Improved Pixel-Based Rate Allocation For Pixel-Domain Distributed Video Coders Without Feedback Channel Marleen Morb´ee1 , Josep Prades-Nebot2 , Antoni Roca2 , Aleksandra Piˇzurica1 and Wilfried Philips1 ? 1
TELIN-IPI-IBBT Ghent University Ghent, Belgium
[email protected]
2 GTS-ITEAM Universidad Polit´ecnica de Valencia Valencia, Spain
[email protected]
Abstract. In some video coding applications, it is desirable to reduce the complexity of the video encoder at the expense of a more complex decoder. Distributed Video (DV) Coding is a new paradigm that aims at achieving this. To allocate a proper number of bits to each frame, most DV coding algorithms use a feedback channel (FBC). However, in some cases, a FBC does not exist. In this paper, we therefore propose a rate allocation (RA) algorithm for pixel-domain distributed video (PDDV) coders without FBC. Our algorithm estimates at the encoder the number of bits for every frame without significantly increasing the encoder complexity. For this calculation we consider each pixel of the frame individually, in contrast to our earlier work where the whole frame is treated jointly. Experimental results show that this pixel-based approach delivers better estimates of the adequate encoding rate than the frame-based approach. Compared to the PDDV coder with FBC, the PDDV coder without FBC has only a small loss in RD performance, especially at low rates.
1
Introduction
Some video applications, e.g., wireless low-power surveillance, disposable cameras, multimedia sensor networks, and mobile camera phones require lowcomplexity coders. Distributed video (DV) coding is a new paradigm that fulfills this requirement by performing intra-frame encoding and inter-frame decoding [1]. Since DV decoders and not encoders perform motion estimation and motion compensated interpolation, most of the computational load is moved from the encoder to the decoder. One of the most difficult tasks in DV coding is allocating a proper number of bits to encode each video frame. This is mainly because the encoder does not have ?
This work has been partially supported by the Spanish Ministry of Education and Science and the European Commission (FEDER) under grant TEC2005-07751-C0201. A. Piˇzurica is a postdoctoral research fellow of FWO, Flanders.
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M. Morb´ee, J. Prades-Nebot, A. Roca, A. Piˇzurica and W. Philips
access to the motion estimation information of the decoder and because small variations in the allocated number of bits can cause large changes in distortion. Most DV coders solve this problem by using a feedback channel (FBC), which allows the decoder to request additional bits from the encoder when needed. Although this way an optimal rate is allocated, it is not a valid solution in unidirectional and offline applications, and increases the decoder complexity and latency [2]. In this paper, we propose a rate allocation (RA) algorithm for pixel-domain distributed video (PDDV) coders that do not use a FBC. Our algorithm computes the number of bits to encode each video frame without significantly increasing the encoder complexity. The proposed method is related to our previous work [3] on PDDV coders without FBC. However, in this paper, the algorithm is improved by estimating the error probabilities for each pixel separately instead of for the whole frame jointly. We also adapted the algorithm for the case of lossy (instead of lossless) coding of the key frames. The experimental results show that the RA algorithm delivers good estimates of the rate and the frame qualities provided by our algorithm are quite close to the ones provided by a FBC-based algorithm. Furthermore, we observe that the rate estimates and frame quality are significantly improved compared to our previous work [3]. The paper is organized as follows. In Section 2, we study the basics of PDDV coding. In Section 3, we study the RA problem and the advantages and inconveniences of using a FBC. Then, in Section 4, we describe the RA algorithm. Subsequently, in Section 5, we compare the performance of a DV coder using a FBC and the performance of the same DV coder using our RA algorithm. Finally, the conclusions are presented in Section 6.
2
Pixel-Domain DV coding
In DV coders, the frames are organized into key frames (K-frames) and WynerZiv frames (WZ-frames). The K-frames are coded using a conventional intraframe coder. The WZ-frames are coded using the Wyner-Ziv paradigm, i.e., they are intra-frame encoded, but they are conditionally decoded using side information (Figure 1). In most DV coders, the odd frames are encoded as K-frames, and the even frames are encoded as WZ-frames [3–5]. Coding and decoding is done unsequentially in such a way that, before decoding the WZ-frame X, the preceding and succeeding K-frames (XB and XF ) have already been transmitted and decoded. Thus, the receiver can obtain a good approximation S of X by ˆ B and X ˆ F ). S is used as part of interpolating its two closest decoded frames (X the side information to conditionally decode X, as will be explained below. The DV coders can be divided into two classes: the scalable coders [2, 3, 5], and the non-scalable coders [4]. The scalable coders have the advantages that the rate can be flexibly adapted and that the rate control is easier than in the non-scalable case. In this paper, we focus on the practical scalable PDDV coder depicted in Figure 1 [2, 3, 5]. In this scheme, we first extract the M Bit Planes (BPs) Xk (1 ≤ k ≤ M ) from the WZ-frame X. M is determined by the number
Improved Pixel-Based Rate Allocation for PDDV Coders without FBC
Receiver
Transmitter Slepian-Wolf codec Turbo Encoder
Parity Buffer bits
FBC
Rate Allocation
XB XF
ˆB, X ˆF X Intra-frame Encoder
Xk Turbo Decoder
...
...
WZ-frames Xk BP X extraction &selection
3
ˆ X Rec.
... Sk
BP extraction
S
Frame Interpolation
Intra-frame Decoder
Intra-frame Decoder
ˆB X ˆF X
K-frames Fig. 1. General block diagram of a scalable PDDV coder.
of bits by which the pixel values of X are represented. Subsequently, the m most significant BPs Xk (1 ≤ k ≤ m, 1 ≤ m ≤ M ) are encoded independently of each other by a Slepian-Wolf (SW) coder [6]. The transmission and decoding of BPs is done in order of significance (the most significant BPs are transmitted and decoded first). The SW coding is implemented with efficient channel codes that yield parity bits of Xk , which are transmitted over the channel. At the receiver side, the SW decoder obtains the original BP Xk from the transmitted parity bits, the corresponding BP Sk extracted from the interpolated frame S, and the previously decoded BPs {X1 , . . . , Xk−1 }. Note that Sk can be considered the result of transmitting Xk through a noisy virtual channel. The SW decoder is a channel decoder that recovers Xk from its noisy version Sk . Finally, the decoder obtains the reconstruction x ˆ of each pixel x ∈ X by using the decoded bits xk ∈ Xk (k = 1, . . . , m) and the corresponding pixel s of the interpolated frame S through xL , s < xL x ˆ = s, (1) xL ≤ s ≤ xR xR , s > xR with xL =
m X i=1
xi 28−i and xR = xL + 28−m − 1.
(2)
4
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M. Morb´ee, J. Prades-Nebot, A. Roca, A. Piˇzurica and W. Philips
The rate allocation problem
In PDDV coders, the optimum rate R∗ is the minimum rate necessary to losslessly1 decode the BPs Xk (k = 1, . . . , m). The use of a rate higher than R∗ does not lead to a reduction in distortion, but only to an unnecessary bit expense. On the other hand, encoding with a rate lower than R∗ can cause the introduction of a large number of errors in the decoding of Xk , which can greatly increase the distortion. This is because of the threshold effect of the channel codes used in DV coders. A common RA solution adopted in DV coders is the use of a FBC and a rate-compatible punctured turbo code (RCPTC) [7]. In this configuration, the turbo encoder generates all the parity bits for the BPs to be encoded, saves these bits in a buffer (see Figure 1), and divides them into parity bit sets. The size of a parity bit set is N/Tpunc , where Tpunc is the puncturing period of the RCPTC and N is the number of pixels in each frame. To determine the adequate number of parity bit sets to send for a certain BP Xk , the encoder first transmits one parity bit set from the buffer. Then, if the decoder detects that the residual error probability Qk (for the calculation see Section 4.4) is above a threshold t, it requests an additional parity bit set from the buffer through the FBC. This transmission-request process is repeated until Qk < t. If we denote by Kk the number of transmitted parity bit sets, then the encoding rate Rk for BP Xk is Rk = r K k
N , Tpunc
(3)
with r being the frame rate of the video. However, although the FBC allows the system to allocate an optimal rate, this FBC cannot be implemented in offline applications or in those applications where communication from the decoder to the encoder is not possible. In those applications, an appropriate RA algorithm at the encoder can take over its role. In the following section, we will describe this RA algorithm to suppress the FBC in more detail.
4
The rate allocation algorithm
The main idea of the proposed method is to estimate at the encoder side, for each BP of the WZ-frames, the optimal (i.e. the minimal required) number of parity bits for a given residual error probability. An important aspect of the proposed approach is also avoiding underestimation of the optimal number of parity bits. Indeed, if the rate is underestimated, the decoding of the BPs of the frames will not be error-free and this will lead to a large increase in distortion. Let us denote by U the difference between the original frame and the side information frame: U = X − S. As in [3–5], we assume that a pixel value u ∈ U 1
In practical PDDV coding, SW decoders are allowed to introduce a certain small amount of errors
Improved Pixel-Based Rate Allocation for PDDV Coders without FBC
5
follows a Laplacian distribution with a probability density function (pdf) p(u) = where α =
√
ˆB, X ˆF X, X
α (−α|u|) e 2
(4)
2/σ and σ is the standard deviation of the difference frame U .
Estimation of σ 2
σ ˆ2
Estimation of {Pk }
{Pk } Estimation of {Rk }
{Rk }
Fig. 2. Rate allocation module at the encoder.
As every BP of a WZ-frame X is separately encoded, a different encoding rate Rk must be allocated to each BP Xk . As the virtual channel is assumed to be a binary symmetric channel, to obtain Rk , we need to know the bit error probability Pk of each BP Xk . To calculate this probability, we first make an estimate σ ˆ 2 of the parameter σ 2 (Section 4.1). Then, for each BP Xk , we use σ ˆ to estimate Pk (Section 4.2). Once Pk is estimated, we can determine the encoding rate Rk for BP Xk by taking into account the error correcting capacity of the turbo code (Section 4.3). In Figure 2, a block diagram of the RA module is depicted. Although we aim at an overestimation of the rate, this is not always achieved. Therefore, once the parity bits have been decoded, the residual error probability ˆ k ) (Section 4.4). If Q ˆ k is above a threshold t, Qk is estimated at the decoder (Q the parity bits of the considered BP are discarded and the frame is reconstructed with the available previously decoded BPs. This way, we prevent an increase in the distortion caused by an excessive number of errors in a decoded BP. In the following, we explain each step of our RA algorithm in more detail. 4.1
Estimation of σ 2
We estimate σ 2 at the encoder so the estimate should be very simple in order to avoid significantly increasing the encoder complexity. We adopt the approach of [3], but we take the coding of the K-frames into account. σ ˆ 2 is then the mean squared error (MSE) between the current WZ-frame and the average of the two closest decoded K-frames: σ ˆ2 =
1 N
X (v,w)∈X
X(v, w) −
ˆ B (v, w) + X ˆ F (v, w) 2 X 2
(5)
with N denoting the number of pixels in each frame. The decoded frames are obtained by the intra-frame decoding unit at the encoder site (see Figure 1). In general, the resulting σ ˆ 2 is an overestimate of the real σ 2 since it is expected that the motion compensated interpolation performed at the decoder to
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M. Morb´ee, J. Prades-Nebot, A. Roca, A. Piˇzurica and W. Philips
obtain the side information will be more accurate than the simple averaging of the two closest decoded K-frames. This is exactly what is required for our purpose, since we prefer an overestimation of the encoding rate to an underestimation, as explained above. 4.2
Estimation of the error probabilities {Pk }
Let us assume that the most significant k − 1 bits of the pixel value x ∈ X have already been decoded without errors. Hence, both the encoder and the decoder know from {x1 , . . . , xk−1 } that x is in the interval [xL , xR ] where xL and xR are as in (2) with m = k − 1. At the encoder, the bit value xk shrinks this interval in such way that x ∈ [xL , xC ] if xk = 0, and x ∈ [xC + 1, xR ] if xk = 1 with xL + xR . (6) xC = 2 An error in xk occurs if x ∈ [xL , xC ] and s ∈ [xC + 1, xR ] or if x ∈ [xC + 1, xR ] and s ∈ [xL , xC ]. By assuming a Laplacian pdf for the difference between the original frame and the side information, the conditional pdf of s given x and xL ≤ s ≤ xR is α −α|x−s| 2e if xL ≤ s ≤ xR P(x L ≤ s ≤ xR |x) p(s|x, xL ≤ s ≤ xR ) = . (7) 0 otherwise From (7), the error probability of bit value xk of pixel value x is estimated through Z xR p(s|x, xL ≤ s ≤ xR ) ds if xk = 0 xc +0.5 Pe (xk ) = Z (8) xc +0.5 p(s|x, xL ≤ s ≤ xR ) ds if xk = 1 xL
Note that the integration intervals are extended by 0.5 in order to cover the whole interval [xL , xR ]. For the first BP X1 , no previous BPs have been transmitted and decoded and, consequently, xL = 0, xR = 255, and xC = 127 for all the pixels. Finally, we estimate the average error probability Pk for the entire BP Xk . Therefore, we take into account the histogram of the frame H(x), which provides the relative frequency of occurrence for each pixel value x. Pk is then estimated through 255 X Pk = H(x)Pe (xk ). (9) x=0
Improved Pixel-Based Rate Allocation for PDDV Coders without FBC
4.3
7
Estimation of the encoding rates {Rk }
Once Pk is estimated, we choose the corresponding encoding rate Rk that enables us to decode the estimated number of errors with a residual error probability Qk below a threshold t (Qk < t). The calculation of Qk is explained in Section 4.4. To estimate Rk , we need to express the residual error probability Qk as a function of input error probability Pk and the number of parity bit sets Kk [3]. We estimate these functions experimentally by averaging simulation results over a large set of video sequences with a wide variety of properties. Using these experimental functions and knowing Pk and the threshold t, we estimate the adequate number of parity bit sets Kk . Finally, we obtain Rk from Kk through (3), with r the frame rate, Tpunc the puncturing period and N the number of pixels in each frame. 4.4
Estimation of the residual error probabilities {Qk }
If the rate allocated to encode a BP is too low, the decoded BP can contain such a large number of errors that the quality of the reconstructed frame is worse than the quality of the side information. To prevent this situation, we need to know the residual error probability Qk of each BP at the decoder. We estimate Qk as [8] N X 1 ˆk = 1 (10) Q N n=1 1 + e|Ln | where N is the number of pixels in each frame and Ln the log-likelihood ratio ˆ k is above a certain threshold of the nth bit in the considered BP Xk [8]. If Q ˆ (Qk > t), the decoded BPs are discarded and the frame is reconstructed with the available previously error-free decoded BPs.
5
Experimental Results
In this section, we experimentally study the accuracy of our RA algorithm when it is used in a PDDV coder without FBC (RA-PDDV coder) and compare it with the rate allocations provided by the same coder using a FBC (FBC-PDDV coder). We will also discuss the improvement compared to our previous work [3]. The PDDV coder used in the experiments first decomposes each WZ-frame into its 8 BPs. Then, the m most significant BPs are separately encoded by using a RCPTC; the other BPs are discarded. In our experiments, m is chosen to be 3. The turbo coder is composed of two identical constituent convolutional encoders of rate 1/2 with generator polynomials (1, 33/31) in octal form. The puncturing period was set to 32 which allowed our RA algorithm to allocate parity bit multiples of N/32 bits to each BP, where N is the number of pixels in each frame. The K-frames were either losslessly transmitted or intra-coded using H.263 with quantization parameter QP . The interpolated frame was generated at the decoder with the interpolation tools described in [5].
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M. Morb´ee, J. Prades-Nebot, A. Roca, A. Piˇzurica and W. Philips
Video sequence Akiyo Carphone Foreman Salesman Mobile
Method
≤-24 kb/s
% of frames with ∆R -12 0 +12 kb/s kb/s kb/s
current previous current previous current previous current previous current
0 12.1 0 7.4 1.0 7.5 0 8.0 0
0 14.7 5.4 10.1 2.5 17.6 0 10.1 2.0
100 59.7 42.6 23.5 25.8 23.1 93.9 45.0 38.5
≥+24 kb/s
0 10.1 40.5 34.9 30.8 13.6 6.1 26.8 58.1
0 3.4 11.5 24.2 39.9 38.2 0 10.1 1.4
Table 1. Percentage of frames that differ by ∆R from the rate of the FBC (for the first BP). The K-frames are losslessly transmitted. The previous method is the method described in [3].
Video sequence Akiyo Carphone Foreman Salesman Mobile
≤-24 kb/s 0 0 2.5 0 0
% of frames with ∆R -12 0 +12 kb/s kb/s kb/s 0 8.1 4.0 0 0
47.3 39.9 41.4 66.2 60.8
52.7 43.9 21.7 33.8 36.5
≥+24 kb/s 0 8.1 30.3 0 2.7
Table 2. Percentage of frames that differ by ∆R from the rate of the FBC (for the first BP). The K-frames are intra-coded with H.263 (QP = 10).
We encoded several test QCIF sequences (176×144 pixels/frame, 30 frames/s) with two RA strategies: our RA algorithm and the allocations provided by the ˆ k (our RA approach) FBC-PDDV coder. The threshold t for Qk (FBC) and for Q is set to N1 , where N is the number of pixels in each frame. Tables 1 and 2 show the difference between the RA (in kb/s) provided by our algorithm and the RA using the FBC when encoding the first BP of each frame. More specifically, the percentage of frames with a difference in rate of ∆R kb/s is shown. In Table 1 the K-frames are losslessly coded while in Table 2 the Kframes are intra-coded with H.263 and QP = 10. Note that for the lossless case the ideal rate is allocated in between 25% and 100% of the frames (depending on the sequence), whereas in our previous work [3], the ideal rate was allocated in between 23% and 60% of the frames. For Akiyo, Carphone, Foreman and Salesman, we observe an increase in the percentage of respectively 40.3%, 19.1%,
Improved Pixel-Based Rate Allocation for PDDV Coders without FBC
Video sequence Akiyo Carphone Foreman Salesman Mobile
Method
≤-24 kb/s
current previous current previous current previous current previous current
0 0.7 0 0 0 0 0 0 0
% of frames with ∆R -12 0 +12 kb/s kb/s kb/s 0.7 8.0 0.7 2.0 0 1.5 0.7 10.1 1.4
87.2 31.5 14.9 7.4 19.2 12.6 43.9 31.5 27.0
9
≥+24 kb/s
10.1 28.9 37.8 16.1 24.8 10.5 44.6 18.1 37.8
2.0 30.9 46.6 74.5 56.1 75.4 10.8 40.3 33.8
Table 3. Percentage of frames that differ by ∆R from the rate of the FBC (for the second BP). The K-frames are losslessly transmitted. The previous method is the method described in [3].
Video sequence Akiyo Carphone Foreman Salesman Mobile
≤-24 kb/s 0 0 0 0 0
% of frames with ∆R -12 0 +12 kb/s kb/s kb/s 0.7 0 1.5 25.7 0.7
0 20.3 26.3 74.3 31.8
93.9 49.3 21.2 0 37.8
≥+24 kb/s 5.4 30.4 51.0 0 29.7
Table 4. Percentage of frames that differ by ∆R from the rate of the FBC (for the second BP). The K-frames are intra-coded with H.263 (QP = 10).
Video sequence Akiyo Carphone Foreman Salesman Mobile
≤-24 kb/s 0.7 0 0 0.7 0
% of frames with ∆R -12 0 +12 kb/s kb/s kb/s 74.3 4.1 0.5 25.0 0.7
17.6 31.1 17.7 39.9 16.2
5.4 14.9 8.6 24.3 27.7
≥+24 kb/s 2.0 50.0 73.2 10.1 55.4
Table 5. Percentage of frames that differ by ∆R from the rate of the FBC (for the third BP). The K-frames are losslessly transmitted.
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M. Morb´ee, J. Prades-Nebot, A. Roca, A. Piˇzurica and W. Philips
Video sequence Akiyo Carphone Foreman Salesman Mobile
≤-24 kb/s 0 0 0 0 0
% of frames with ∆R -12 0 +12 kb/s kb/s kb/s 0 2.0 0 0 0
100 21.0 4.0 0 2.7
0 27.7 19.7 37.2 18.9
≥+24 kb/s 0 49.3 76.3 62.8 78.4
Table 6. Percentage of frames that differ by ∆R from the rate of the FBC (for the third BP). The K-frames are intra-coded with H.263 (QP = 10).
2.7% and 48.9%. Moreover, we notice that with the current approach for only very few frames the rate is underestimated, which is desirable for our purpose (as explained in Section 4). The results for the case of lossy coding of the K-frames are a little worse but similar. Also here, non-optimal rate allocations are nearly always overestimations. Tables 3, 4, 5 and 6 also show the difference between the RA (in kb/s) provided by our algorithm and the RA using the FBC but now for the second and third BP of each frame. In Tables 3 and 5 the K-frames are losslessly coded while in Tables 4 and 6 the K-frames are intra-coded with H.263 and QP = 10. Similar improvements of the pixel-based approach compared to the frame-based approach [3] as for the first BP can be noticed. We observe that the inaccuracy of the RA increases when the BPs are less significant, like in [3]. In Figures 3 and 4, we show the RD curves of Carphone, Foreman, Salesman, and Mobile for the RA-PDDV coder, and we compare them with the corresponding RD curves when, for the given puncturing period, an optimal rate is allocated (FBC-PDDV coder). In Figure 3 the K-frames are losslessly coded while in Figure 4 the K-frames are intra-coded with H.263 and QP = 10. The value of the PSNR at rate 0 shows the average quality of the interpolated frame S. For both lossless and lossy coding of the K-frames, we observe that the loss in RD performance of the RA-PDDV coder when compared to the FBC-PDDV coder is very small for low rates. The difference in RD performance increases with higher rates to an extent that varies from sequence to sequence. The acceptability of this performance loss is application-dependent.
6
Conclusion
In this paper, we presented an RA algorithm for rate-compatible, turbo codebased PDDV coders. Without complicating the encoder, the algorithm estimates the appropriate number of bits for each frame. In this calculation the error probabilities are estimated for each pixel individually and not for the whole frame jointly, as was the case in our previous work. The proposed pixel-based RA
Improved Pixel-Based Rate Allocation for PDDV Coders without FBC 36.5
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Fig. 3. RD performance of our RA algorithm for the sequences (a) Carphone, (b) Foreman, (c) Salesman and (d) Mobile. Compared is the RD performance for the case of optimal rate allocation. The K-frames are losslessly transmitted.
algorithm delivers more accurate estimates of the encoding rate than the framebased approach. This pixel-based RA algorithm allows to remove the FBC from the traditional scheme, with only a small loss in RD performance, especially for low rates.
References 1. Puri, R., Ramchandran, K.: PRISM: A new robust video coding architecture based on distributed compression principles. In: Proc. Allerton Conference on Communication, Control, and Computing, Allerton, IL, USA (October 2002) 2. Brites, C., Ascenso, J., Pereira, F.: Feedback channel in pixel domain Wyner-Ziv video coding: myths and realities. In: 14th EUSIPCO’06, Florence, Italy (September 2006) 3. Morb´ee, M., Prades-Nebot, J., Piˇzurica, A., Philips, W.: Rate allocation algorithm for pixel-domain distributed video coding without feedback channel. In: ICASSP, Hawaii, USA (April 2007)
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Fig. 4. RD performance of our RA algorithm for the sequences (a) Carphone, (b) Foreman, (c) Salesman and (d) Mobile. Compared is the RD performance for the case of optimal rate allocation. The K-frames are intra-coded with H.263 (QP = 10).
4. Aaron, A., Zhang, R., Girod, B.: Wyner-Ziv coding of motion video. In: Proc. Asilomar Conference on Signals and Systems, Pacific Grove, California, USA (November 2002) 5. Ascenso, J., Brites, C., Pereira, F.: Improving frame interpolation with spatial motion smoothing for pixel domain distributed video coding. In: 5th EURASIP Conference, Slovack, Republic (June 2005) 6. Slepian, J., Wolf, J.: Noiseless coding of correlated information sources. IEEE Trans. Inf. Theory 19(4) (July 1973) 7. Rowitch, D., Milstein, L.: On the performance of hybrid FEC/ARQ systems using rate compatible punctured turbo codes. IEEE Trans. Comm. 48(6) (June 2000) 948–959 8. Hoeher, P., Land, I., Sorger, U.: Log-likelihood values and monte carlo simulation– some fundamental results. In: Int. Symp. on Turbo Codes and Rel. Topics. (September 2000) 43–46
