ee372_pres.ppt

Department of Electrical EngineeringStanford University

Xiaoqing Zhu

EE372 Final Project

Congestion-aware Bite Allocation For Multi-path Video Streaming Over Ad Hoc Wireless Networks

X. Zhu: EE372 Project Presentation December 3, 2003

Outline Video streaming over ad hoc wireless network

Bit allocation over multiple paths, across many frames Problem formulation Modeling of encoder distortion-rate function Modeling of network congestion effect Two allocation modes: scalable vs. repetition

Optimal bit allocation via Two heuristic schemes Gradient descent Iterative descent

Experimental results Gaussian samples over M/M/1 channels Video sequence over simulated network


Video Over Wireless Ad Hoc Networks Ad Hoc Wireless Networks:

Wireless nodes self-configure into a network Restricted bandwidth and power resources, adverse channel

conditions=> limited and varying transmission rate on each link

Many applications with multimedia: search-and-rescue, highway automation, Internet access etc.

Video streaming challenges: High bandwidth requirement Stringent delay constraint

Combined: the self-congesting effect


Multi-path Video Streaming

Benefit of path diversity: Expansion of available bandwidth More robust to correlated packet losses

[J. Apostolopoulos, 1999][S. Mao et al., 2003]

Need bit allocation over multiple paths,

across different frames


Problem Formulation: Notations

Bit allocation matrix [Rml] Path index: m = 1, … M Frame index: l = 1, …, L

Packet playout deadline: Tplayout,

Packet size: B Video frame rate: Vfps

Number of nodes in the network: N Link capacity from node i to node j: Cij, i,j = 1, …, N

Cross traffic bitrate from node i to node j: Fij, i,j = 1, …, N


Problem Formulation: Optimization

To find the optimal rate allocation matrix R :

Minimize Exp [Ddec] = f(D(l)enc(R), Pm(R, Vfps, Tplayout,

B))Subject to: Rml ¸ 0

Rml · Rml(max)

(Vfps/L)Ll=1(Rml) · Cij-Fij, (i,j)2Pm

m = 1, …, M, l = 1, …, L

Where D(l)

enc(.) is encoder distortion-rate function for the matrix R

Pm(.) is the function for packet drop rate due to congestion

f(.) denotes taking expectation over D(l)enc according to Pm(.)


Wavelet Video Coder

TemporalWavelet

Transform

TemporalWavelet

Transform

Spatial Wavelet

Transform

Spatial Wavelet

Transform

7654

321

0

HH

LLL LLHLH

LH

Original

video framesH

HHHH

HHHH

HHHH

HHH

EmbeddedQuantization &Entropy Coding

EmbeddedQuantization &Entropy Coding

[Taubman & Zakhor, 1994] [Ohm, 1994] [Choi & Woods, 1999] [Hsiang & Woods, VCIP ’99] . . .

Scalable bitstream


Encoder Distortion Model Now l indexes the sub-band image in the wavelet coefficient

domain High rate approximation of transform vector quantization:

D(R) = Mi=1Ki2-2Bi/Ni, where Ki , (Ni/N)Cni\

||pi||Ni/(2+Ni) ,

[M. Goldburg 1993] Therefore, model the RD curve of each sub-band image as

sum of exponentials:

d (l)enc(r) = K

i=1i e-i r , l = 1, …, L

Further assume additive contribution

from each sub-band image:

Exp(Ddec) = Ll=1Exp(D(l)

enc(R))


Network Congestion Model

Assume independent delays on each path, congestion dominated by the bottleneck link Cm, Fm for path m.

M/M/1 queuing model for delay distribution: Exponential: Xm ~ fX(x)=1/m e-mXm

Average delay: Exp(Xm)=1/m = B/(Cm-Fm-Sm)

Drop rate: Pm = e-m Tplayout = e -(Cm-Fm-Sm)Tplayout/B

Usually the drop rate is overestimated, need a correction factor


Code Mode: Scalable vs. Repetitive

Scalable rate allocation: Non-overlaping information on each path Higher efficiency in error-free situation D(l)

enc(Ra, Rb) = d(l)enc(Ra + Rb)

Repetitive rate allocation: Repeating the starting part of the bitstream on both

paths Sacrifice coding efficiency Better robustness to channel errors and packet loss D(l)

enc(Ra, Rb) = min(d(l)enc(Ra), d(l)

enc( Rb))

Path 1

Path 2

Path 1

Path 2


Heuristic Scheme

Rate allocation across all frames minimizing the Lagrangian cost function for all sub-band images:

R(l)total= argminR D(l)

enc(R) + R

Rate allocation over each path w.r.t. the bottleneck link A: proportional to residual capacity B: inverse water-filling: equal residual capacity

Optimal source coding strategy, heuristic allocation over multiple paths


Cost function non-convex w.r.t. the rate matrix R Cost function convex w.r.t. individual Rml’s

Initialize the rate matrix using the heuristic scheme

Search for a local minimum: Gradient descent algorithm Iterative descent algorithm

Alternatives: random initialization

Optimal Scheme Via Gradient Descent


Numerical calculation with i.i.d Gaussian samples: Denc(R) = 2 e-2R

Pm(R) = e -(Cm-Fm-Sm)Tplayout/B, where Sm =(Vfps/L) Ll=1Rml

Randomly chosen capacity and cross traffic rate for M=2 channels

Network simulation with video: Foreman QCIF video sequence at Vfps=30 frame/second 3-D wavelet-based coded scalable bistream, L = 300 frames A network with 15 randomly placed nodes, M = 2 paths Link capacities calculated based on Shannon’s formula for

AWGN Cross traffic randomly fills up to 70% of link capacity Simulation performed with ns-2 (http://www.isi.edu/nsnam/ns/

)

Experimental Setup


Gaussian Results: Scalable Mode

0 1 2 3 4 5 6 7 80

10

20

30

40

50

60

70

80

90

100

Rate (bit)

Dist

ortio

n E(

X2 )

Distortion-Rate Performance for Gaussian, Residual Channel Rate = (4.29,3.16), Scalable

encoderheuristic

Aheuristic

Boptimal

0 1 2 3 4 5 60

10

20

30

40

50

60

70

80

90

100

Rate (bit)

Dis

torti

on E

(X2 )

Distortion-Rate Performance for Gaussian, Residual Channel Rate = (1.74,3.61), Scalable

encoderheuristic

Aheuristic

Boptimal

Variance: 2 = 100;Residual link capacity:Channel 1: 4.29 bits/useChannel 2: 3.16 bits/use



Gaussian Results: Repetition Mode

0 1 2 3 4 5 6 7 8 90

20

40

60

80

100

120

Rate (bit)

Dis

torti

on E

(X2 )

Distortion-Rate Performance for Gaussian, Residual Channel Rate =( 5.47, 2.95), Repetition

encoderheuristic

Aheuristic

Boptimal

0 2 4 6 8 10 12 140

20

40

60

80

100

120

Rate (bit)

Dis

torti

on E

(X2 )

Distortion-Rate Performance for Gaussian, Residual Channel Rate =( 6.53, 5.86), Repetition

encoderheuristic

Aheuristic

Boptimal




Video Results: Repetition Mode

Sequence : Foreman QCIF (Y)

Sequence length : 300

Frame rate : 30 fps

GOP length: 16 frames

Temporal trans.: 1-level Haar

Spatial transf.: 3-level bi-9/7

Playout deadline : 150 ms

Packet Size: 1000 bytes

Random loss rate: 0 %

Simulation time: 10,000 seconds

No. of realizations: 39

Figure: scalable

0 50 100 150 200 250 300 350 40010

15

20

25

30

35rate vs. psnr

Rate (kbps)

PS

NR

(dB

)

encoderheuristicoptimal

Residual channel rates = [141.89, 258.15] T

playout = 150 ms

Packet size = 1000 bytes Code mode = 'repetition'

PSNR(dB)

Model simulation

Heuristic 30.45 30.49Optimal 31.09 31.28


Video Results: Scalable Mode

0 50 100 150 200 250 300 350 4000

5

10

15

20

25

30

35rate vs. psnr

Rate (kbps)

PS

NR

(dB

)

encoderheuristicoptimal

Residual channel rates: [141.89, 258.15] kbps T

playout = 150 ms

Packet size = 1000 byte Code mode = 'scalable'

Sequence : Foreman QCIF (Y)

Sequence length : 300

Frame rate : 30 fps

GOP length: 16 frames

Temporal trans.: 1-level Haar

Spatial transf.: 3-level bi-9/7

Playout deadline : 150 ms

Packet Size: 1000 bytes

Random loss rate: 0 %

Simulation time: 10,000 seconds

No. of realizations: 39

PSNR(dB)

Model simulation

Heuristic 32.76 33.02Optimal 33.30 33.59


Summary Optimize rate-allocation considering both the encoder rate-

distortion trade-off and the effect of packet drop rates due to network congestion

Modeling of encoder distortion-rate performance based on high-rate quantization theory

Modeling of network congestion effect based on M/M/1 queuing theory

Initialize from a heuristic scheme Optimization via gradient descent or iterative descent

Numerical results for Gaussian random samples Experimental results for video streaming over simulated ad hoc

wireless network, gain from heuristic scheme around 0.5dB in PSNR for received video quality


Problem Formulation: Objective Function

On the mth path: Data rate: Sm = Sm(Vfps, R(m,:)) Set of links: Pm = {(i,j)|path m includes nodes i and j} End-to-end delay distribution:X ~ fX(x) depends on

{Cij|(i,j)2 Pm}, {Fij2 Pm}, and Sm

Packet drop rate: P(m)= Pr{X>Tplayout} =Pm(R, Vfps, Tplayout ,B)

For the lth frame: Encoder performance: D(l)

enc(r)

Expected distortion at the decoder: Ddec = f(Denc(R), P(R, Vfps, Tplayout, B)) Depends on the code mode: scalable vs. repetition

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