## 4 Testing and Comparison of Error Detection Capability
### Simulation and Comparison of Error Detection Capabilities
\begin{table}
\begin{tabular}{c c c c c c c c c c c c c} \hline \hline  & & & & \multicolumn{6}{c}{Error Model} & & & \\ \cline{3-13}
**MFM Arch.** & **Scheme** & \(P\) & **Prob.** & \multicolumn{1}{c}{**SBE**} & **SPSCE** & **SPMCE** & \multicolumn{1}{c}{**MPSCE**} & \multicolumn{1}{c}{**SIMPE**} & \multicolumn{1}{c}{**Error PE Location**} \\ \cline{4-13}  & & & & **One-bit** & **One-PE** & **Two-PE** & **Three-PE** & **Two-PE** & **Three-PE** & **Two-PE** & **Three-PE** & **Three-PE** & \\  & & & & **Error** & **Error** & **Error** & **Error** & **Error** & **Error** & **Error** & **Error** & **Error** & \\ \hline \multirow{4}{*}{**Type-8**} & Parity [36] & 8 bit & P(\%) & 100 & 100 & 100 & 100 & 100 & 100 & 100 & \(\times\) \\ \cline{2-13}  & Style-1[36] & \(2^{8}-1\) & P(\%) & 100 & 99.895 & 100 & 100 & 100 & 100 & 100 & \(\times\) \\ \cline{2-13}  & \multirow{2}{*}{\multirow{2}{*}{Style-II (Ours)}} & 3 & P(\%) & 100 & 85.432 & _97.878_ & _99.691_ & _97.878_ & _99.691_ & _97.878_ & _99.691_ & _\(\surd\)_ \\ \cline{2-13}  & & 7 & P(\%) & 100 & 95.227 & _99.772_ & _99.898_ & _99.772_ & _99.898_ & _99.772_ & _99.898_ & _\(\surd\)_ \\ \cline{2-13}  & & 31 & P(\%) & 100 & 99.012 & 99.990 & 100 & 99.990 & 100 & 99.990 & 100 & \(\surd\)_ \\ \hline \multirow{4}{*}{_Type-16_} & Parity [36] & 8 bit & P(\%) & 100 & 100 & 100 & 100 & 100 & 100 & 100 & \(\times\) \\ \cline{2-13}  & Style-1[36] & \(2^{8}-1\) & P(\%) & 100 & 100 & 100 & 100 & 100 & 100 & 100 & \(\times\) \\ \cline{2-13}  & \multirow{2}{*}{\multirow{2}{*}{Style-II (Ours)}} & 3 & P(\%) & 100 & 85.995 & _97.925_ & _99.701_ & _97.925_ & _99.701_ & _97.925_ & _99.701_ & \(\surd\)_ \\ \cline{2-13}  & & 7 & P(\%) & 100 & 95.293 & _99.778_ & _99.990_ & _99.778_ & _99.990_ & _99.778_ & _99.990_ & _\(\surd\)_ \\ \cline{2-13}  & & 31 & P(\%) & 100 & 99.097 & _99.992_ & 100 & 99.992 & 100 & 99.992 & 100 & \(\surd\)_ \\ \hline \multirow{4}{*}{_Type-32_} & Parity [36] & 8 bit & P(\%) & 100 & 100 & 100 & 100 & 100 & 100 & 100 & \(\times\) \\ \cline{2-13}  & Style-1[36] & \(2^{32}-1\) & P(\%) & 100 & 100 & 100 & 100 & 100 & 100 & 100 & \(\times\) \\ \cline{2-13}  & \multirow{2}{*}{\multirow{2}{*}{Style-II (Ours)}} & 3 & P(\%) & 100 & 85.597 & _97.925_ & _99.701_ & _97.925_ & _99.701_ & _97.925_ & _99.701_ & \(\surd\)_ \\ \cline{2-13}  & & 7 & P(\%) & 100 & 95.294 & _99.778_ & _99.990_ & _99.778_ & _99.990_ & _\(\surd\)_ \\ \cline{2-13}  & & 31 & P(\%) & 100 & 99.097 & _99.992_ & 100 & _99.992_ & 100 & 99.992 & 100 & \(\surd\)_ \\ \hline \multirow{4}{*}{_Type-64_} & Parity [36] & 8 bit & P(\%) & 100 & 100 & 100 & 100 & 100 & 100 & 100 & \(\times\) \\ \cline{2-13}  & Style-1[36] & 2^{84}-1 & P(\%) & 100 & 100 & 100 & 100 & 100 & 100 & 100 & \(\times\) \\ \cline{2-13}  & & 3 & P(\%) & 100 & 85.998 & _97.925_ & _99.701_ & _97.925_ & _99.701_ & _97.925_ & _99.701_ & \(\surd\)_ \\ \cline{2-13}  & & 7 & P(\%) & 100 & 95.295 & _99.779_ & _99.990_ & _99.779_ & _99.990_ & _\(\surd\)_ \\ \cline{2-13}  & & 31 & P(\%) & 100 & 99.098 & _99.992_ & 100 & _99.992_ & 100 & 99.992 & 100 & \(\surd\)_ \\ \hline \hline \end{tabular}
\end{table} 
Table 2: The comparison of error detection capability. For a simplified description, we used Parity, Style-I, and Style-II to represent the error detection scheme in [36; 40], and in this paper. Table 2 shows simulation results of all three schemes. As shown in Table 2, for the SBE model, all three methods detected 100% of the errors. For the other error models, Style-II exhibited a poorer error detection capability than Style-I and Parity, due to its extremely small p value. However, Style-II architectures with \(p=7\) and \(p=31\) were similar to Style-I and Parity in error detection performance. When there were three or more erroneous PEs, Style-II could detect 99.898% or more errors, slightly behind that of Style-I and Parity. Despite the lag in detection ability, Style-II has an advantage over the two contrastive methods--once an error was detected in a PE, the erroneous PE could be located 100%.