## 4 Experimental Results  
A performance comparison is made among the presented DI-TIE, a typical TIE [18], a multiple TIE (MTIE) [20] and an EEENNS. Since TIE-based and EEENNS VQ codebook searches are conducted, a 100% search accuracy is obtained by such four algorithms as compared with a full search approach. For this sake, performance is compared in terms of search complexity. The test objects are those selected out of a Chinese language speech database, containing 1694 syllables out of 50 sentences for a duration over 445 s and 22,244 frames. Table 3 gives a comparison on the average number of searches for coding modes with bitrates between 8.85 and 23.85 kbps, while Table 4 lists a comparison on the percentage complexity reduction with the search load required in a full search algorithm as a benchmark. An observation in Tables 3 and 4 reveals two findings. Firstly, DI-TIE is found to provide a remarkable search complexity reduction, relative to its counterparts. Secondly, the percentage complexity reduction is found to have a strong dependence on the codebooks over which a codeword search is carried out, particularly in the case of TIE, and it must be noted that DI-TIE is found to outperform EEENNS. Figure 1: Flowchart of the presented triangular inequality elimination (TIE) algorithm combined with a dynamic mechanism and an intersection mechanism (DI-TIE) search algorithm. Taking the codebook CB22 as an instance, the complexity reduction is well maintained at 60.26% in the case of DI-TIE, while plunges to 13.85% and 8.77% in the cases of MTIE and TIE, respectively. This might be due to the reason that CB22 contains a great number of similar codewords, that is, they are very close to each other. Thus, it is respectively required to search a great number of codewords over the search space in MTIE and TIE. In contrast, the search space in DI-TIE is efficiently downsized in such a way that a high search performance can be maintained over codebooks. Furthermore, Table 5 gives a comparison on the average number of searches for the 6.60 kbps mode, and Table 6 gives a complexity reduction comparison with the full search as a benchmark. The performance superiority of DI-TIE is demonstrated again over EEENNS, MTIE and TIE, particularly in the CB21 case, a finding in agreement with Tables 3 and 4. Table 7 gives an overall performance comparison with the full search as a benchmark, and is presented as well as a bar graph in Figure 2. The overall performance refers to the total search load, defined as the sum of the average number of searches multiplied by the vector dimension in each codebook. As clearly indicated in Figure 2, this proposal is experimentally validated as a superior candidate relative to the EEENNS and the TIE-based counterparts. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multicolumn{2}{c}{**Method**} & \multicolumn{2}{c}{**Full Search (Benchmark)**} & \multicolumn{1}{c}{**TIE**} & \multicolumn{1}{c}{**MTIE**} & \multicolumn{1}{c}{**EEENNS**} & \multicolumn{1}{c}{**DI-TIE**} \\ \hline \multirow{2}{*}{Stage 1} & CB1 & 0 & 52.74\% & 66.79\% & 76.01\% & 81.10\% \\  & CB2 & 0 & 37.14\% & 56.51\% & 75.62\% & 83.49\% \\ \hline \multirow{2}{*}{Stage 2} & CB11 & 0 & 11.83\% & 18.08\% & 56.26\% & 70.54\% \\  & CB12 & 0 & 19.62\% & 27.64\% & 71.55\% & 84.53\% \\ \cline{1-1}  & CB21 & 0 & 1.83\% & 1.93\% & 16.96\% & 37.28\% \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Complexity reduction representation of Table 5.