Robust Linear Video Transmission Over Rayleigh ... - IEEE Xplore

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IEEE TRANSACTIONS ON COMMUNICATIONS, VOL. 62, NO. 8, AUGUST 2014

Robust Linear Video Transmission Over Rayleigh Fading Channel Hao Cui, Chong Luo, Member, IEEE, Chang Wen Chen, Fellow, IEEE, and Feng Wu, Fellow, IEEE

Abstract—This research addresses the problem of robust linear video transmission over the Rayleigh fading channel, where only statistical channel state information (CSI) is available to the sender. We observe that discarding low-priority (LP) data and saving the channel uses for high-priority (HP) data can significantly improve the quality of the received video. We formulate an optimization problem that aims to minimize the total squared error of a multi-variant Gaussian random vector under the given bandwidth and power resources. To tame the complexity of this NP-hard problem, we analyze two sub-problems, namely power allocation and bandwidth allocation, and propose an iterative algorithm to approximate the solution. Subsequently, we propose a one-pass two-step fast algorithm that further reduces both algorithmic and computational complexity. A linear video transmission system is implemented based on the proposed algorithm. Simulations show that our system significantly outperforms SoftCast, and the PSNR gain at 5th percentile of 1000 test runs is between 4.0 dB and 7.5 dB under varying noise levels. Index Terms—Multimedia communication, cross layer design, diversity methods.

I. I NTRODUCTION

R

ECENTLY there has been a surge of interest in linear video communication [1]–[4]. The basic idea is to skip the non-linear processing, such as quantization and entropy coding, in the video encoder and to transmit linearly transformed video signals with amplitude modulation. The optimal power allocation through linear coding under additive white Gaussian noise (AWGN) channel was derived by Lee and Petersen [5] and has been applied in the pioneering linear video communication system called SoftCast [1]. SoftCast achieves similar end-to-end distortion to conventional digital methods while maintaining robustness to channel variations and lowering computational complexity [6]. Moreover, a linear system would provide a substantial net performance gain for multicast sessions as it allows receivers to obtain video quality that is commensurate with their channel conditions. Manuscript received January 2, 2014; revised June 10, 2014; accepted June 16, 2014. Date of publication June 24, 2014; date of current version August 20, 2014. The editor coordinating the review of this paper and approving it for publication was M. Kieffer. H. Cui and F. Wu are with the Department of Electronic Engineering and Information Science, University of Science and Technology of China, Hefei, Anhui 230026, China (e-mail: [email protected]; fengwu@ustc. edu.cn). C. Luo is with the Internet Media Group, Microsoft Research Asia, Beijing 100080, China (e-mail: [email protected]). C. W. Chen is with the Department of Computer Science and Engineering, University at Buffalo, The State University of New York, Buffalo, NY 14260 USA (e-mail: [email protected]). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TCOMM.2014.2332502

Despite these merits, the robustness of linear video communication under fast fading channels has not been studied before. If high-priority (HP) data (e.g. DC coefficient after DCT transform) unfortunately experience a deep fade, the overall distortion would be dramatically increased. Simply allocating more power to the HP coefficients does not solve the problem if only statistical channel state information (CSI), and not the precise CSI, is available to the sender. Experience in digital communications has shown that diversity increases robustness and improves the symbol error rate (SER) performance in fading channels [7], [8]. This suggests that we may sacrifice the transmission opportunity of some low-priority (LP) data and save the channel bandwidth for HP data to ensure the quality. While the optimal power allocation for the AWGN channel has already been addressed in previous work, the optimal joint bandwidth and power allocation for fading channels remains an open problem. Although conventional digital communication is also constrained by limited bandwidth and power, the resource allocation problem does not appear to create hardships. This is because conventional digital methods are built upon Shannon’s source-channel separation principle [9] and the entropy coding in the source encoder elegantly resolves the difficulties. In particular, entropy coding allocates a different number of bits to different coefficients according to their entropy or importance. Each encoded bit essentially carries the same amount of information. They are treated with equal importance during channel coding and modulation. As such, power and bandwidth allocations are coupled through bit allocation. In linear video communication, however, each coefficient is directly transmitted with amplitude modulation, consuming a power that is proportional to its variance. The absence of bit representation makes joint power and bandwidth optimization much more complicated. In this paper, we examine the optimal resource allocation problem under the Rayleigh fading channel. Video sources, after the de-correlating transform, are modeled as a multivariant Gaussian random vector. Although the joint optimization of bandwidth and power is a mixed integer nonlinear programming (MINLP) problem, which is in general NP-hard [10], we can tame the complexity by dividing it into two sub-problems. One sub-problem, the optimal power allocation under given bandwidth allocation, is proven to be a convex optimization problem and therefore can be solved via the gradient method. The joint optimization problem can be approximated through an iterative algorithm that allocates bandwidth in a greedy and progressive manner and evaluates each bandwidth allocation choice by executing the optimal power allocation

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CUI et al.: ROBUST LINEAR VIDEO TRANSMISSION OVER RAYLEIGH FADING CHANNEL

algorithm. The initial results were published in our previous work [11]. This paper makes two additional contributions. First, we provide theoretical analysis of the optimal resource allocation problem. In particular, we derive a necessary condition for the optimal power allocation sub-problem and two properties for the bandwidth allocation sub-problem. For the latter, we show that: 1) in Rayleigh fading channels, transmitting a Gaussian random variable (R.V.) repeatedly in k + 1 time slots results in smaller expected distortion than transmitting it in k time slots, under the same total power constraint; 2) when considering two Gaussian R.V.’s with different variances, both repeatedly transmitted in k time slots, the R.V. with the larger variance has a larger expected distortion reduction if additional channel use is granted. Second, we propose a one-pass two-step fast algorithm that greatly reduces the complexity of the iterative algorithm. Evaluations show that the performance gap to the iterative algorithm is within 0.4% of the achieved video PSNR (peak signal-to-noise ratio). We validate the proposed resource allocation algorithm by implementing a linear video communication system and evaluating it against SoftCast [1]. Extensive simulations show that our system consistently outperforms SoftCast in both average performance and robustness. In particular, we use the 5th percentile of received video PSNR as the robustness measure. Our system achieves significant gains of between 4.0 dB to 7.5 dB over SoftCast under varying channel conditions. The rest of this paper is organized as follows. In Section II, we discuss related work on linear video communication and analog joint source-channel coding (JSCC). In Section III, we formulate the optimization problem. In Section IV, the optimization problem is divided into two sub-problems, and a detailed analysis of each problem is presented. Section V presents an iterative algorithm and a fast algorithm. Section VI first describes the implementation of a linear video communication system based on the proposed algorithm, then presents the evaluation results. We finally summarize the paper in Section VII.

II. BACKGROUND AND R ELATED W ORK A. Linear Video Communication Recently, there has been a surge of interest in linear video communication. The pioneering work in this area is called SoftCast [1]. Its encoder starts from the 3D-DCT, which converts correlated source into (ideally) independent coefficients. The DCT coefficients are then divided into L chunks and these coefficients in a chunk are considered instances drawn from the same zero-mean Gaussian distribution. Let λ1 , . . . λL denote the variances of the coefficients in each of the L chunks, and assume that they are in descending order without loss of generality. In the next step, a linear coding or power scaling for each coefficient is performed. It has been determined that under average power constraints and an MSE distortion criterion, the scaling factor for coefficients belonging to the ith Gaussian −(1/4) , and such a distribution should be proportional to λi design yields the optimal performance in the AWGN channel.

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Subsequently, there has been follow-up research, including ParCast [2], Dcast [3], [12], and Cactus [4]. These systems share the same core modules with SoftCast, but differ from each other in how they remove or utilize the source redundancy. Among these methods, Parcast is the most related to our research. It concerns linear video transmission across the MIMO-OFDM channel. The basic idea is to separate the MIMO-OFDM channel into a set of orthogonal sub-channels and then match the more important source (belonging to a Gaussian distribution with a larger variance) to a higher gain sub-channel. Let si be the ith largest channel gain, then the optimal power allocation is to scale each coefficient with a factor proportional to (λi s2i )−(1/4) . Although Parcast considers fading channels, it assumes the availability of the precise CSI at the transmitter. In our previous research [11], we considered linear video transmission in a fast fading channel where only statistical CSI is available to the transmitter. A greedy algorithm based on heuristics was proposed to approximate the optimal power and bandwidth allocation. However, rigorous proof was not given and the proposed algorithm is still too complex for real-time scenarios. B. Analog JSCC Linear video communication is essentially a joint sourcechannel coding (JSCC) scheme. Therefore, we review related work in analog JSCC. Among the large body of theoretical work on analog JSCC, linear coding and single-letter coding have attracted the most attention for their simplicity and low delay. At the intersection of these two coding schemes, there is a so called uncoded transmission strategy in which no compression or channel coding is used and the source samples are transmitted by appropriately scaling according to the transmitter power constraint P . Surprisingly, such a simple strategy has been shown to achieve optimality in certain practical cases [13], [14]. A famous example is to transmit a uniform-distributed binary source with a Hamming distance distortion metric over a binary symmetric channel. Another example is to transmit a Gaussian source with a squared-error distortion metric over an AWGN channel. The linear transmission strategy concerned in this research is slightly different from the above two examples, because the source under consideration is modeled by a multi-variate Gaussian random vector. Source samples belonging to different Gaussian distributions should be scaled by different factors to achieve optimality. Lee and Petersen [5] carried out a comprehensive investigation on this optimal linear coding problem, and SoftCast and ParCast are straightforward implementations based on their results. Unfortunately, they did not consider what happens when the fading channel parameter is not available at the transmitter. Considering the fading channels, and under a more realistic assumption that the receiver has perfect CSI while the transmitter has only statistical information about the channel state, Kashyap et al. [15] derived the performance of the linear coding scheme. They found that for the Rayleigh fading channel, while linear coding is suboptimal in general, it is close to

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Fig. 1. Linear transmission paradigm.

optimal in the low SNR regime. Xiao et al. [16] also considered the linear coding of a discrete memoryless Gaussian source transmitted through a discrete memoryless fading channel with AWGN. They showed that among all single-letter codes, linear coding achieves the smallest MSE. However, these works do not consider the multi-variate Gaussian source. Although there are other non-linear JSCC strategies [17], [18] and hybrid digital-analog strategies [19]–[21] that have shown near-optimal performance, we focus this paper on linear coding strategies. In particular, we are interested in transmitting a multi-variate Gaussian random vector over fast fading channels, a problem rooted in wireless video communications. III. P ROBLEM

where hm ∼ CN (0, σh2 ) is the fading parameter, and em ∼ CN (0, σ 2 ) is the additive noise. It is assumed that only the CSI statistics, i.e. σh and σ, are known to the sender. Without changing the nature of the problem, we can normalize σh2 to 1 for simplicity. The value of hm can be estimated at the receiver, through pilot symbols, based on common coherence time assumptions. However, the exact value of em cannot be known by either sender or receiver. Destination: Let k = (k1 , k2 , . . . , kN )T be a bandwidth allocation solution, where kn is the number of transmission opportunities for cn . The fading parameters of the kn transmissions can be stacked into a vector Hn . We use xn to denote a complex wireless symbol formed by two instances of cn . The receiver would obtain kn noisy versions of xn , and they can be stacked into a vector:

A. System Model The system model for linear transmission is shown in Fig. 1. Source: A video sequence is divided into GOPs. GOP size can vary from 8, 16, to 30 or 32. Usually, each GOP independently allocates resources, such as bandwidth and power, to avoid delay. In linear video transmission, 3D-DCT is performed over each GOP, and the DCT coefficients are divided into N equal-sized chunks. Let λn denote the variance of the nth (1 ≤ n ≤ N ) chunk. We consider the coefficients in the nth chunk to be random variables drawn from a Gaussian distribution Dn = N (0, λn ). Because all the chunks have the same size, we can simply model the source as a random vector (c1 . . . cN )T with cn ∼ Dn . The objective of resource allocation is to find the power scaling factor gn and the number of repeated transmissions kn for random variable cn . Once the two values are determined, each instance of cn will be multiplied by gn and be repeated for kn times. Let sni and snj be two scaled coefficients from the same chunk (i.e. the same distribution Dn ), they form one wireless complex symbol: sni + i · snj √ . xm = 2 Then all complex symbols within a GOP are interleaved to ensure that they experience independent fading during transmission. Channel: We consider a fast Rayleigh fading channel with AWGN. In particular, for each transmitted symbol xm , the received symbol ym can be written as: y m = hm · x m + em

Yn = Hn xn + En where En = (e1 , e2 , . . . , ekn )T is the additive noise on the corresponding channel. The receiver performs the standard maximum ratio combining (MRC) to obtain an estimation of the transmitted symbol: x ˆn =

H∗n Yn = xn + eˆn Hn 2

where eˆn ∼ N (0, σ 2 /Hn 2 ) (see Fig. 1). Through minimum mean squared error (MMSE) detection, the corresponding DCT coefficients are recovered from the real and imaginary parts of x ˆn . snj = sˆni + iˆ

gn2 λn

g n λn ·x ˆn + σ 2 /Hn 2

B. Problem Statement Define the distortion as the Euclidean norm εn = ˆ sn − sn 2 . The expected distortion under known fading gain and noise power is E[εn |Hn , σ 2 ] =

λn σ 2 λn = Hn 2 gn2 λn + σ 2 Hn 2 ρn + 1

(1)

where ρn = gn2 λn /σ 2 is the signal-to-noise power ratio for the nth chunk. Given the total bandwidth M and the total transmission power P , we find the bandwidth allocation, i.e. k and the


power allocation, i.e. ρ, to minimize the total mean distortion. Mathematically, N

min

E[εn |σ 2 ]

n=1 N

s.t.

kn ≥ 0, kn ∈ Z kn ρn =

n=1

P σ2

ρn ≥ 0, ρn ∈ R.

(2)

Note that εn = f (λn , ρn , Hn ) is a multi-variable function and Hn depends on the channel use allocation kn . E[εn |σ 2 ] is computed by taking expectation of (1) over the channel fading gain Hn . IV. A NALYSIS The optimization problem as defined in (2) is a mixed integer nonlinear programming (MINLP) problem, which has been proven to be NP-hard [10]. To tame the complexity, we divide the optimization problem into two sub-problems, namely power allocation and bandwidth allocation, and perform a detailed analysis. The objective function of problem (2) can be rewritten into: N N E[εn |k, σ 2 ] kn = M . (3) min min ρ k n=1

A. Power Allocation Problem Under a given bandwidth allocation k, the power allocation problem is: N

E[εn |k, σ 2 ]

(6)

(7)

By definition, t ≥ 0 and ρn ≥ 0, therefore 2t2 /(ρn t + 1)3 ≥ 0. Unless P(t = 0) = 1 which is impossible in practice, (∂ 2 E[εn |k, σ 2 ]/∂ρ2n ) > 0, i.e. E[εn |k, σ 2 ] is a strict convex function of ρn . Therefore, (4) is a convex optimization problem. Simplification of Notations: Under independent Rayleigh fading channel, t = Hn 2 is the sum of kn i.i.d. Chi-square random variables, and therefore obeys the Gamma distribution t ∼ Γ(kn , 1). The probability density function of t is: d (P(t)) =

1 kn −1 −t t e dt. Γ(kn )

(8)

Now let’s define

∞ Φ(k, x) =

1 x k−1 −t t e dt Γ(k) t + x

(9)

0

n=1

With this expression, it is clear that one sub-problem is to find the optimal power allocation under a given bandwidth allocation, and the other sub-problem is to find the optimal bandwidth allocation given that the first sub-problem can be solved.

min

When kn = 0, the coefficients in the nth chunk are not transmitted. Thus, the expected distortion is simply the variance of the chunk. Next, we will focus on cases when kn ≥ 1. Based on the Leibniz integral rule, we can derive the first order and second order partial derivative of E[εn |k, σ 2 ] for kn ≥ 1. According to (1) and let t = Hn 2 ,

∂E[εn |k, σ 2 ] t = − λn d (P(t)) ∂ρn (ρn t + 1)2

2t2 ∂ 2 E[εn |k, σ 2 ] = λ d (P(t)) . n 2 ∂ρn (ρn t + 1)3

kn = M

n=1

N

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∞ Ω(k, x) =

1 Γ(k + 1)

x t+x

2

tk e−t dt.

(10)

0

It easy to derive that 0 ≤ Φ(k, x) ≤ 1 and 0 ≤ Ω(k, x) ≤ 1. By substituting (9) into (5) and (10) into (6), we can simplify the expressions into: 1 2 E[εn |k, σ ] = λn · Φ kn , (11) ρn ∂E[εn |k, σ 2 ] 1 = − λ n · kn · Ω kn , . (12) ∂ρn ρn

n=1

s.t.

N

P kn ρn = 2 σ n=1 ρn ≥ 0, ρ ∈ R

(4)

where the expectation is taken over the channel fading gains. Theorem 1: The power allocation problem as defined in (4) is a constrained convex optimization problem. Proof: E[εn |k, σ 2 ] is a piecewise function: E[εn |Hn , σ 2 ]d (P(Hn )) kn ≥ 1 2 E[εn |k, σ ] = . (5) λn kn = 0

Next, we derive a necessary condition for the optimal power allocation through the analysis of the Karush-Kuhn-Tucker (KKT) condition of (4). Theorem 2: Let k be a given bandwidth allocation and + T + ρ = (ρ+ 1 . . . ρN ) be a power allocation scheme. A necessary condition for ρ+ being the optimal power allocation is that ∀kn ≥ 1 the following constraint holds, where C is a real number

1 λ n · Ω kn , + ρn

= C.

(13)

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Proof: The Lagrangian L : RN × R × RN → R associated with (4) is

transmitting a variable with more channel uses will result in a smaller distortion even when the overall transmission power is the same. The distortion reduction could be significant for variables with large variance. If this is true, we may sacrifice the transmission opportunities of some LP data (with small variances) and allow the HP data to use more channel uses so that the overall distortion could be reduced. Next, we will present two theorems that confirm our conjecture. Theorem 3: Consider the repeated transmission of a Gaussian variable over a Rayleigh fading channel. Let ρσ 2 be the total power budget. Transmitting the R.V. in k + 1 time slots results in a smaller distortion than transmitting it in k time slots, where k ≥ 1. Proof: It has been shown in [16] that, under the total power constraint, equal power division over k available channel uses minimizes the distortion. When there are k time slots, ρσ 2 /k is allocated to each transmission. When there is an additional channel use, the power of each transmission is ρσ 2 /(k + 1). According to the relationship between the distortion and the Φ function as given in (11), and let x = 1/ρ, we prove

N

L(ρ, γ0 , γ1 , . . . , γN ) =

E[εn |k, σ 2 ]

n=1

+ γ0

N

P kn ρn − 2 σ n=1

−

N

γn ρn .

(14)

n=1

The KKT conditions are ⎧ ∂E[εn |k,σ2 ] + γ 0 kn − γ n = 0 ⎪ ∂ρn ⎪ ⎪ ⎪ N ⎪ ⎪ ⎨ kn ρn − σP2 = 0 ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎩

n=1

(15a) (15b)

γn ρn = 0 γn ≥ 0 ρn ≥ 0.

(15c) (15d) (15e)

Substituting (15a) into (15c), we have ∂E[εn |k, σ 2 ] + γ0 kn ρn = 0. ∂ρn

(16)

For the data that will be transmitted, ρn > 0. Hence, ∂E[εn |k, σ ] + γ0 kn = 0. ∂ρn

Φ(k, kx) > Φ (k + 1, (k + 1)x) . Let’s define

2

Δ1 = Φ (k, (k + 1)x) − Φ(k, x)

∞ kx (k + 1)x 1 = − tk−1 e−t dt Γ(k) t + (k + 1)x t + kx

(17)

Substituting (17) into (15b), we can derive that N ∂E[εn |k, σ 2 ] ρi ∂E[εi |k, σ 2 ] = kn . P ∂ρn ∂ρi i=1 σ 2

0

=

Therefore, by (18) and (12), the conclusion (13) holds. The above analyses suggest that there are at least two ways to solve the power allocation problem. One is through solving (13), and another is through gradient descent based on the convexity of the problem. The latter is considered a tractable solution in practice. B. Bandwidth Allocation Problem Now that we have a tractable algorithm to solve the power allocation problem, then the optimal bandwidth allocation problem can be written as: min k

s.t.

min ρ

N

N

E[εn |k, σ 2 ]

n=1

kn = M

n=1

kn ≥ 0, kn ∈ Z.

∞

(18)

(19)

To find the optimal bandwidth allocation scheme k+ , we shall test all the possible combinations of (k1 . . . kN ) by running the optimal power allocation algorithm and comparing the achieved minimum distortion. The computational complexity is apparently too high. Therefore, we shall look for some guidelines for bandwidth allocation to reduce the complexity. Intuitively,

kx 1 tk e−t dt Γ(k + 1) (t + (k + 1)x) (t + kx)

0

and Δ2 = Φ (k, (k + 1)x) − Φ (k + 1, (k + 1)x) 1 Ω (k, (k + 1)x) (k + 1)x .

∞ 1 (k + 1)x = tk e−t dt Γ(k + 1) (t + (k + 1)x)2

=

0

Since ∀t > 0 and x > 0, we have (k + 1)x kx xt − = > 0. t + (k + 1)x t + kx (t + (k + 1)x) (t + kx) Therefore, Δ2 > Δ1 , i.e. Φ(k, kx) > Φ(k + 1, (k + 1)x). Theorem 4: Consider the repeated transmission of multiple Gaussian random variables and assume that we have an optimal power allocation scheme under a given bandwidth allocation. If L variables are allocated with the same number of channel uses, i.e. k1 = k2 · · · = kL , then the one with the largest variance has the maximum distortion reduction when it is allocated with an additional channel use while keeping its total power budget unchanged. Proof: Let λ1 . . . λL denote the variances of the L Gaussian random variables. Without loss of generality, we


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assume λ1 ≥ λ2 ≥ · · · ≥ λL . From the distortion analysis, we know that the total distortion of the L random variables is L 1 λ i Φ ki , . ρi i=1

algorithmic and computational complexity are further reduced with marginal performance loss. The proposed fast algorithm allows a video source to be processed in real time.

To minimize the above distortion, the values of the Φ functions should be in descending order, i.e. 1 1 1 ≤ Φ k2 , ≤ · · · ≤ Φ kL , Φ k1 , ρ1 ρ2 ρL

We first approximate the optimal solution through an iterative algorithm. The algorithm inputs are the variances of the R.V., denoted by λ = (λ1 . . . λN )T , the total power constraint P , the number of available channel uses M , and the noise power σ 2 . We assume that λ’s have been sorted in descending order. The expected outputs are the bandwidth allocation scheme k+ = (k1 . . . kN ) and the power allocation scheme ρ+ = (ρ1 . . . ρN ).

Hence, we have ρ1 ≥ ρ2 ≥ · · · ≥ ρL . If an additional channel use is assigned to λi and ρi is unchanged, the distortion reduction, denoted by ΔDi , will be 1 ki + 1 − Φ ki + 1, ΔDi = λi Φ ki , ρi ki ρi We allocate the additional channel use to the R.V. with the maximum ΔDi . According to Theorem 2, the following equations hold for an optimal resource allocation scheme: 1 1 1 = λ 2 Ω k2 , = · · · = λ L Ω kL , =C λ 1 Ω k1 , ρ1 ρ2 ρL Divide the distortion reduction by C, and define: f (x) =

Φ(k, kx) − Φ (k + 1, (k + 1)x) Ω(k, kx)

According to the definitions of Φ(·) and Ω(·), we have: Φ(k, kx) − Φ (k + 1, (k + 1)x)

∞ = 0

xt tk e−t dt (t + (k + 1)x)2 (t + kx) Γ(k + 1)

Ω(k, kx)

∞ =

kx (t + kx)

2

tk e−t dt Γ(k + 1)

0

A. An Iterative Algorithm

Algorithm 1: Iterative Algorithm Data: λ, P , M , σ 2 Result: k+ , ρ+ 1 // Initialize k+ , ρ+ , D(0) : 2 for n = 1 . . . N do 3 kn+ = M/N ; 4 if n ≤ M mod N then 5 kn+ ← kn+ + 1; 6 end 7 end 8 (ρ+ , D(0) ) ← P owerAlloc(λ, k+ , P, σ 2 ); t = 0 9 // Iterative Processing: 10 repeat 11 t ← t + 1 + , n ≥ 2} 12 St = {1} {n|kn+ < kn−1 13 nd ← the largest index n that kn+ ≥ 1 14 for each nt in St do 15 k = k+ , except knd = kn+d − 1, knt = kn+t + 1 16 (ρ, D) ← P owerAlloc(λ, k, P, σ 2 ); 17 end 18 D(t) = min{D} 19 if D(t) < D(t−1) then 20 ρ+ ← ρ corresponding to the min D 21 k+ ← k corresponding to the min D 22 end 23 until D(t) ≥ D(t−1)

Let’s define g(x) =

xt (t+(k+1)x)2 (t+kx) 2 kx (t+kx)

∀t > 0, g (x) < 0. Hence, g(x) is a decreasing function of x. Since the integral is operated on t, therefore, f (x) is a decreasing function of x. Therefore, ΔD1 has the maximum value among all ΔDi ’s, meaning that the additional channel use should be assigned to the R.V. with largest variance λ1 . V. S OLUTION Based on the above analyses, we first came out with an iterative solution that has tractable complexity. Then, both

In initialization, all the R.V.’s are allocated with the same number of channel uses. If M cannot be divided by N , then the first M mod N R.V.’s with larger variances are allocated with one more channel use. Then, the power allocation algorithm is applied to initialize ρ+ , and the minimum distortion is computed. In each iteration, we take one allocated channel use from the R.V. with the smallest variance and try to assign it to other R.V.’s. According to Theorem 4, among the R.V.’s that are allocated with the same number of channel uses in the previous iteration, the one with the largest variance will have the largest distortion reduction. Therefore, only a few candidates need be considered. In the algorithm description, this set is denoted by St . Fig. 2 gives an illustrative example. The variables are sorted in descending order according to their variances. We try

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s.t.

N i=1 N

κi θ i = 0 θi2 = 1

(20)

i=1

Fig. 2. An illustrative example of iterative bandwidth allocation.

to take the channel use of the last variable (marked with a cross) and allocate it to higher priority variables. Only five positions marked with question marks should be considered for getting the additional channel use. For each possible bandwidth reallocation k, we perform power allocation and compute the minimum total distortion. Then, we select the bandwidth reallocation option that results in the minimum total distortion. The iterative process ends if the reallocation does not reduce total distortion. In Algorithm 1, we call function P owerAlloc(·) twice. Algorithm 2 presents the detailed gradient descent algorithm P owerAlloc(·), which solves the optimal bandwidth allocation problem. Algorithm 2: Power Allocation Algorithm P owerAlloc(·) Data: λ, k, P , σ 2 Result: ρ+ , D 1 // Initialize ρ+ : 2 for n = 1 . . . N do√ √ λn · (P/σ 2 N 3 ρ+ n = sgn(kn ) · i=1 ki λi ) 4 end 5 // Gradient descent approximation: 6 t = 0; D(0) = +∞ 7 repeat 8 t←t+1 9 κ = k ∗ sgn(ρ+ ) 10 ω = −(∂E[εn |κ, σ 2 ]/∂ρ)|ρ=ρ+ 11 θ = α1 (ω − (κ · ω/κ2 )κ) 12 ρ+ = α2 max{ρ+ + δθ, 0} 2 13 D(t) = N n=1 E[εn |κ, σ ] (t) (t−1) 0 is the normalization factor that N i=1 θi = 1. In line 9, the notation ∗ denotes element wise multiplication. We force the bandwidth allocation to zero if the power allocation evolves to zero. We perform this operation because power is a non-negative scalar and should be bounded by zero if it evolves to a negative value. α2 is a normalization factor that 2 ensures α2 N i=1 κi ρi = P/σ . B. Proposed Fast Algorithm We propose a fast algorithm that reduces both the algorithmic and computational complexity of the proposed iterative algorithm. First, we find that the iterative process can be simplified into a one-pass two-step process with marginal performance loss. Second, we observe that the computation of the distortion and the first order derivative of the distortion consume a great deal of resources because both terms contain integral components that are hard to precisely compute. We propose a method to compute both terms through recursion that greatly reduces the computational complexity. Algorithm 3: Fast Algorithm Data: λ, P , M , σ 2 Result: k+ , ρ+ 1 // Initialize k+ , ρ+ , D(0) : 2 Same as line 2–8 in Algorithm 1. 3 // Bandwidth allocation: 4 repeat 5 t ← t + 1 + , n ≥ 2} 6 St = {1} {n|kn+ < kn−1 7 nd ← the largest index n that kn+ ≥ 1 8 for each nt in St do 9 k = k+ , except knd = kn+d − 1, knt = kn+t + 1 + + 10 ρ = ρ+ , except ρnt = (ρ+ nt · knt + ρnd )/knt 2 11 D ← E[εn |k, ρ, σ ] 12 end 13 D(t) = min{D} 14 if D(t) < D(t−1) then 15 ρ+ ← ρ corresponding to the min D 16 k+ ← k corresponding to the min D 17 end 18 until D(t) ≥ D(t−1) 19 // Power allocation: 20 (ρ+ , D) ← P owerAlloc(λ, k+ , P, σ 2 );


Reducing Algorithmic Complexity: Algorithm 3 gives the details of the proposed fast algorithm. Comparing it with the iterative algorithm (Algorithm 1), we find that the computationally costly function P owerAlloc(·) is only called twice in initialization and 20 (final decision). Actually, we can simplify the power initialization step by using only line 3 in Algorithm 2 to further reduce the complexity. Although the bandwidth allocation is still an iterative process, we decouple power allocation from it by replacing line 16 in Algorithm 1 with line 10 and 11 in Algorithm 3. In particular, we do not seek the optimal power allocation for the tested new bandwidth allocation, but simply reallocate the power of the dropped coefficient (nd ) to coefficient nt , and compute the distortion under bandwidth + + allocation k and power allocation ρ. Note that ρ+ nt · knt + ρnd in line 10 is the new total power for coefficient nt , and it is evenly divided among knt time slots. After the bandwidth allocation is decided, P owerAlloc(·) is called in line 20 to make the final power allocation decision. We will show through evaluation that this fast algorithm incurs marginal performance loss compared to the iterative algorithm. Reducing Computational Complexity: In both the bandwidth allocation and power allocation processes, we need to compute the expectation of distortion and its partial derivative as defined in (11) and (12). However, we need to compute integrals in evaluating Φ and Ω functions according to their definitions in (9) and (10). Next, we propose an efficient way to compute the integrals based on recursion. When k = 1,

∞ Φ(1, x) =

x −t e dt = xex t+x

∞

1 −t e dt t

x

0 x

= x (−e Ei(−x))

(22)

where Ei(−x) is the exponential integral function. ∀k > 1, we have the following recursion.

∞ Φ(k, x) =

x k−1 −t 1 t e dt Γ(k) t + x

0

x = Γ(k)

∞

t k−2 −t t e dt t+x

0

⎛ x ⎝ = Γ(k)

∞

tk−2 e−t dt −

0

=

∞

⎞ x k−2 −t ⎠ t e dt t+x

0

x (1 − Φ(k − 1, x)) k−1

(23)

In addition,

∞ Ω(k, x) =

1 Γ(k + 1)

x t+x

2

tk e−t dt

0

∞ ∞ 1 −x2 k −t 1 x2 k−1 −t = t e + t e dt Γ(k + 1) t + x Γ(k) t+x 0 0

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Fig. 3. Source processing in a linear video transmission system.

∞ −

1 x2 k −t t e dt Γ(k + 1) t + x

0

= x (Φ(k, x) − Φ(k + 1, x))

(24)

The exponential integral function −ex Ei(−x) can be implemented by a lookup table. Therefore, by recursion, the integral can be very efficiently computed. In addition, when there is enough memory, e.g. 1 MB, the function Φ(k, x) for k = 1, 2, . . . , 100 can also be implemented by a lookup table which further reduces the computation cost. VI. E VALUATION A. Implementation Fig. 3 shows the source processing of the linear video transmission system. The processing unit is a group of pictures (GOP). The GOP size is 8 in our implementation. We perform 3D-DCT over a GOP after subtracting 128 from each pixel value. Then, DCT coefficients in each transformed picture are divided into equal-size rectangular chunks as shown in Fig. 3. The coefficients in a chunk are considered i.i.d. zero mean Gaussian distributed random variables and the variance is the average energy of the chunk. Using more chunks would produce better performance, but incurs higher overhead as well. Usually, 64 equal chunks per picture (or 512 chunks per GOP) introduces negligible overhead with little harm to performance [23]. Then, the resource allocation algorithm is performed based on the chunk variances and the coefficients in each chunk are scaled and duplicated accordingly. The scaled coefficients are pair wisely mapped to the amplitude of in phase and quadrature phase transmission signals. Note that the variances of the chunks should be faithfully transmitted to receivers as meta data. Therefore, they are encoded and transmitted in a digital manner. We adopt BPSK and 1/2 channel coding to ensure reliable transmission. At the receiver, with the correct variance information, both the scaling factors and the channel use assignment can be computed. If multiple channel uses are allocated to any single chunk, maximum ratio combining (MRC) is performed. Based on the estimated CSI and the refined noise power by MRC, the coefficients can be obtained with the minimum distortion by MMSE detection. Finally, the video can be reconstructed through inverse 3D-DCT and adding 128 to the pixel value. Since this paper focuses on the transmission for linear video, SoftCast is considered a reference system. We follow all the implementation details of SoftCast as outlined in [1], including

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TABLE I AVERAGE PSNR ( IN dB) ACHIEVED BY O UR S YSTEM AND S OFTCAST

the whitening step using the Hadamard matrix. For a fair comparison, all systems use GOP size 8 and rectangular-shaped equal-size 8 × 8 chunks per frame. Note that our system transmits the same amount of meta data as SoftCast. According to [1], the overhead is only 0.014 bpp (bits per pixel).

over all pixels in the frame. The PSNR of a sequence is the averaged PSNR over all frames. To evaluate the robustness of the transmission scheme, we conduct 1,000 test runs for each test video for each target channel SNR. The tested video sequences are different in their data energy distribution. The average PSNR and its 5th and 95th percentiles are recorded.

B. Settings Video Source: We use monochrome video sequences for our evaluation. In particular, only the luma (Y ) components in the Y UV video signals are transmitted. If color videos are of interest, the chrominance (U and V) components can be processed and transmitted in the same way as the luma components. Chunks from different color components will not be discriminated in resource allocation, as resource allocation decisions are made solely based on chunk variations. In most evaluations, we use CIF sequences with resolution of 352 × 288 and frame rate of 30 fps (frame per second). Hence, the source bandwidth is 1.52 MHz (in complex symbols). The 12 standard video test sequences used are ‘akiyo,’ ‘bus,’ ‘coastguard,’ ‘container,’ ‘flower,’ ‘football,’ ‘foreman,’ ‘husky,’ ‘mobile,’ ‘news,’ ‘soccer’ and ‘stefan’. Physical Layer Configurations: After power allocation, the scaled coefficients are directly used to modulate the amplitude of in-phase and quadrature-phase signals. Therefore, one complex symbol can be generated by two coefficients. The complex symbols are transmitted through OFDM so that the channel fading gain can be considered as a complex scalar. At the receiver end, different versions of a transmitted symbol from multiple channel use are combined by Maximum Ratio Combining (MRC). Channel Configurations: We use Rayleigh fading channel with the fading parameter hm ∼ CN (0, 1). We change hm every 40 μs to simulate a fast fading channel. The random noise is generated based on the AWGN model. In most of the simulations, Es /N0 equal to 5 dB, 10 dB, 20 dB and 30 dB are considered. Except for the bandwidth compaction evaluation, the total bandwidth, i.e. the number of available channel use, is in default equal to the number of coefficients. Evaluation Metrics: We use the objective video quality assessment, named peak signal-to-noise ratio (PSNR) in dB, as the evaluation metric. The PSNR of a frame is PSNR = 10 log10 (2552 /MSE), where MSE is the mean squared error

C. Results Comparison Against Reference System Softcast: We first compare the performance of our system with Softcast. Table I lists the average PSNR achieved for the 12 test videos. Our system consistently outperforms Softcast, and the average gain is between 1.7 dB to 2.4 dB under varying channel conditions. Table II gives the 5th percentile of the achieved PSNR, i.e. in 95% of all the 1,000 test runs, this PSNR can be achieved. This metric indicates the robustness of a transmission scheme. We find that our system achieves an enormous gain over Softcast, ranging from 4.0 dB to 7.5 dB under varying channel conditions. Besides, comparing the average PSNR and the 5th percentile of our system, we find that the gap is very small. The results confirm that we have achieved our design goal to build a robust linear video transmission system. We have also tested our system for videos with different resolutions and under different evaluation metrics. Fig. 4 shows the comparison between our system and SoftCast for a high definition (1280 × 720) video ‘City’ under both PSNR and SSIM (structural similarity) measures. Results show that we achieve similar (slightly larger) PSNR gain over SoftCast for high definition videos as for CIF videos. The improvement over SSIM measure is also significant. Impact of Inaccurate CSI and Multicast: The proposed resource allocation algorithm needs the noise level at the receiver (denoted by σ 2 ) as an input. The provided σ 2 may be inaccurate under three situations. First, when σ 2 itself is not precisely measured. Second, when the estimated channel fading parameter h is larger or smaller than the actual value, it is equivalent to reducing or amplifying the additive noise. Third, when a multicast session is considered, multiple receivers may have varying CSI. To evaluate the impact of inaccurate CSI, we run our system at typical target SNRs and evaluate the receiver PSNR when the actual noise power ranged from 5 dB to 30 dB. Table III lists


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TABLE II 5 TH P ERCENTILE PSNR ( IN dB) OF O UR S YSTEM AND S OFTCAST

Fig. 4. Comparison between the proposed method and SoftCast for 720p video ‘City’ under PSNR and SSIM measures. The shadowed regions are bounded by the 5th and 95th percentiles and the lines in the region indicate the average performance. TABLE III T HE M EAN AND VARIANCE OF THE ACHIEVED PSNR W HEN THE CSI MAY BE I NACCURATE

the average PSNR and the standard deviation (SD) averaged over all 12 test sequences. We observe that underestimating Es /N0 will decrease the achieved PSNR, but the variation decreases as well. When the actual channel condition is poor or moderate (Es /N0 equals to 5 dB and 10 dB in the table), inaccurate CSI has a little impact on the achieved PSNR. However, when the channel condition is good, significantly underestimating the channel may incur a large loss. In the extreme case that the actual Es /N0 is 30 dB but the algorithm input is 5 dB, the loss in average PSNR could be as large as 10.7 dB. In contrast, overestimating the channel is not so harmful. The loss in average PSNR is below 1 dB under varying conditions. The table also gives the performance of Softcast. As Softcast does not need CSI input, it only has one row of results. The PSNR variation of Softcast is significantly larger than our system. In addition, when a multicast session is considered, we shall use the CSI of strong receivers as the algorithm input. As

Fig. 5. Performance of our system and Softcast under bandwith compaction ratio 1/2 and 1 (Video source: Foreman).

an example, when we use 30 dB as the input Es /N0 , our system would consistently outperform Softcast with receiver Es /N0 ranging from 5 dB to 30 dB. Performance Under Bandwidth Compaction: In practice, the channel bandwidth is often smaller than the source bandwidth. The ratio between them is called bandwidth compaction ratio denoted by r. In this experiment, we evaluate the impact of bandwidth compaction (r = 0.5) on the average performance and robustness of our system, through the comparison with the r = 1 case and with the reference system Softcast. When r = 1/2, Softcast simply discards the less important half of the coefficient chunks (with smaller variances). The representative video test sequence Foreman is used, and the power constraint is unit power per channel use on average.

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Fig. 6. Bandwidth allocation results by the iterative and the fast algorithm for the first GOP of Foreman.

Fig. 5 shows the performance of our system and Softcast under bandwidth compaction ratio r = 1/2 and r = 1 (no compaction) at varying channel noise levels. Both average PSNR and the 5th and the 95th percentiles are shown in the figure. We find that our system is very robust under bandwidth compaction. The gap between the 5th and 95th percentiles when r = 0.5 remains very small as in the r = 1 case. In contrast, the 5th percentile of Softcast drops to 16.32 dB, which is more than 11 dB lower than when r = 1, when the channel Es /N0 is 5 dB. Performance and Complexity Evaluation of the Fast Algorithm: The proposed fast algorithm dramatically reduces the complexity of the iterative algorithm. In this experiment, we first evaluate the changes in bandwidth allocation as well as the performance loss of the fast algorithm. Fig. 6 compares the bandwidth allocation results (kf denotes the fast algorithm and ks denotes the iterative algorithm) for the first GOP of Foreman, with the two algorithms under typical channel conditions. We notice that the fast algorithm tends to allocate more time slots to the first few high-priority R.V.’s, but the overall allocation does not differ much. We also run evaluations for the iterative algorithm over all 12 test sequences. The achieved results by the fast algorithm and iterative algorithm are very close, and the differences in average PSNR, 5th and 95th percentiles are all within 0.4%. We next evaluate the computational complexity of the proposed fast algorithm. We run the algorithm for the first GOP (8 frames) of 12 test sequences, and record the time taken by bandwidth allocation and power allocation respectively. The desktop PC has an Intel core [email protected] GHz. We run the algorithm in a single thread to provide a benchmark. The average times taken by the bandwidth and power allocation are 0.358 s and 1.414 s respectively, so the total encoding time is 1.772 s per GOP on average. The longest encoding time is 2.08 s for the 9th sequence. If one considers a video sequence with a frame rate of 30 fps, parallel processing using eight threads can ensure real-time encoding for all sequences. VII. C ONCLUSION We have considered robust linear video transmission over fast fading channels in this paper. We have found that, similar to conventional digital communications, diversity increases

robustness and reduces distortion under the total power constraint. We have carried out theoretical analysis on the problem of optimal power and bandwidth allocation for the minimum MSE of a Gaussian random vector. Practical algorithms have been derived and a linear video transmission system has been implemented. Evaluations have shown that our system achieves significant gains over Softcast, demonstrating the effectiveness of the proposed algorithm. The current bandwidth allocation scheme only supports the allocation of an integer number of channel uses. In the future, we plan to investigate fractional bandwidth allocation, which will provide finer-granularity resource adjustment. A possible way to realize this challenging idea is through linear channel coding in real number field (or analog channel coding). We believe that there is great potential in analog channel coding design for improving the efficiency of linear video transmission. R EFERENCES [1] S. Jakubczak and D. Katabi, “A cross-layer design for scalable mobile video,” in Proc. 17th Annu. ACM Int. Conf. MobiCom Netw., Las Vegas, NV, USA, 2011, pp. 289–300. [2] X. L. Liu, W. Hu, Q. Pu, F. Wu, and Y. Zhang, “ParCast: Soft video delivery in MIMO-OFDM WLANs,” in Proc. 18th Annu. ACM Int. Conf. MobiCom Netw., Istanbul, Turkey, 2012, pp. 233–244. [3] X. Fan, F. Wu, D. Zhao, and O. Au, “Distributed wireless visual communication with power distortion optimization,” IEEE Trans. Circuits Syst. Video Technol., vol. 23, no. 6, pp. 1040–1053, Jun. 2013. [4] H. Cui et al., “Cactus: A hybrid digital-analog wireless video communication system,” in Proc. 16th ACM Int. Conf. MSWiM, Barcelona, Spain, 2013, pp. 273–278. [5] K. H. Lee and D. P. Petersen, “Optimal linear coding for vector channels,” IEEE Trans. Commun., vol. 24, no. 12, pp. 1283–1290, Dec. 1976. [6] S. Jakubczak, J. Sun, D. Katabi, and V. Goyal, “Performance regimes of uncoded linear communications over AWGN channels,” in Proc. 45th CISS, Mar. 2011, pp. 1–6. [7] W. Wong, R. Steele, B. Glance, and D. Horn, “Time diversity with adaptive error detection to combat Rayleigh fading in digital mobile radio,” IEEE Trans. Commun., vol. 31, no. 3, pp. 378–387, Mar. 1983. [8] G.-T. Chyi, J. Proakis, and C. Keller, “On the symbol error probability of maximum-selection diversity reception schemes over a Rayleigh fading channel,” IEEE Trans. Commun., vol. 37, no. 1, pp. 79–83, Jan. 1989. [9] C. E. Shannon, “A mathematical theory of communication,” Bell Syst. Tech. J., vol. 27, no. 3, pp. 379–423, Jul. 1948. [10] C. A. Floudas, Nonlinear and Mixed-Integer Optimization: Fundamentals and Applications. London, U.K.: Oxford Univ. Press, 1995. [11] H. Cui, C. Luo, C. W. Chen, and F. Wu, “Robust uncoded video transmission over wireless fast fading channel,” in Proc. IEEE 33rd INFOCOM, 2014, pp. 1–9.


[12] X. Fan, F. Wu, D. Zhao, O. C. Au, and W. Gao, “Distributed soft video broadcast (DCAST) with explicit motion,” in Proc. DCC, Apr. 2012, pp. 199–208. [13] J. Goblick and T. Goblick, Jr., “Theoretical limitations on the transmission of data from analog sources,” IEEE Trans. Inf. Theory, vol. 11, no. 4, pp. 558–567, Oct. 1965. [14] M. Gastpar, B. Rimoldi, and M. Vetterli, “To code, or not to code: Lossy source-channel communication revisited,” IEEE Trans. Inf. Theory, vol. 49, no. 5, pp. 1147–1158, May 2003. [15] A. Kashyap, T. Basar, and R. Srikant, “Minimum distortion transmission of Gaussian sources over fading channels,” in Proc. 42nd IEEE Conf. Decision Control, Dec. 2003, vol. 1, pp. 80–85. [16] J. J. Xiao, Z. Q. Luo, and N. Jindal, “CTH16-2: Linear joint sourcechannel coding for Gaussian sources through fading channels,” in Proc. IEEE GLOBECOM, Nov. 2006, pp. 1–5. [17] G. de Oliveira Brante, R. Demo Souza, and J. Garcia-Frias, “Analog joint source-channel coding in Rayleigh fading channels,” in Proc. IEEE ICASSP, May 2011, pp. 3148–3151. [18] Y. Hu, J. Garcia-Frias, and M. Lamarca, “Analog joint source-channel coding using non-linear curves and MMSE decoding,” IEEE Trans. Commun., vol. 59, no. 11, pp. 3016–3026, Nov. 2011. [19] Y. Kochman and R. Zamir, “Analog matching of colored sources to colored channels,” IEEE Trans. Inf. Theory, vol. 57, no. 6, pp. 3180–3195, Jun. 2011. [20] U. Mittal and N. Phamdo, “Hybrid digital-analog (HDA) joint sourcechannel codes for broadcasting and robust communications,” IEEE Trans. Inf. Theory, vol. 48, no. 5, pp. 1082–1102, May 2002. [21] Y. Wang, F. Alajaji, and T. Linder, “Hybrid digital-analog coding with bandwidth compression for Gaussian source-channel pairs,” IEEE Trans. Commun., vol. 57, no. 4, pp. 997–1012, Apr. 2009. [22] J. B. Rosen, “The gradient projection method for nonlinear programming. Part I. Linear constraints,” J. Soc. Ind. Appl. Math., vol. 8, no. 1, pp. 181– 217, Mar. 1960. [23] R. Xiong, F. Wu, J. Xu, and W. Gao, “Performance analysis of transform in uncoded wireless visual communication,” in Proc. IEEE ISCAS, May 2013.

Hao Cui received the B.S. degree in electronic engineering and the Ph.D. degree in signal and information processing from the University of Science and Technology of China in 2008 and 2014, respectively. His research interests include source coding, channel coding and signal processing for wireless multimedia communication and networking.

Chong Luo (M’05) received the B.S. degree from Fudan University, Shanghai, China, in 2000, the M.S. degree from the National University of Singapore in 2002, and the Ph.D. degree from Shanghai Jiao Tong University in 2012. She has been with Microsoft Research Asia since 2003, where she is a Lead Researcher in the Internet Media group. Her research interests include wireless networking, wireless sensor networks and multimedia communications.

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Chang Wen Chen (F’04) received the B.S. degree from the University of Science and Technology of China in 1983, the M.S.E.E. degree from the University of Southern California, Los Angeles, CA, USA, in 1986, and the Ph.D. degree from the University of Illinois at Urbana-Champaign, IL, USA, in 1992. He is a Professor of Computer Science and Engineering at the State University of New York at Buffalo. Prof. Chen has been the Editor-in-Chief for IEEE T RANSACTIONS ON M ULTIMEDIA since January 2014. He also served as the Editor-in-Chief for IEEE T RANSACTIONS ON C IRCUITS AND S YSTEMS FOR V IDEO T ECHNOLOGY from January 2006 to December 2009. He has served as an Editor for P ROCEEDINGS OF THE IEEE, IEEE J OURNAL ON S ELECTED A REAS IN C OMMUNICATIONS , IEEE J OURNAL ON E MERGING AND S ELECTED T OP ICS IN C IRCUITS AND S YSTEMS , IEEE Multimedia Magazine, Journal of Wireless Communication and Mobile Computing, EUROSIP Journal of Signal Processing: Image Communications, and Journal of Visual Communication and Image Representation. He has also chaired and served in numerous technical program committees for IEEE and other international conferences. He was elected an IEEE Fellow for his contributions in digital image and video processing, analysis, and communications, and elected an SPIE Fellow for his contributions in electronic imaging and visual communications.

Feng Wu (F’13) received the B.S. degree in electrical engineering from XIDIAN University in 1992, and the M.S. and Ph.D. degrees in computer science from the Harbin Institute of Technology, Harbin, China, in 1996 and 1999, respectively. He joined Microsoft Research Asia, Beijing, China, in 1999, where he was a Principle Researcher/Research Manager. He has been a Professor of electronic engineering and information science at the University of Science and Technology of China since 2014. Prof. Wu serves as an Associate Editor for various publications, such as the IEEE T RANSACTIONS ON C IRCUITS AND S YSTEMS FOR V IDEO T ECHNOLOGY and IEEE T RANSACTIONS ON M ULTIMEDIA . He served as the Technical Program Committee (TPC) Chair for MMSP 2011, VCIP 2010 and PCM 2009, the TPC Track Chair for ICME 2013, ICIP 2012, ICME 2012, ICME 2011 for ICME 2009, and the Special Sessions Chair for ISCAS 2013 and ICME 2010. He was the recipient of the Best Paper Award at IEEE T-CSVT 2009, PCM 2008, and SPIE VCIP 2007. He was elected an IEEE Fellow for his contributions to visual data compression and communication.