Modeling the Energy Consumption of the HEVC Software Encoding Process using Processor events

The convenience of the Internet and mobile devices has increased Internet video traffic lately [1]. In addition, video-focused social networking services are growing, accounting for further video traffic increases, and [1] emphasizes the enormous storage costs, space needs, and increased server-side energy consumption for video content creation. Furthermore, the compression methods used for encoding have evolved immensely in recent years. Modern codecs provide many compression methods, increasing the encoders’ processing complexity [2], resulting in a considerable increase in the energy demand.

For several reasons, research on the energy consumption of video encoders is helpful. Firstly, portable devices are limited in terms of battery capacity. The energy requirements for video encoding are significant, which is a problem for battery-powered devices, where the battery drains fast due to increased energy requirements [3]. Secondly, the total energy consumption of current encoding and decoding systems is globally significant, as online video contributes to $1\%$ of global $\mathrm{CO}_{2}$ emissions [4]. According to [4], there is a considerable energy demand for using various digital equipment in the video processing pipeline and producing such devices [4]. Thirdly, most video-on-demand services use massive server farms in data centers for encoding [5]. A recent study states that such data centers, which predominantly perform CPU encoding, currently consume about 3% of global power consumption, which is expected to reach more than 1,000 TW by 2025, equivalent to 1 trillion tons of coal [6]. To enable energy-aware video-based services in modern video communication applications, we need robust and energy-efficient video codecs that optimize energy.

Few works have explicitly addressed the encoder’s processing energy, such as [7], which establishes a relationship between the quantization, spatial information, and coding energy for the intra-only High Efficiency Video Coding (HEVC) encoder. However, it did not consider the presets that quantify the encoding speed and compression performance. A study on detailed energy consumption of the x265 encoder is presented in [8]. In [9], energy-rate-quality trade-offs of state-of-the-art video codecs were studied. Furthermore, Mercat et al. measured the energy of a software encoder for different sequences and encoding configurations and presented various energy reduction opportunities[10]. In a carbon footprint-limited future, the energy efficiency of video coding is more relevant. The complex and laborious nature of energy measurements is a limitation in searching for energy-efficient algorithms. Therefore, we need simple energy estimation models to overcome the drawback of time-consuming measurements. There is extensive literature on estimating the energy demand of the decoding process, such as [11, 12, 13]. However, only some recent works explicitly addressed the estimation of the energy demand of the encoding process. For instance, [7] performs encoding energy estimation using quantization parameter (QP), albeit restricted to all-intra encoding.

Furthermore, [14] introduces a model that uses the encoder processing time to estimate the energy consumption of the x265 encoder. However, the energy encoding process has to be performed on a target device for estimation. Moreover, [14] also introduces a practical and lightweight encoding time-based encoding energy estimator, which uses the ultrafast (UF) preset’s encoding time to enable prior estimation of the encoding energy demand of the other presets. However, the estimation error is more than 15%, especially for complex presets. Lastly, [15] introduces a bit stream feature-based energy estimator that uses the compressed video bit stream features (BSF) obtained using a bit stream analyzer [15] after encoding to estimate the energy using bit streams. Even though this model makes accurate estimations, it is limited to specific applications, such as estimating the energy of crowd-sourced video data, since the bit stream is required for estimation. To this end, this work explores the feasibility of accurately estimating the HEVC software encoders’ energy demand using processor events (PEs).

In order to achieve this, we perform energy measurements and obtain processor events (PEs) using a dedicated open-source profiling software [16] and then study the relationship between PEs and encoding energy, followed by a study of feasibility for estimating the HEVC software encoder’s energy demand. Ultimately, we propose two simple models to efficiently estimate encoding energy without measuring it directly before and after the encoding process using certain PEs obtained using existing open-source profiling tools. The models proposed in this work have two practical applications: to estimate the energy for CPU encoding, for example, in data centers, and study the energy distribution of the encoding process, i.e., to obtain the energy of encoding sub-processes.

The rest of this paper is structured as follows: Section 2 presents the experimental setup used to measure the energy demand of the encoding process, along with sequences used, as well as encoding configurations, then explains the profiling, and further examines the relation between PEs and energy consumed during the encoding process. Further, Section 3 introduces the proposed encoding energy estimation models. Section 4 introduces the evaluation method, discusses the results, and presents an examplary application of the proposed models. Lastly, Section 5 concludes this work.

Our work uses the x265 encoder implementation [17] on an Intel Xeon processor to perform multi-core encoding. We encode the first eight frames of each sequence at various x265 presets ultrafast, superfast, veryfast, faster, fast, medium, slow, slower, veryslow and various Constant Rate Factor (CRF) values, 18, 23, 28, 33. In contrast to the previous works [14], and [15], the x265 encoder used in this work is built using Netwide Assembler (NASM), i.e., it uses Single Instruction Multiple Data (SIMD) instructions.

We consider 22 sequences from the JVET common test conditions [18] with various sequence characteristics such as frame rate, resolution, and content. Ultimately, we generated 792-bit streams and further used them to evaluate the models. In addition, we record the QP, encoding time, and bit stream features to enable a comparison with the estimation models from the literature [7], [14], and [15]. As in [13], we describe the energy demand of the encoding process using two consecutive measurements. First, the total energy consumed during the encoding process is described as follows:

$$\small E_{\mathrm{total}}=\int_{t=0}^{T}P_{\mathrm{total}}(t)dt,\vspace{-0.15cm}$$

(1)

where $T$ is the duration of the encoding process and $P_{\mathrm{total}}$ is the total power consumed while encoding. Then, the energy consumed in idle mode over the same encoding duration $T$ is described as follows:

$$\small E_{\mathrm{idle}}=\int_{t=0}^{T}P_{\mathrm{idle}}(t)dt,\vspace{-0.15cm}$$

(2)

where $P_{\mathrm{idle}}$ is the power consumed by the device in idle mode. Ultimately, the encoding energy $E_{\mathrm{enc}}$ is the difference between these two measurements. In this work, we used a desktop PC with an Intel Xeon CPU with 16 cores and CentOS 8 as an operating system (OS). We employed the integrated power meter in the Intel CPUs, Running Average Power Limit (RAPL) [19], that directly returns aggregated energy values $E_{\mathrm{total}}$ and $E_{\mathrm{idle}}$. Additionally, we perform the confidence interval test proposed in [20], to ensure the statistical significance of the measured encoding energies as in [14].

Furthermore, we employed dedicated open-source profiling software, Valgrind, to obtain the PEs [16]. Valgrind analyzes any desired process for instructions, memory accesses, memory leaks, cache misses, and other processor events. In this work, we take the HEVC encoding process and profile it with the Cachegrind tool of the Valgrind framework [21]. The Cachegrind simulates encoding processes’ interaction with the machine’s cache hierarchy, independent first-level instruction, and data caches (I1 and D1) backed by a second-level cache (L2) [21]. Yet, some modern machines have three or four levels of cache, and Cachegrind can auto-detect the cache configuration for these machines. Hence, Cachegrind simulates the first-level (I1 and D1) and last-level (LL) caches. This is because the last-level cache influences runtime, as it masks access to the main memory. Also, the L1 caches often have low associativity, so simulating them can detect processes’ bad interaction with the cache. Even though the application of this profiling tool is straightforward, it slows the original process by a factor of 5, depending on the encoding preset. Therefore, for energy measurements, we used the encoding process without profiling. All the recorded PEs are tabulated in Table 1.

To illustrate the relationship between the PEs and the encoding energy, we calculate the Pearson Correlation Coefficient (PCC) proposed in [20] to express the correlation in numbers. The correlation between the encoding energy and all considered PEs (PCC) are listed in Table 1. We can observe that the encoding energy correlates to most of the PEs except the last-level cache misses, which have a low correlation. In addition, from Table 1, we can observe that the highest correlations are obtained for the number of instructions (Ir) followed by the data reads (Dr), date writes (Dw), Conditional branches executed (Bc), Indirect branches executed (Bi), Conditional branches mispredicted (Bcm), and Indirect branches mispredicted (Bim).

Based on the above observations, we propose a PE-based posterior estimation model, i.e., we estimate the encoder processing energy after the encoding process. The model exploits the linear relationship between encoding energy and PEs, such that the energy can be estimated by

$$\small\hat{E}_{\mathrm{enc}}=\sum_{\forall\text{{i}}}n_{\textit{i}}\cdot e_{\text{{i}}},\vspace{-0.15cm}$$

(3)

where i denotes the processor event ID as mentioned in Table 1, and $n_{\text{i}}$ is the number of occurrences of the respective processor event (PE). The parameter $e_{\text{{i}}}$ can be interpreted as a constant mean energy required to execute a certain PE. It must be noted that the estimates can only be obtained when the encoding process is executed once, as the encoding process needs to be profiled by Valgrind. Therefore, we adjust model (3) to allow prior estimation, i.e., energy estimation, without executing the encoder. In this context, we interpret encoding at the ultrafast preset as a preprocessing step for slower presets and investigate the modeling of the utrafast presets’ PEs on encoding energies of all the presets, as the ultrafast PEs are relatively less costly to obtain when compared to that of other presets. When we replace the PEs of respective presets with the PEs of ultrafast preset, we can also observe similar linear behavior. Therefore, we adapt the model in (3) to enable prior estimation of energy consumption of the encoding process using the PEs of ultrafast preset as the UF PE-based prior estimation model as follows:

$$\small\hat{E}_{\mathrm{enc}}=\sum_{\forall\text{{i}}}n_{\text{{i},UF}}\cdot e_{\text{{i}}},\vspace{-0.15cm}$$

(4)

where i denotes ID as mentioned in Table 1, and $n_{\text{{i},UF}}$ is the number of occurrences of the respective ultrafast PE. $e_{\text{{i}}}$ is the model parameters later obtained by training as explained in Section 4.

Depending on the operating system, CPU architecture, and encoding algorithms, the energy consumed during the encoding process and the PEs may vary. However, we have a strong indication that the linear relationship between the energy demand of the encoding process and the PEs remains the same. Therefore, the proposed models can be extended to different operating systems, CPU architecture, and encoding algorithms with differing model parameters. This claim is supported by related work on decoding energy [22] and [23], which showed that this kind of model is valid for different operating systems, CPU architectures, and codecs.

We evaluate the proposed models using the mean absolute percentage error (MAPE), as we strive to estimate the encoding energy accurately independent of the absolute energy, which varies by several orders of magnitude. Thus, we calculate the absolute percentage error of the measured encoding energy concerning the estimated encoding energy for a single bit stream $b$, i.e., each bit stream $b$ corresponds to a single input sequence coded at a specific CRF, and preset $X$. Then, we calculate the mean absolute percentage error ${{\epsilon}_{X}}$ for each preset $X$ over $B$ bit streams to obtain the overall estimation error as MAPE for each preset as follows:

$$\small{\epsilon}_{X}=\frac{1}{B}\sum_{b=1}^{B}|r_{X,b}|,\vspace{-0.15cm}$$

(5)

where $r_{X,b}$ is the percentage errors for a given preset $X$ and bit stream $b$ and is given as:

$$\small r_{X,b}=\left(\frac{\hat{E}_{\mathrm{enc}}-E_{\mathrm{enc}}}{E_{\mathrm{enc}}}\right)\cdot 100,\vspace{-0.15cm}$$

(6)

where $\hat{E}_{\mathrm{enc}}$ is the estimated encoding energy and $E_{\mathrm{enc}}$ the measured encoding energy. To determine the model parameters $e_{\textit{i}}$ for each preset, we perform a least-squares fit using a trust-region-reflective algorithm as presented in [24]. We use the measured energies for a subset of the sequences referred to as the training set and their corresponding variables as input, which are the PEs. As a result, we obtain the least-squares optimal parameters for the input training set, where we train the parameters such that the mean relative error is minimized. Ultimately, these model parameters validate the model’s accuracy on the remaining validation sequences. The training and validation data set are determined using a ten-fold cross-validation proposed in [25].

Furthermore, to assess the performance of the proposed energy estimator models, we used a confidence interval analysis on the estimation errors, i.e., percentage errors. To this end, we obtained the confidence interval $CI_{X}$ for a 95% confidence level with ${m}_{X}$ being mean and ${\sigma}_{X}$ being standard deviation of the percentage errors of all the B bit streams associated with preset $X$, $r_{X}=[r_{X,1},...,r_{X,B}]$. Then, for each preset $X$, and $B$ bit streams, the confidence interval is defined as follows:

$$CI_{X}={m}_{X}\pm z\cdot({\sigma}_{X}/\sqrt{B}),$$

(7)

where z is the z-score corresponding to the chosen confidence level, which is 1.96 for 95% confidence level. In Table 2 and Table 3, we report the MAPE for each preset, the average MAPE over all the presets, and the confidence intervals of the percentage errors for all the presets of the proposed models. In subsequent subsections, we evaluate the posterior and prior estimation models, followed by a discourse on their practical applications.

Energy measurements are pivotal in developing energy-efficient video coding algorithms. Nonetheless, such measurements are complex and costly. Thus, we need valid and simple energy estimation models. This work demonstrates that, for the HEVC software encoding process, a lightweight PE-based posterior estimation model provides an accurate prior estimation of encoding energy, exhibiting a mean absolute percentage error of 5.36%. Moreover, this work also presents the PE-based posterior modeling approach, which yields the average sub-process-specific energies, aiding in analyzing the energy demand of encoding sub-processes. In addition, we presented an examplary energy consumption analysis of the HEVC encoding process on a functional level using the PE-based posterior model. In the future, we plan to extend the proposed models to other encoders and extend the energy consumption analysis of the encoding process on a functional level, such as motion estimation and compensation.