Post on 04-Jul-2018
(Error Control) Coding for Wireless Networks
IAB 2005
Predrag Spasojevic
WINLAB, Rutgers University
reliability
adaptability
Wireless Networks: Performance Analysis
link quality
spectral efficiency
radio processing capabilities
layered information
service requirements
observability
can radios collaborate?
topology
low delay
performance evaluation
multiple access
performance prediction
channel model
signaling schememodulation
Parallel Channel Modeling
+
=> parallel channel model
network topology
+
performance analysis
=>
block-fading
frequency hopping
multi-carrier
incremental redundancy HARQ
time hopping
frequency diversity
time diversity
unequal error protection
spatial diversity
multi-user diversity
cooperative diversity
multi-path
MIMO
cooperative multi-hop
multilevel codingBICM layered signaling
broadcast/multicast
multiplexing
puncturing
rate adaptation
collision channel
orthogonal signaling
adaptive modulation
Parallel Channels: Models
block-fading
incremental redundancy HARQ
cooperative diversitycooperative multi-hop
multilevel codingBICM layered signaling
broadcast/multicast
puncturing
rate adaptation
adaptive modulation
Parallel Channels: Performance of Good Codes for
Codeword transmission over parallel channels
Rcv
Tx
mother codeword (n bits)
Ch 1
Ch 2
Ch 3
On the Performance of Good Codes over Parallel Channels
This work has been supported in part by the NSF Grant SPN-0338805.
Ruoheng Liu, Predrag Spasojevic Emina SoljaninWINLAB, Rutgers University Bell Labs, Lucent
What is a “good” code?
• good codes:– a sequence of binary linear codes
– achieve arbitrarily small word error probability (WEP) over a noisy channel at a nonzero threshold rate.
– include turbo codes, LDPC codes, and RA codes
• capacity achieving codes – good codes
– rate threshold is equal to the channel capacity
∞== 1)}({ iinΧΧ=
MacKay 99
0)( ,0)(lim Γ>Γ=Γ
∞→
nWn
PΧ
-2 0 2 4 6
10-3
10-2
10-1
100
Es/N0 (R=0.7)
WE
P
n=500n=5000
-2 0 2 4 6
10-3
10-2
10-1
100
Es/N0 (R=0.7)
WE
P
n=500n=5000
-2 0 2 4 6
10-3
10-2
10-1
100
Es/N0 (R=0.7)
WE
P
n=500n=5000
Threshold behavior of good codes
• an example of turbo codes– R=0.7– n=500, 5000– binary input AWGN channel
• code goodness implies there exists a threshold Γ0
Γ: received SNR.
Receiver SNR Γ
Code Goodness (Liu etal. 2004)
codebook design requirement(transmitting a codeword x)
– distance from x to other codewords is large
– the number of x’s neighbors is small(low weight spectrum slope of a good code)
)(min ∞→nd Χ
∞<∞→
)(suplim )(n
n
nfS Χ
-2 0 2 4 6
10-3
10-2
10-1
100
Es/N0 (R=0.7)
WE
P
n=500n=5000 • single channel
– Richardson and Urbankeiterative decoding
– Jin, McEliece, et. al. typical pair decoding
– Sason and Shamaimaximum likelihood (ML) decoding
– Ashikhmin, et. al. (Exit chart)
• parallel channel model?
?
Receiver SNR Γ
R=0.7
Threshold calculation
αj : (asymptotic) assignment rate 11
=∑=
J
jjα
Parallel channel model
• under what channel conditions will the communication be reliable?
• codeword is partitioned and transmitted over parallel channels
Reliable channel regionTurbo codes with R=1/3, two parallel AWGN channel, α1=α2=1/2
0 0.2 0.4 0.6 0.8 1 1.2 1.40
0.2
0.4
0.6
0.8
1
1.2
1.4
Channel 1: Es/N0
Cha
nnel
2: E
s/N
0
TC k=3840, WEP=10-2
TC k=3840, WEP=10-3
Pw[Χ(n)] 0
Pw[Χ(n)]≈1
Channel 1: Γ1
Chan
nel 2
: Γ 2
Union Bhattacharyya (UB) threshold
UB reliable channel region
if
then average ML decoding WEP
– UB threshold
– normalized weight spectrum
– average Bhattacharyya noise parameter
δδ
δ
)( suplim max)]([
10
][0
n
n
rcΧ
Χ
∞→≤≤=
0lim )]([ =∞→
nWn
P Χ
][0ln Χc>− γ
∑=j
jjγαγ
⎣ ⎦( )
ln)(
)]([)]([
nnA
rn
n δδ
ΧΧ =
effectiveBhattacharyya distance
Two code parameter description
if
then average ML decoding word error probability
average channel mutual infomation
.0lim )]([ =∞→
nWn
P Χ
][][ and ln ΧΧPP RIc ζγ +>>−
∑=
=J
jjj II
1α
Single parameter description: simple threshold (Liu etal. 2004)
if
then the average ML decoding word error probability
{ }][][][][ )exp(1 : min ΧΧΧΧPPPP
Rccc ζ+≥−−=∗
0lim)]([=
∞→
nW
nP
Χ
][*ln Χc>− γ
UB threshold vs simple threshold
• an example of turbo code (R=1/7, k=768, and J=3 RSC encoders)
– UB threshold
– simple threshold
dBc 77.6 21.0][0 −⇒=Χ
dBc 70.7 17.0][* −⇒=Χ
Puncturing and Block Fading Channel• punctured simple code threshold
– : punctured rate
• simple threshold bound on block fading channel coding
– decoding is done with full channel state information (CSI)
)1()exp(ln)(
][*
][* τ
ττ−+−
=C
C
cc P
τ−1
[ ]{ } )1(ln
)()(][
*
)]([)]([
ocPPP n
W
nW
+≤−≤
=Χ
ΧΧ
γγγ E
Adaptive Modulation for Variable-Rate Turbo-BICM
Ruoheng Liu, Jianghong Luo and Predrag SpasojevicWINLAB, Rutgers University
This work has been supported in part by the NSF Grant SPN-0338805.
Motivationkey requirements in 4G or B3G communications systems:
a wide range of data rates according to economic and service demands
QoS for packet oriented services
high-speed wireless systems: bandwidth efficient turbo coding scheme
Turbo BICM -- Goff 94’ [simplicity]
Parallel concatenated TCM -- Benedetto 95’
Turbo-TCM -- Roberton, 98’
channel fluctuating in the wireless propagation environment
communication reliability and error prediction
lack of closed-form expressions for error probability of turbo coded modulation
mother TCencoder
randompuncturing
bitinterleaver
Gray-mappingM-QAM
mother code rater0
code rater0/(1-λ)
punctured rateλ
demodulationdeinterleaverdepunctureriterativedecoder
channeltransmission rate
m r0/(1-λ)
System model
Rate threshold for VR-Turbo-BICM
Theorem:
For a VR-Turbo-BICM coding scheme using a mother code ensemble [C] of rate r0employed over an AWGN channel with a channel SNR ρ we define the rate threshold
If
then the average ML decoding word error probability approaches zero.
⎪⎩
⎪⎨
⎧
>−≤≤⋅
<=°
∞ )()],(1[)()(),()(
)(0),(
mmrmmmImmb
mmr
m ςρργςρηρ
ηρρ
),( mrr ρ°≤
-5 0 5 10 15 20 250
0.5
1
1.5
2
2.5
3
SNR ρ (dB)
rate
thre
shol
ds (b
it/re
al d
imen
sion
)
simulation (m=1)simulation (m=2)simulation (m=3)rate thresholdsAWGN capacity
vs. simulation results (FER=0.01)
Rate Threshold vs SNR
64 QAM
16 QAM
QPSK
) ,( mr ρ°
-5 0 5 10 15 20 250
0.5
1
1.5
2
2.5
3
Pav (dB)
Rav
(bits
/real
dim
ensi
on)
Near-optimum power allocationergodic capacity
Adaptive Turbo-BICM in slow fading
( )[ ][ ]
{ }.,...3,2,1,0)( ,0)( )(
)(),(max )(),(
∈≥≤
°
gmgPPgPE
gmgPrE
av
nmnP
to subject
Allocation Problem:
given an average power constraint Pav, the optimum power and modulation index maximize the expected rate threshold
Cooperative Diversity with Incremental Redundancy (IR) Turbo Coding
for Quasi Static Wireless Networks
This work has been supported in part by the NSF Grant SPN-0338805.
Ruoheng Liu, Predrag Spasojevic Emina SoljaninWINLAB, Rutgers University Bell Labs, Lucent
broadcast
Source Sink
traditional multi-hop transmission
Source Relay Sink
direct transmission
Source
Relay
Sinkcooperative transmission
☺
Cooperation benefit: reliability
wireless communications
Reliable transmission
Deep fading
Diversity ☺
Error rate ~ SNR-2
Error rate ~ SNR-1
M-user Cooperation
– M users share radio channel
– orthogonal frequency-division multiple access scheme
– 2 Hops scheme (for each user)
M-user Cooperation (cont.)• Large SNR (asymptotic result)
– Using cooperative coding each user can achieve full (M) diversity gain
• Medium and low SNR (how to get benefit ? cooperation criteria …)– the user-to-destination channel quality is good (same to two user case)– partners are sufficiently close (cluster behavior)
non-cooperative routingcooperation enhanced routing
Wireless cooperative routing in networkswith quasi-static fading
collaborating cluster
Frame error rate of the cooperative routing scheme
• simple threshold upper bound
– θ(F): effective cluster-to-destination SNR
• asymptotic upper bound (small c*[TC] and large ρ, λ)
∑−
=
+−++−
+−⋅
⎟⎟⎠
⎞⎜⎜⎝
⎛ −≤
1
0
)1()1(][
*,, )!1)((
)(1][
*
M
k
kkMM
c(M)
kkMcM
kM
λρρλ
TC
CFER
( ){ }kcPkPk
MM
k
(M) =≤⋅=⎟⎟⎠
⎞⎜⎜⎝
⎛ −≤ ∑
−
=
FFF TC |)(1 ][
*
1
0
θFER
Diversity Gain vs M
-10 -5 0 5 10 15 20 2510-6
10-5
10-4
10-3
10-2
10-1
100
cluster-to-destination SNR λ (dB)
FER
simulationupper bound
M=1
M=2
M=5
fast fading
13 dB8 dB8 dB
Cluster-to-destination SNR vs. M
0 1 2 3 4 50
5
10
15
20
25
cluster size M
clus
ter-t
o-de
stin
atio
n S
NR
λ (d
B) FER=10-3
Rate Design for Layered Broadcast using Punctured LDPC Codes and Multilevel Coding
Ahmed Turk and Predrag Spasojević
Coding for Broadcast
• superposition structure– successive refineable
sources
– hierarchical channel coding
• code rate selection– different channel conditions
– unequal error protection
Multilevel Broadcast System Encoder
21 RRRt +=
Graymapping4‐ASK
C2
C1
a
q2 Regular LDPCencoder
R0,2
Random puncturing
λ2
Punctured LDPC encoder
R2
q1 Regular LDPCencoder
R0,1
Random puncturing
λ1
Punctured LDPC encoder
R1
2
2,02 1 λ−=
RR
1
1,01 1 λ−=
RR
Goodput vs worst user SNR(n,3,4) mother code in each level
minδ
Incremental Multi-Hop based on Punctured Turbo Codes
Ruoheng Liu, Predrag Spasojevic Emina SoljaninWINLAB, Rutgers University Bell Labs, Lucent
System Model
• one-dimensional multi-hop network with P nodes
• equal distance between the neighboring nodes
0,13,22,1 dddd PP ==== −L
Performance Analysis (1)
Given:
Step 2Step 1
)1(1)exp(1 ][
01 γ
α−
−−>
Χc [ ])1(1
)2(1)exp(1 1][
02 γ
γαα−
−−−−>
Χc
1α
Performance Analysis (cont.)
Step 3 Step 4
[ ])1(1
)1(1)exp(11
1
][0
γ
γαα
−
+−−−−−>
∑−
=
j
kk
j
kjc Χ
Given: 11 ,, −jαα L
IR multi-hop transmission scheme (2)
Node 2
Node 3
Node 4
Node 1
mother codeword (n bits)
Hop 1: α1n bits
Hop 2: α2n bits
Hop 3: α3n bits
• High SNR0:QSNR
1lim0
=∞→η
Energy Savings
• low SNR0: ∑ =−→
= Q
jmSNR j1
0
1lim0
η
• energy ratios:∑ =
−−
=== Q
j
Q
total
Qtotal
jQEE
1)1(
)(
)1(
)(
)()1(1γ
γααη
-10 -5 0 5 100
0.2
0.4
0.6
0.8
1
SNR0 (dB)
ener
gy ra
tio
Q=1Q=2Q=4Q=10
Traditional vs. IR Multi-hop Transmissions
-10 -5 0 5 100
0.2
0.4
0.6
0.8
1
SNR0 (dB)
ener
gy ra
tioQ=1Q=2Q=4Q=10
m=3m=2energy savings
Repetition Coding vs. IR Schemes
5 10 15 200.5
0.6
0.7
0.8
0.9
1
1.1
index of node j (m=2)
ener
gy ra
tio E
tota
lj
/Eto
tal
1
5 10 15 200.5
0.6
0.7
0.8
0.9
1
1.1
index of node j (m=3)
Repetition codingIncremental redundancy
Repetition codingIncremental redundancy
• SNR0=0 dB
• m=2,3
coding gain