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Sergio Sanz-Rodríguez, Thomas Schierl

A rate control algorithm for HEVC with

hierarchical GOP structures

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A RATE CONTROL ALGORITHM FOR HEVC WITH HIERARCHICAL GOP STRUCTURES

Sergio Sanz-Rodr´

ıguez, Thomas Schierl

Multimedia Communications, Fraunhofer HHI, Berlin, Germany.

ABSTRACT

In this paper a buffer-constrained rate control (RC) algorithm for

High Efficiency Video Coding (HEVC) with hierarchical group of

pictures structures is proposed. Specifically, a quantization parame-

ter (QP) cascading approach, which the QP value is increased from

one temporal layer to the next, is employed to achieve high cod-

ing efficiency while maintaining the buffer fullness at secure levels.

When compared to the current state-of-the-art RC algorithm, the ex-

perimental results show that our proposal achieves a slightly better

rate-distortion performance and a remarkably better buffer control

with an acceptable increase in computational complexity.

Index Terms—High Efficiency Video Coding (HEVC), hierar-

chical video coding, rate control, quantization parameter cascading.

1. INTRODUCTION

Hierarchical coding patterns have been adopted by the High Effi-

ciency Video Coding (HEVC) standard as they have been shown to

improve compression efficiency compared to classical coding pat-

terns [1, 2]. Particularly, in hierarchical coding the pictures inside a

group of pictures (GOP) are split up into temporal levels, with the

length of the GOP as the distance between two pictures belonging to

the lowest temporal level, which are key (K) pictures. These pictures

can be either I-coded (to allow random access points) or P-coded by

referring to pictures belonging to the same temporal level, whereas

the remaining pictures are P or B-coded from references belonging

to lower temporal levels as illustrated in Fig. 1 for two well-known

GOP structures: hierarchical IB...BP and hierarchical IP...PP. Addi-

tionally, as already stated in [3], in hierarchical IP...PP a picture can

be referred to the most recent encoded picture to also allow for a

short-distance reference and, thus, improve the motion-compensated

prediction especially in high motion video sequences.

For providing high coding efficiency in hierarchical GOP struc-

tures, several non-normative temporal level dependent quantization

parameter (QP) setting strategies have been proposed in the liter-

ature: Within the H.264/Advanced Video Coding (AVC) and Scal-

able Video Coding (SVC) frameworks, some simple QP cascading

(QPC) algorithms were proved to be reasonably robust for a wide

range of tested video sequences, but not as efficient as that proposed

in [2] describing a content-dependent approach for QP selection. In

HEVC, a simple QPC method has been adopted by the Joint Col-

laborative Team on Video Coding (JCTVC) as default QP setting in

the HEVC test model (HM) reference software [4], but in [5] those

QP values are further recomputed for the sake of rate-distortion (R-

D) performance. Naturally, the objective behind these QPC methods

is to increase the QP value from one temporal level to the next in

order to provide high-fidelity reference pictures for efficient motion-

compensated prediction and, even if they may result in large quality

fluctuations, the subjective quality is not adversely affected [1].

Nevertheless, in a video transmission application these QP set-

ting methods becomes impractical in most cases, since they do not

Fig. 1. Hierarchical IB...BP (top) and hierarchical IP...PP (bottom).

guarantee the constraints imposed by the hypothetical reference de-

coder (HRD) [6], which is virtually connected to the output of the

video encoder, for bit stream conformance1. In order to provide de-

liverable bit streams, a rate control (RC) algorithm must be embed-

ded into the encoder. The objective of the RC algorithm is the reg-

ulation of some encoder parameters (typically the QP) affecting the

bit rate so that the average bit rate of compressed video meets a spe-

cific target bit rate without exceeding the HRD constraints, while

minimizing the distortion of reconstructed video. For this purpose, a

target bit budget is allocated to a video segment and, subsequently, a

suitable QP value is derived from rate-quantization (R-Q) modeling.

The RC problem for hierarchical GOP structures has been stud-

ied extensively in H.264/AVC and SVC (the reader can be referred

to [7] and [8] for details), but only a few RC algorithms have been

proposed for the HEVC standard, of which those described in [9]

and [10] are highlighted. Specifically, the algorithm proposed by

Li et al in [10], in which a novel R-Lagrange multiplier (λ) model

for bit rate regulation is presented, has been adopted by the JCTVC

as the new reference RC algorithm in [4]. Nevertheless, although a

noticable better R-D performance is achieved in comparison with its

predecessor [9], the HRD constraints are not taken into account for

a proper transmission and decoding of compressed video.

In this paper we propose an RC algorithm for hierarchical HEVC

with HRD constraints. In particular, the proposed rate controller fo-

cuses on ensuring QPC for coding efficiency maximization, as long

as the buffer occupancy is not close to underflow or overflow.

The rest of this paper is organized as follows. In Section 2 a brief

description of the state-of-the-art RC algorithm in [10] is provided.

In Section 3 the proposed RC algorithm is described in detail. In

Section 4 the method we use for λcomputation is given. In Section

5 both experimental results are reported and discussed, to end up

with some conclusions and future work in Section 6.

1A bit stream complying with the HRD constraints entails that both the

encoder buffer, which is required to transmit at the specified target bit rate,

and the decoder buffer, which performs the opposite buffering process for a

subsequent decoding and play out, will not incur in underflow and overflow.

2. REFERENCE RATE CONTROL ALGORITHM [10]

Assuming that the bit rate is more sensitive to λthan QP, Li et al [10]

propose an R-λmodel for rate-controlled HEVC. Specifically, the

well-known Cauchy-density-based R-D function for transform coef-

ficient modeling [11] is deployed to estimate, from the bit budget

targeted to a video segment, the required λvalue for R-D optimiza-

tion [12], and then a simple λ-QP mapping function [5] is employed

for final QP computation.

Owing to its excellent coding performance under bit rate con-

straints, this algorithm actually constitutes the current state of the art

in RC for HEVC and, therefore, a benchmark for comparison pur-

poses. Nevertheless, it also deserves some critical comments con-

cerning the frame bit allocation method, QP estimation and HRD

consideration that will be discussed in detail in Section 5.

3. PROPOSED RATE CONTROL ALGORITHM

In the following subsections we describe the proposed rate con-

troller, which operates on three layers: intra period (IP) layer,

picture layer, and coding tree block (CTB) layer. However, for the

sake of conciseness, some expressions commonly used in RC will

not be included, but the reader is referred to [13] to find them.

3.1. Intra Period Layer

IP is defined in hierarchical video coding as the distance between

two consecutive I pictures and it can be composed of either one or

several GOPs. If we assume that the jpicture within an IP is to

be encoded, in this layer the amount of target bits for the remaining

pictures in the IP, Brj, is computed.

3.2. Picture Layer

In this layer a QP value, QPj, for the current picture is estimated.

For this purpose, the following four stages are conducted: bit alloca-

tion,QP estimation,QP-cascading-based clipping,buffer underflow

and overflow prevention, and parameter updating. These stages are

described in the sequel.

3.2.1. Bit Allocation

The target frame bit budget is computed in this stage as:

Tj=b

Tj,if I picture

(1 −β)e

Tj+βb

Tj,otherwise, (1)

The term b

Tjstands for a hierarchy-based bit allocation that aims

to properly distribute Brjamong the rest of pictures in the IP, i.e.,

Tj=e

XI/l,j

XI,jNrI,j +PNL−1

u=0 e

Xu,jNru,j Brj−f

Hrj+ehI/l,j ,(2)

where e

XI/u,j denotes a prediction of the coding complexity, in

terms of product of texture bits (i.e., the bits used to encode the

transform coefficients) and quantization step, for the current intra

picture/inter picture at temporal level u. This complexity measure-

ment is updated by means of exponential average with a forgetting

factor set to 0.5in our experiments. NrI/u,j is the number of re-

maining intra pictures/inter pictures at level uin the IP. NLdenotes

the number of temporal levels. ehI/l,j is a prediction of the header

bits for the current intra picture/inter picture at level l, which is also

updated by means of exponential average with a forgetting factor

fixed to 0.5in our experiments. And f

Hrjrepresents a prediction of

the header bits for the remaining pictures in the IP.

The term e

Tjwatches over the buffer status by measuring the

difference between the current fullness, Vj, and a prediction of the

fullness after encoding the picture, e

Vj+1, i.e.,

Ti(j) = RT

f+δe

Vj+1 −Vj,(3)

being RTthe target bit rate, fthe frame rate, and δa convergence

factor that is set to 0.5in our experiments to provide a good trade-

off between QP fluctuation and target buffer level adaptation. Since

this term for frame bit budget calculation is very useful for those

applications requiring a tight buffer control, the factor that weights

both bit allocation methods, β, is set to 0.75 for low delay (LD)

coding and 1for random access (RA) coding in our experiments.

Finally, in order to satisfy the HRD constraints, Tjis upper and

lower bounded.

3.2.2. QP Estimation

The QP value is estimated by means of the Cauchy-density-based

R-Q function stated in [11], i.e.,

R=aQ−α,(4)

where Ris the bit rate in terms of target texture bits, Tj−ehI/l,j,Qis

the quantization step value associated with QPj, and {a, α}are the

model parameters whose values depend on the hierarchy level (due

to the R-D differences between temporal levels) and, besides, on the

picture type for the lowest temporal level (see Subsection 3.2.5).

3.2.3. QP-Cascading-Based Clipping

Generally, when using analytical R-Q modeling for rate-controlled

video coding, the estimated QP value is restricted in a small range

in order to ensure quality consistency. Particularly, in this paper we

propose a novel QPC-based clipping method that also attempts to

maximize the coding efficiency.

For non-K pictures (l > 0), the QP value derived from Eq. (4)

is bounded as follows:

QPj= min [QPREF,l>0+ 2,max [QPREF,l>0−2, QPj]] ,(5)

being QPREF,l>0a reference QP at level lthat is computed by

means of the following expresion that is based on the default QP

setting in [4]:

QPREF,l>0=QPK+l+ (K pic =I−type?1 : 0),(6)

where QPKis the QP value used to encode the last K picture. It is

worth noticing that Eq. (6) might be replaced by another QPC-based

approach to be proved more efficent in terms of R-D performance.

Afterwards, QPjis bounded with respect to QPLST,l06=l, the QP

value used to encode the last picture belonging to a temporal level l0

different to the current one l, specifically:

QPj=max [QPLST,l06=l, QPj],if l0<l

min [QPLST,l06=l, QPj],if l0>l.(7)

For K pictures, the estimated QP value is limited as follows:

QPj= min QPLST,l06=l+ ∆ + 2,· · · (8)

max QPLST,l06=l+ ∆ −2, QPj,(9)

where ∆is a target QP range for the GOP that is computed as the dif-

ference between the actual QPj(from Eq. (7)) and QPREF,l=L−1

(from Eq. (6)) if QPKwas set to QPj.

3.2.4. Buffer Underflow and Overflow Prevention

In order to reduce the underflow and overflow risk in the encoder

buffer, QPjcan be modified as follows:

QPj=QPj−1,if Vj≤2×RT

QPj+ 4,if Vj≥0.8×BS,(10)

where BS denotes the buffer size. Finally, QPjis bounded by the

maximum and minimum values allowed in HEVC.

3.2.5. Parameter Updating

Once the current picture at level lhas been encoded, the model pa-

rameters for that level, aland αl(the subindex lis included to spec-

ify the hierarchy level dependence), are updated. On the one hand,

the updating expression for alobeys:

al,j+J=tjQαl

j,if I picture

(1 −θ)al,j +θtjQαl

j,otherwise, (11)

where Jis, depending on which case, the distance between two con-

secutive I pictures or between two consecutive pictures belonging to

the same temporal level, tjis the amount of consumed texture bits,

and θis a forgetting factor that is set to 0.5in our experiments.

On the other hand, αlis recalculated, for RA coding, every IP

and, for LD coding, every 8GOPs by means of the following linear

model:

αl=1.1,if I picture

c1−c2

NP XL ,otherwise, (12)

where c1and c2are the model parameters, which have been obtained

empirically (see Table 1), and NP XL is the number of luminance (Y)

and crominance (U and V) pixels in the picture.

3.3. Coding Tree Block Layer

A finer adjustment to the frame target bits can be achieved if the

QP value is regulated on a CTB basis. For the first CTB in the jth

picture, the QP value is that obtained at picture layer. Otherwise, the

amount of target texture bits for the kth CTB, Tj,k, is computed first:

Tj,k =al,k

PNB

v=kal,v Brj,k −f

Hrj,k,(13)

where al,k is the R-Q model parameter corresponding to the current

CTB, which can also be seen as a coding complexity measurement,

NBis the number of CTBs in the picture, and, finally, Brj,k and

Hrj,k stand for the amount of target total bits and a prediction of

the header bits for the remaining CTBs in the picture, respectively.

Then, the corresponding QP value, QPj,k, is estimated by

means of Eq. (4), where specific parameter values, al,k and αl,k, are

used for each CTB. Thus, a particular temporal level has model pa-

rameters operating at picture layer and, besides, a set of NBmodel

parameters operating at CTB layer.

Next, for the sake of quality consistency within the picture,

QPj,k is bounded ±1unit with respect to QPj,k−1and ±4units

with respect to QPj.

Finally, after encoding the kth CTB, al,k is updated as in Eq.

(11) from co-located CTBs at the same temporal level, and αl,k as

in Eq. (12). If the encoded CTB is the last one, the average QP for

whole picture is also calculated for the RC process at picture layer.

It is also worth noticing that for K pictures CTB layer is dis-

abled (i.e., Qjis used to encode all CTBs) in order to keep the dis-

tortion as low as possible and, hence, provide more efficient motion-

compensated predictions for non-K pictures.

Table 1. Parameter values for the linear model in Eq. (12).

LD RA

Layer c1c2c1c2

01.54 0.22 1.39 0.10

12.32 0.23 2.10 0.43

22.46 0.57 2.37 0.69

3- - 3.05 0.34

4. λCOMPUTATION

The Lagrange formulation [12] plays a paramount role in the R-D

optimization process aimed at finding the best prediction mode and

motion vector for a coding unit. The relative importance between D

and Ris weighted by λthat is obtained in the HM reference software

[4] by the following widely-accepted empirical function:

λ=(Φ×2QP −12

3,if K picture

max2,min4,QP −12

6×Φ×2QP −12

3,otherwise, (14)

where Φis a QP factor that depends on the temporal level and picture

type. In particular, Eq. (14) is designed to attach more importance

to Das the temporal level decreases (to improve the quality in those

pictures used as references). Furthermore, given that λis derived

from QP , it should be recalculated whenever the QP value is mod-

ified in some way. So, unlike the RC scheme in [10], Eq. (14) is

the method we employ for λcomputation at both picture and CTB

layers, which is the result of many observations and experiences.

5. EXPERIMENTS AND RESULTS

5.1. Experimental Setup

The proposed RC algorithm was implemented on the HM reference

software version HM-9.0-dev [4] that already includes our bench-

mark for performance evaluation: the RC algorithm described in

[10]. In order to guarantee fair comparisons, CTB layer was enabled

in both schemes, hierarchical bit allocation was enabled in [10] and,

since in [10] there is no buffering mechanism itself, the buffer size

for the proposed rate controller was set to 1s, which is large enough

to properly bear the variable output bit rate of the video encoder.

Following the recommendations specified in [14], the set of test

video sequences, encoder configurations and target bit rates were

selected. In particular, the set of target bit rates was obtained from

previous codings using the default hierarchical QP setting in [4] with

the following four base QP values: 22,27,32 and 37.

5.2. Results and Discussion

The average Bjøntegard difference (BD)-rate measurement, which

compares two R-D curves by means of a single number, was used to

assess both RC schemes from the R-D performance point of view.

Table 2 reports the BD-rate results for two specific encoder configu-

rations: RA Main and LD Main. As can be observed, the proposed

RC algorithm generally achieved a sligthly better R-D performance

(a negative percentage means that the tested algorithm outperforms

the reference one) for each sequence class. One reason for these R-

D differences might be related to the frame bit allocation algorithm:

while a set of prefixed weighting factors is employed in [10] for bit

budget distribution among temporal levels, changes in video com-

plexity can be followed in the proposed bit allocation approach by

means of a continuous updating of the coding complexities e

XI/l,j .

Table 2. BD-rate performance of the proposed RC algorithm com-

pared to the reference RC algorithm in [10].

Sequence RA Main LD Main

Class Y U V Y U V

A-1.3% -2.0% -1.2% - - -

B-0.7% -3.9% -0.7% -5.7% -2.6% -1.2%

C-3.3% -8.6% -7.4% -2.4% 1.8% 1.9%

D-4.3% -6.2% -4.7% -4.5% -5.2% -5.4%

E- - - -8.4% -4.6% -4.4%

Overall -2.3% -5.1% -3.3% -5.1% -2.5% -2.1%

Enc. Time 100% 102%

Table 3. Bit rate error (average/maximum) of the reference RC al-

gorithm in [10] and the proposed RC algorithm, and number of un-

derflows, #U, (average/maximum) of the proposed RC algorithm.

Encoder Bit Rate Error [%] #U [%]

Configuration Reference Proposed Proposed

RA Main 0.28/3.17 0.20/2.33 1.45/11.00

RA HE10 0.29/3.05 0.18/0.78 1.44/9.67

LD Main 0.12/1.22 0.11/1.17 0.25/4.80

LD HE10 0.13/1.28 0.13/1.42 0.22/4.20

LD P Main 0.12/1.26 0.12/1.96 0.27/4.40

LD P HE10 0.13/1.39 0.11/1.25 0.23/5.20

Additionally, in order to discuss the results concerning the

quality consistency, representative behaviors of the Y PSNR and

QP time evolutions are shown in Figs. 2 and 3 for the test video

sequences ParkScene 1920x1080 24 (RA Main) and KristenAnd-

Sara 1280x720 60 (LD Main), respectively. In comparison with the

reference RC algorithm, our proposal was able to produce smoother

QP time evolution, thus resulting in a better quality consistency,

since stricter clipping conditions for QP assigment are imposed at

both picture and CTB layers.

Regarding the encoder buffer behavior, on the one hand, the

experimental results proved that in our proposal buffer overflow

never happened and buffer underflow remained bellow an accept-

able threshold (see Table 3 for details) taking into account that the

target buffer level after encoding each IP was set to 0% of the buffer

size. On the other hand, as shown in the buffer occupancy time

evolution in Figs. 2 and 3 for the two sequences under study, the ref-

erence RC scheme is not prepared for applications that may require

restricted buffer sizes, since the HRD constraints are not considered

(and so, no numerical results are provided for lack of significance).

In terms of target bit rate adjustment, Table 3 shows that the pro-

posed rate controller was able to reduce the average and maximum

bit rate errors in most of the tested encoder configurations. Further-

more, since the reference RC algorithm pursues a long-term bit rate

adaptation, the potential bit resource over-use or under-use may in-

cur in QP increases or decreases especially at the end of the coding

process in order to meet the target bit rate (see the QP time evolution

in Figs. 2 and 3 from the pictures #220 and #550, respectively).

Finally, from the complexity perspective, the average coding

time consumed by the video encoder with the proposed rate con-

troller compared to that yielded with the reference RC approach is

also reported in Table 2. The results indicate that our approach is

up to 2% heavier computationally, but acceptable given the coding

performance benefits achieved under HRD constraints. Neverthe-

less, it should be pointed out that these complexity results are just

0 50 100 150 200

Picture Number

Y PSNR [dB]

ParkScene_1920x1080_24 (RA Main) / Target Bit Rate: 1449.28 kbps

Reference Proposed

0 50 100 150 200

100

Picture Number

Buffer Occupancy [%]

0 50 100 150 200

Fig. 2. Y PSNR, QP and buffer occupancy time evolutions for

ParkScene 1920x1080 24 (RA Main). Target bit rate: 1449.28 kbps.

0 100 200 300 400 500

Y PSNR [dB]

KristenAndSara_1280x720_60 (LD Main) / Target Bit Rate: 699.14 kbps

Reference Proposed

0 100 200 300 400 500

−40

−20

Picture Number

Buffer Occupancy [%]

0 100 200 300 400 500

Fig. 3. Y PSNR, QP and buffer occupancy time evolutions for Kris-

tenAndSara 1280x720 60 (LD Main). Target bit rate: 699.14 kbps.

for guidance, since the HM reference software is not computation-

ally optimized, thus affecting the comparisons, and the simulations

were performed on a system with shared resources.

6. CONCLUSIONS AND FUTURE WORK

In this paper a buffer-constrained RC algorithm for real-time HEVC

with hierarchical GOP structures has been proposed. On the one

hand, the HRD constraints are considered in order to properly trans-

mit and decode the compressed video. On the other hand, a novel

QPC-based approach for QP assignment is employed in order to also

provide high coding efficiency. When compared to the RC algorithm

described in [10], our proposal achieves a slightly better R-D perfor-

mance and a remarkably better buffer control at the expense of an

acceptable increase in computational complexity.

In future work we plan to improve the performance of the RC al-

gorithm by using other QP scaling strategies, such as those described

in [3] and [5], for the proposed QPC-based clipping method.

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