(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