-\)45.1937 & 7.6489 \\ \(R\) & \(576\times 1152\) & 32 & 3456 & 116.7 & 3641 & 39.456 & 75 & 3987 & 39,456 & \(-\)35.7326 & 9.5029 \\ \(R\) & \(576\times 1152\) & 48 & 3456 & 178.97 & 5580 & 38,736 & 99.71 & 6085 & 38,736 & \(-\)44.2868 & 9.0502 \\ \(R\) & \(576\times 1152\) & 64 & 3456 & 230.15 & 7883 & 38,160 & 124.91 & 8210 & 38,160 & \(-\)45.7267 & 4.1482 \\ \(R\) & \(576\times 1152\) & 96 & 3456 & 343.69 & 11,822 & 37,800 & 181.45 & 12,165 & 37,800 & \(-\)47.2053 & 2.9014 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Comparison of implementations of QC-LDPC decoders with and without architecture based on a Token Ring. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Type** & \(L_{c}\) **\(P_{d}\) [mW]** & \(E_{d}\) **[n]** & **ALM** & **Mem** \\ \hline \(I\) & 416 & 178.24 & 185.36 & 11,868 & 34,064 \\ \(R\) & 440 & 66.41 & 73.05 & 8199 & 33,920 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Comparison of energy efficiency of decoders based on regular and irregular matrices for \(M\times N\ =\ 512\times\ 1024\), \(P=64\), \(Z=3072\) and \(f=400\) MHz. Results presenting the mentioned dependencies are shown in Table 5 as well as Figures 6-8, where \"[cyc/it]\" denotes the number of ticks of a global clock needed to perform one decoding iteration. Figure 6 shows the dependence of \(L_{c}\) on the value of \(P\). Figure 7 shows the dependence of the hardware demand for ALM units on the value of \(P\). One can see an approximately linear increase in hardware requirements with increasing values of \(P\). Figure 8 shows the dynamic energy consumption \(E_{d}\) depends on the value of \(P\).