## 5 Experimental Results and Discussion
### Performance Evaluation and Analysis
#### 5.3.1 Rate Controlling Performance  
The percentage deviations of the final bit rate achieved after encoding using the proposed (with joint rate and decoding-complexity controlling) and state-of-the-art algorithms (with rate controlling enabled) are presented in the Table 1. Here, the video sequences are encoded at four different bit rates (described in Section 5.1) and the averaged percentage error is presented for comparison. It can be observed that the rate-controlling algorithm implemented in the HM 16.0 reference encoder shows 1.75% average error, which is less than the 3.08% deviation from the target bit rate experienced by [PERSON] et al. [20]. This is mainly due to the content and QP-agnostic nature of the algorithm, despite its use of PU level prediction modes, integer-pel vs. fractional-pel motion vectors, and in-loop filtering decisions. However, ref. [46] uses QP-dependent trade-off factors for both rate and decoding-complexity; thus the impact on the rate controller is significantly improved compared to [PERSON] et al. [20]. In contrast, the proposed algorithm uses a content-adaptive, decoding-complexity, rate, and distortion model to derive the QP as well as rate and decoding-complexity trade-off factors to determine the set of coding modes and structures that minimize the distortion while achieving a given bit and decoding-complexity budget. Therefore, as illustrated in the Table 1, the proposed algorithm achieves the allocated bit rate targets with \(<\)1% error indicating that both CTU-level bit allocation as well as coding parameter selection are more accurate and content-adaptive compared to the state-of-the-art approaches. In addition, the frame-wise rate-controlling performances of the encoding algorithms were analyzed using the percentages of error between the allocated bits and actual bits per frame. A graphical illustration of this frame-wise percentage error is presented in the Figure 2. It can be observed that the rate-controlling algorithms implemented in HM 16.0 and other state-of-the-art encoding algorithms suffer from large percentage errors throughout the video sequence. The incorporation of a third parameter within the mode selection cost function in [PERSON] et al. [20] and [PERSON] et al. [46] crucially affect the rate controller in achieving the allocated number of bits for a given block. For example, \begin{table}
\begin{tabular}{l l l l l l} \hline \hline  & & \multicolumn{2}{c}{**Proposed L2**} & \multicolumn{1}{c}{**HM 16.0**[49]} & **[PERSON] et al. [20]** & **[PERSON] et al. [46]** \\  & & \(\mathbf{R_{e}\) \%} & \(\mathbf{R_{e}\) \%} & \(\mathbf{R_{e}\) \%} & \(\mathbf{R_{e}\) \%} \\ \hline Band & (AM, LT) & 0.350 & 0.093 & \(-\)0.03 & 0.002 \\ Beergarden & (LM, HT) & 0.189 & 3.050 & 8.22 & 3.319 \\ Cafe & (AM, LT) & 0.010 & 1.229 & 0.12 & 0.443 \\ Dancer & (AM, LT) & 1.448 & 2.344 & 1.56 & 0.010 \\ GTFly & (HM, LT) & 0.018 & 0.067 & 0.14 & 0.129 \\ Kimono & (AM, HT) & 0.014 & 4.097 & 6.34 & 1.607 \\ Musicians & (LM, HT) & 1.125 & 0.054 & 3.78 & 0.725 \\ Parkscene & (HM, HT) & 0.105 & 2.352 & 4.56 & 0.386 \\ Poznan St. & (LM, HT) & 0.359 & 2.548 & 3.07 & 2.579 \\
**Average** & & **0.40** & **1.75** & **3.08** & **1.02** \\ \hline \hline \multicolumn{5}{l}{The sequence categories (i.e., LM, AM, HM, LT, and HT) are defined as follows. LM: low motion; AM: average motion; HM: high motion; LT: low texture; HT: high texture.} \\ \end{tabular}
\end{table} 
Table 1: Rate controlling performances of the encoding algorithms. both these algorithms use an RD-optimization-based bit allocation, QP, and Lagrangian parameter determination approach [48] for the rate control while utilizing three parameters in the cost function (rate, distortion, and decoding-complexity) for the coding mode selection.