Transcript The Turbo Decoding Principle Tutorial Introduction and

Iterative Detection and Decoding
for Wireless Communications
Matthew Valenti
Dissertation Defense
July 8, 1999
Advisor: Dr. Brian D. Woerner
VIRGINIA POLYTECHNIC INSTITUTE & STATE UNIVERSITY
MPRG
MOBILE & PORTABLE RADIO RESEARCH GROUP
Mobile and Portable Radio Research Group
Bradley Department of Electrical and Computer Engineering
Virginia Tech
Blacksburg, Virginia
irginia
V
Tech
1872
VIRGINIA POLYTECHNIC INSTITUTE
AND STATE UNIVERSITY
Outline

Introduction and background

Outline


Turbo codes for the wireless channel



Turbo codes
Iterative decoding algorithms
Performance over fading channels
Receiver/system design for time-varying channels
Multiuser detection for coded multiple-access networks



Distributed multiuser detection
Turbo-MUD: iterative multiuser detection and error correction
Cooperative decoding for TDMA networks
Error Correction Coding

Channel coding adds structured redundancy to a
transmission.
Introduction
m





Channel
Encoder
x
The input message m is composed of K info bits.
The output code word x is composed of N code bits.
Since N > K there is redundancy in the output.
The code rate is r = K/N.
(Hamming) weight



Number of ones in the message m
For linear codes, high weight code words are desired
Minimum distance dmin limits performance
Power Efficiency of
Coding Standards
1.0
Iridium
1998
Code Rate r
Spectral Efficiency
Uncoded
BPSK
Pioneer
1968-72
Turbo Code
1993
0.5
Globalstar
1999
Voyager
1977
Galileo:LGA
1996
Odenwalder
Convolutional
Codes 1976
Galileo:BVD
1992
Mariner
1969
Pb  105
-2
-1
0
1
2
3
4
Eb/No in dB
5
6
7
8
9
10
Convolutional Codes

xi( 0 )
mi
D
D


xi(1)
Constraint Length Kc = 3
A convolutional encoder encodes a
stream of data.
The size of the code word is
unbounded.
The encoder is a Finite Impulse
Response (FIR) filter.




k binary inputs
n binary outputs
Kc -1 delay elements
All operations over GF(2)


Addition: XOR
Multiplier coefficients are either 1 or 0
Recursive Systematic
Convolutional Encoding

Input
Systematic output
xi( 0 )
mi
xi
ri
D


D

(1)
i
x
Parity output
An RSC encoder is constructed
from a standard convolutional
encoder by feeding back one of
the outputs.
An RSC code is systematic.
The input bits appear directly in the
output.
An RSC encoder is an Infinite
Impulse Response (IIR) Filter.


Many low weight inputs produce high
weight outputs.
Some inputs will cause low weight
outputs.
Turbo Codes:
Parallel Concatenated Codes
with Nonuniform Interleaving

Turbo Codes



A stronger code can be created by encoding in parallel.
A nonuniform interleaver changes the ordering of bits at
the input of the second encoder.
It is very unlikely that both encoders produce low weight
code words.
MUX increases code rate from 1/3 to 1/2.
Systematic Output
Input
Encoder
#1
xi
MUX
Nonuniform
Interleaver
Encoder
#2
Parity
Output
Turbo code performance

Coding dilemma:
Turbo Codes


Random coding argument:



“All codes are good, except those that we can think of.”
Truly random codes approach capacity, but are not feasible.
Turbo codes appear random, yet have enough structure to
allow practical decoding.
Distance spectrum argument:

Traditional code design focused on maximizing the
minimum distance.


dmin determines performance at high SNR
With turbo codes, the goal is to reduce the multiplicity of
low weight code words.

Even with small dmin, remarkable performance can be achieved
at low SNR.
Minimum-distance Asymptote
0
10
Convolutional Code
CC free distance asymptote
Turbo Code
TC free distance asymptote
-2
10

d min  18
~
N min w
min
lim
 187
K 
K

E
Pb  187Q 18 b
No

BER
-4
10





For turbo code:
d min  6
~
N min w
3 2
min

K
65536

E
Pb  9.2 105 Q 6 b
No

-6
10
-8
10
0.5
For convolutional code:
1
1.5
2
2.5
Eb/No in dB
3
3.5
4




Performance for various
frame/interleaver sizes
0
10
K=1024
K=4096
K=16384
K=65536
-2


10

BER


-4
10
-6
10
-8
10
0.5
1
1.5
2
Eb/No in dB
2.5
3
Kc = 5
Rate r = 1/2
18 decoder iterations
Log-MAP decoder
AWGN Channel
The Turbo-Principle
Iterative decoding

Turbo codes get their name because the decoder uses
feedback, like a turbo engine.
Iterative Decoding
Deinterleaver
Extrinsic
Information
Extrinsic
Information
Iterative decoding
systematic
data
parity
data
Decoder
#1
Interleaver
Decoder
#2
DeMUX
hard bit
decisions
Interleaver

There is one decoder for each elementary encoder.




Estimates the a posteriori probability (APP) of each data bit.
Extrinsic Information is derived from the APP.
The Extrinsic Information is used as a priori information by
the other decoder.
Decoding continues for a set number of iterations.
 Obeys law of diminishing returns
Soft-Input Soft-Output (SISO)
Decoding Algorithms
Trellis-Based
Estimation Algorithms
Viterbi algorithm
Iterative decoding
1967 Viterbi
SOVA
Viterbi
Algorithm
MAP
Algorithm
1989 Hagenauer/Hoeher
Improved SOVA
1996 Papke/Robertson/Villebrun
SOVA
max-log-MAP
MAP algorithm
1974 Bahl/Cocke/Jelinek/Raviv
Improved
SOVA
log-MAP
max-log-MAP
1990 Koch and Baier
Sequence
Estimation
Symbol-by-symbol
Estimation
log-MAP
1994 Villebrun
Performance as a Function of
Number of Iterations
0
10

-1

10
1 iteration

-2
10

2 iterations
-3

BER
10
-4
10
6 iterations
3 iterations
-5
10
10 iterations
-6
10
18 iterations
-7
10
0.5
1
1.5
Eb/No in dB
2
Kc = 5
r = 1/2
K = 65,536
Log-MAP algorithm
AWGN
Summary of Performance Factors
and Tradeoffs

Latency vs. performance
Turbo Codes


Complexity vs. performance




Decoding algorithm
Number of iterations
Encoder constraint length
Spectral efficiency vs. performance


Frame/interleaver size
Overall code rate
Other factors



Interleaver design
Puncture pattern
Trellis termination
Turbo Codes
for Fading Channels
Fading channels

Many channels of interest can be modeled as a
frequency-flat fading channel.



Because of the time-varying nature of the channel, it is
necessary to estimate and track the channel.


Fading: channel is time-varying
Flat: all frequencies experience same attenuation
Channel estimation is difficult for turbo codes because they
operate at low SNR.
Questions:


How do turbo codes perform over fading channels?
How can the channel be estimated in a turbo coded system?

Goal is to develop channel estimation techniques that take
into account the iterative nature of the decoder.
System Model
turbo
encoder
xl
xl
channel
interleaver
fading
symbol
mapper
filter
s (t )
n(t )
y(t )
s (t )
yn
pulse shaping
filter
AWGN
c(t )
y(t ) matched
vn
channel
Fading channels
mi
transmitter
Input
data
channel
estimator
zn
symbol
demapper
rl
channel
deinterl.
rl
turbo
decoder
mˆ i Decoded
data
receiver
2 *
cˆn
ˆ 2
Fading Channel Types

c(t )   A  X (t )  jY (t ) .
Fading channels

X(t), Y(t) are Gaussian random processes.



A is a constant.


Represents the scattering component
Autocorrelation: Rc()
Represents the direct LOS component
Types of channels

AWGN: A=constant and X(t)=Y(t)=0
Rayleigh fading: A=0
Rician fading: A > 0, =A2/22
Correlated fading: Rc ()  J 0 (2f d )

Fully-interleaved fading: Rc ()  ()



Effect of Channel Correlation
0
10

Channel:


-2
10

Rayleigh fading
Correlated
Channel interleaver
BER


-4
10

f d Ts = .0025
f d Ts = .005
f d Ts = .01
no interleaving
block interleaving
fully interleaved
-6
10
0
2
4
6
Eb/No in dB


8
10
Perfect Estimates
Turbo code:


Depth = 32 symbols
Rate 1/2
KC=3
K=1024
Decoder:


Improved SOVA
8 iterations
Effect of Fading Distribution

SOVA
Log-MAP
Rayleigh
Rician, Gamma=1
Rician, Gamma=10
AWGN
0
10
Channel:



BER


10



-6
Perfect Estimates
Rate 1/2
KC=4
K=1024
8 decoder iterations

0
1
2
3
Eb/No in dB
4
5
6
Depth = 32 symbols
Turbo code:

-4
fdTs = .005
Channel interleaving

-2
10
10
Correlated fading

Log-MAP
Improved SOVA
Channel Estimation
for Turbo Codes

The turbo decoding algorithm requires accurate
estimates of channel parameters.
Fading channels

Branch metric:  (si  si1 )  ln P[mi ]  zis xˆis  zip xˆip
zi 
No

Noise variance:   2rE
Fading amplitude: an  cn

Phase: n  cn

2
2

2
yi ci*
b

(required for coherent detection)
Because turbo codes operate at low SNR, conventional
methods for channel estimation often fail.

Therefore channel estimation and tracking is a critical issue
with turbo codes.
Case 1:
Known Phase
Fading channels

Assume that the receiver is able to obtain accurate
estimates of the carrier phase n



PLL: Phase locked loop
Costas loop
The amplitude can be estimated using a Wiener filter:
aˆn 

Nc
w
i  Nc
i
y n i
The noise variance can be estimated as:
ˆ 2  CVar yn  aˆn 
1 N


ˆ
ˆ





y

a

y

a



n
n
i
i 
N  1 n1 
N i 1

C
N
2
Channel Estimation
with Known Phase
0
0
10
10
SOVA: Estimated SI
SOVA: Perfect SI
Log-MAP: Estimated SI
Log-MAP: Perfect SI
-1
10
-1
10
-2
-2
10
BER
BER
10
-3
10
-4
-4
10
10
-5
SOVA: Estimated SI
SOVA: Perfect SI
Log-MAP: Estimated SI
Log-MAP: Perfect SI
-5
10
10
-6
10
-3
10
-6
0
0.5


1.5
Eb/No in dB
2
2.5
AWGN
Turbo Code Parameters:


1
3
10
0



2
3
Eb/No in dB
4
5
6
Rayleigh flat-fading

r=1/2, Kc=4, L=1024
8 decoder iterations
1
FdTs = .005
Channel interleaver depth 32
Wiener filter w/ Nc = 30
Case 2:
Unknown Phase

Now assume that the receiver is unable to obtain
accurate estimates of the phase n.
Fading channels



Because turbo codes operate at low SNR, the PLL often
breaks down.
Because of the phase ambiguity, we no longer can use
the previous approach.
Coherent detection over Rayleigh fading channels
requires a pilot.

Pilot tone



TTIB: Transparent Tone in Band
1984: McGeehan and Bateman
Pilot symbols


PSAM: Pilot Symbol Assisted Modulation
1987: Lodge and Moher; 1991: Cavers
Pilot Symbol Assisted Modulation
(PSAM)

Pilot symbols:
Fading channels



Known values that are periodically inserted into the transmitted
code stream.
Used to assist the operation of a channel estimator at the
receiver.
Allow for coherent detection over channels that are unknown and
time varying.
segment #1
symbol
#1
symbol
#1
segment #2
symbol
#Mp
pilot
symbol
symbol
#1
symbol symbol
#Mp
#1
pilot symbols added here
symbol
#Mp
pilot
symbol
symbol
#Mp
Pilot Symbol
Assisted Decoding

Fading channels

Pilot symbols are used to obtain initial channel estimates.
After each iteration of turbo decoding, the bit estimates are
used to obtain new channel estimates.


Decision-directed estimation.
Channel estimator uses either a Wiener filter or Moving
average.
y(t )
matched
filter
yn
channel
estimator
 2 *
 2 cˆn 
 ˆ 
vˆn( q )
symbol
mapper
xˆ l( q )
channel
interleaver
xˆ (l q )
Tentative
estimates of
the code bits
(q)
symbol
demapper
rl (q )
channel
deinterl.
rl(q )
turbo
decoder
mˆ (i q)
Final
estimates of
the data
Performance of
Pilot Symbol Assisted Decoding
1

10
DPSK
conventional PSAM, unknown fades
turbo-PSAM, unknown fades
BPSK, perfect SI
0
10
Simulation parameters:


-1
10
Rayleigh flat-fading

Correlated: fdTs = .005

channel interleaving depth 32
Turbo code

r=1/2, Kc =4

1024 bit random interleaver
8 iterations of log-MAP
-2
10
BER


-3

10

At Pb = 10-5
-4

-5

10
10

-6
10
0
1
2
3
4
5
6
Eb/No in dB
7
8
9
10
Pilot symbol spacing: Mp = 8
Wiener filtering: Nc = 30
Noncoherent reception degrades
performance by 4.7 dB.
Estimation prior to decoding
degrades performance by 1.9 dB.
Estimation during decoding only
degrades performance by 0.8 dB.
Performance Factors for
Pilot Symbol Assisted Decoding
Fading channels


Performance is more sensitive to errors in estimates of
the fading process than estimates in noise variance.
Pilot symbol spacing



Type of channel estimation filter



Want symbols close enough to track the channel.
However, using pilot symbols reduces the energy available
for the traffic bits.
Wiener filter provides optimal solution.
However, for small fd, a moving average is acceptable.
Size of channel estimation filter

Window size of filter should contain about 4 pilot symbols.
Improving the Bandwidth
Efficiency of PSAM
1
10

DPSK
turbo-PSAM, Mp = 30
turbo-PSAM, Mp = 18
turbo-PSAM, Mp = 10
BPSK, perfect SI
0
10
Conventional PSAM requires a
bandwidth expansion.

-1

10

-2
BER
10
Previous example required
12.5% more BW.
This is because all code and
pilot symbols are transmitted.
Instead, could replace code
symbols with pilot symbols.
“Parity-symbol” stealing
Simulation Parameters:

-3
10


-4
10
Rayleigh fading


-5
10
Turbo code


-6
10
0
1
2
3
4
Eb/No in dB
5
6
7
8
fdTs = .005
Kc = 4, r = 1/2
L=4140 bit iterleaver
Performance in Rapid Fading
2
10

DPSK
PSAM, Mp=30
PSAM, Mp=18
PSAM, Mp=10
PSAM, Mp=6
ideal BPSK
0
10



BER
-2
-4
10
-6
10
2
3
4
5
6
Eb/No in dB
7
8
9
10
fdTs = .02
Turbo code

10
1
Rayleigh fading channel
Kc = 4, r = 1/2
L=4140 bit interleaver
Other Applications of the
Turbo Principle
Turbo principle


The turbo-principle is more general than merely its
application to the decoding of turbo codes.
Other applications of the turbo principle include:




Decoding serially concatenated codes.
Combined equalization and error correction decoding.
Combined multiuser detection and error correction
decoding.
(Spatial) diversity combining for coded systems in the
presence of MAI or ISI.
Serial Concatenated Turbo Codes
Serial Concatenated Codes
Data
Outer
Convolutional
Encoder
interleaver
Inner
Convolutional
Encoder
interleaver
Inner
Decoder
deinterleaver
n(t)
AWGN
Extrinsic Information
Outer
Decoder
Turbo
Decoder
Estimated
Data
Turbo Equalization
Can model intersymbol interference
channel as an FIR filter
Turbo EQ
Data
(Outer)
Convolutional
Encoder
interleaver
ISI
Channel
interleaver
SISO
Equalizer
n(t)
AWGN
deinterleaver
Extrinsic Information
(Outer)
SISO
Decoder
Turbo
Equalizer
Estimated
Data
Turbo Multiuser Detection
Time-varying FIR filter
Turbo MUD
d1
Convolutional
Encoder
#1
“multiuser interleaver”
interleaver #1
b1
Channel
Parallel
to
Serial
d Ku
Convolutional
Encoder
#K
interleaver #K
y
MAI
Channel
Model
bK
multiuser
interleaver
SISO
MUD
b
multiuser
deinterleaver
Extrinsic Info
Bank of
K SISO
Decoders
n(t)
AWGN
Turbo
MUD
dˆ ( q )
Estimated
Data
Direct Sequence CDMA

CDMA: Code Division Multiple Access

The users are assigned distinct waveforms.
Turbo MUD

Spreading/signature sequences
g k (t ) 

j 0
k, j
pc (t  jTc )
Use a wide bandwidth signal
Processing gain Ns



All users transmit at same time/frequency.


N s 1
Ratio of bandwidth after spreading to bandwidth before
MUD for CDMA

The resolvable MAI originates from the same cell.


Intracell interference.
MUD uses observations from only one base station.
Performance of Turbo-MUD
for CDMA in AWGN
0
0
10
10
Matched Filter
Turbo-MUD: iter 1
Turbo-MUD: iter 2
Turbo-MUD: iter 3
Single User Bound
-1
10
Matched Filter
Turbo-MUD: iter 1
Turbo-MUD: iter 2
Turbo-MUD: iter 3
-1
10
-2
-2
10
BER
BER
10
-3
-3
10
10
-4
-4
10
10
-5
-5
10
10
0
1



2
3
4
Eb/No in dB
5
6
7
K = 5 users
Spreading gain Ns = 7
Convolutional code: Kc = 3, r=1/2
1
2


3
4
5
6
Number of users
Eb/No = 5 dB
1K9
7
8
9
Performance of Turbo-MUD
for CDMA in Rayleigh Flat-fading
0
0
10
10
-1
-1
10
-2
10
10
-2
BER
BER
10
-3
10
-4
-4
10
10
Matched Filter
Turbo-MUD: iter 1
Turbo-MUD: iter 2
Turbo-MUD: iter 3
Single User Bound
-5
10
Matched Filter
Turbo-MUD: iter 1
Turbo-MUD: iter 2
Turbo-MUD: iter 3
-5
10
-6
-6
10
-3
10
10
0
2


4
6
8
10
Eb/No in dB
12
K = 5 users
Fully-interleaved fading
14
16
1
2


3
4
5
6
Number of users
Eb/No = 9 dB
1K9
7
8
9
Time Division Multiple Access

TDMA: Time Division Multiple Access

Turbo MUD




Users are assigned unique time slots
All users transmit at same frequency
All users have the same waveform, g(t)
TDMA can be considered a special case of CDMA,
gk(t) = g(t) for all cochannel k.
MUD for TDMA


Usually there is only one user per time-slot per cell.
The interference comes from nearby cells.


with
Intercell interference.
Observations from only one base station might not be
sufficient.

Performance is improved by combining outputs from multiple
base stations.
Performance of Turbo-MUD
for TDMA in AWGN
1
0
10
-1
10
10
0
10
-1
10
-2
10
-2
BER
BER
10
-3
10
-3
10
-4
10
Matched Filter
Turbo-MUD: iter 1
Turbo-MUD: iter 2
Turbo-MUD: iter 3
Turbo-MUD: iter 4
Single-user bound
-5
10
-4
-5
10
-6
-6
10
Matched Filter
Turbo-MUD: iter 1
Turbo-MUD: iter 2
Turbo-MUD: iter 3
Turbo-MUD: iter 4
10
0
1



2
3
4
5
6
Eb/No in dB
7
8
9
10
K = 3 users
Convolutional code: Kc = 3, r=1/2
Observations at 1 base station
10
1
2


3
4
5
6
Number of users
Eb/No = 5 dB
1K9
7
8
9
Performance of Turbo-MUD
for TDMA in Rayleigh Flat-Fading
0
0
10
-1
10
10
-1
10
-2
-3
10
10
BER
BER
-2
Matched Filter
Turbo-MUD: iter 1
Turbo-MUD: iter 2
Turbo-MUD: iter 3
Turbo-MUD: iter 4
Single-user bound
10
-3
10
-4
-4
10
10
-5
-5
10
-6
10
10
10


Matched Filter
Turbo-MUD: iter 1
Turbo-MUD: iter 2
Turbo-MUD: iter 3
Turbo-MUD: iter 4
-6
0
2
4
6
8
10
12
Eb/No in dB
14
K = 3 users
Fully-interleaved fading
16
18
20
1
2


3
4
5
6
Number of users
Eb/No = 9 dB
1K9
7
8
9
Extension: Multiuser Detection
for TDMA Networks


Turbo MUD


Each base station has a multiuser detector.
Sum the LLR outputs from M base stations.
Pass through a bank of SISO channel decoder.
Feed back LLR outputs of the decoders to the MUD’s.
y1
Extrinsic
Info
Multiuser
Detector
#1
Bank of
K SISO
Channel
Decoders
yM
Multiuser
Detector
#M
dˆ ( q ) Estimated
Data
Distributed Multiuser Detection


First, consider the case where each user is uncoded.
Each base station has a multiuser detector.
Turbo MUD



Implemented with the Log-MAP algorithm.
Produces LLR estimates of the users’ symbols.
Sum the LLR outputs of each MUD.
y1
Multiuser
Detector
#1
dˆ ( q )
yM
Multiuser
Detector
#M
Cellular Network Topology
F3
F4
F2
F1
F3
F5
F7
F4
F2
F1
F5
F7
F6
F3
F6
F4
F2
F1
F5
F7
F6

Conventional layout


Isotropic antennas in cell center
Frequency reuse factor 7

Alternative layout

120 degree sectorized antennas


Located in 3 corners of cell
Frequency reuse factor 3
Performance of Distributed MUD
0
0
10
10
-1
-1
10
10
-2
-2
10
BER
BER
10
-3
10
K=9
K=7
K=5
K=3
Matched Filter
Optimal MUD
Theoretical Bound
-4
10
-5
10
K=9
K=7
K=5
K=3
Matched Filter
Optimal MUD
Theoretical Bound
-4
10
-5
10
-6
10
-3
10
-6
0
5



10
15
Eb/No in dB
20
25
30
Without diversity combining.
Fully-interleaved Rayleigh fading
Output from BS closest to the
mobile used to make decision.
10
0




5
10
15
Eb/No in dB
20
25
30
With diversity combining.
M=3 base stations
Mobiles randomly placed in cell.
Exponential path loss, ne = 3.
Performance of Distributed MUD
0
10

Eb/No = 20 dB
1K9

For conventional receiver:

-1
10
BER

MF at closest BS
MF with MRC
MUD at closest BS
Distributed MUD
-2
10


With multiuser detection:

-3
10

-4
10
1
2
3
4
5
6
Number of users, K
7
8
9

Performance degrades quickly
with increasing K.
Only small benefit to using
observations from multiple BS.
Performance degrades very
slowly with increasing K.
Order of magnitude decrease in
BER by using multiple
observations.
Now multiple cochannel
users per cell are allowed.
Cooperative Decoding
for the TDMA Uplink

Turbo MUD


Now consider the coded case.
The outputs of the MUD’s are summed and passed
through a bank of decoders.
The SISO decoder outputs are fed back to the multiuser
detectors to be used as a priori information.
y1
Extrinsic
Info
Multiuser
Detector
#1
Bank of
K SISO
Channel
Decoders
yM
Multiuser
Detector
#M
dˆ ( q ) Estimated
Data
Performance of
Cooperative Decoding
0
10

K = 3 transmitters

-1
10

BER
10


Matched Filter
MF w/ MRC
Turbo-MUD: iter 1
Turbo-MUD: iter 2
Turbo-MUD: iter 3
Turbo-MUD: iter 4
Single-user bound
-3
10
-4
10

-5
-6
0
2
4
6
8
Eb/No in dB
10
12
14
Corners of cell
path loss ne = 3
Fully-interleaved
Rayleigh flat-fading
Convolutional code

10
10
M = 3 receivers (BS’s)

-2
Randomly placed in cell.
Kc = 3, r = 1/2
Performance of
Cooperative Decoding
0
10


-1
10
Eb/No = 5 dB
1K9


-2
10
BER

M = 3 receivers
For conventional receiver:

-3
10

Matched Filter
MRC
Turbo-MUD: iter 1
Turbo-MUD: iter 2
Turbo-MUD: iter 3
Turbo-MUD: iter 4
-4
10
-5
10



1
2
3
4
5
6
Number of users
7
8
9
Performance degrades quickly
with increasing K.
Only small benefit to using
observations from multiple BS.
With multiuser detection:

-6
10
Randomly placed in cell.
Performance degrades
gracefully with increasing K.
No benefit after third iteration.
Could allow an increase in
TDMA system capacity.
Conclusion

Turbo code advantages:

Conclusion

Turbo code disadvantages:




Remarkable power efficiency in AWGN and flat-fading
channels for moderately low BER.
Long latency due to large frame sizes.
Less beneficial at high SNR.
Because turbo codes operate at very low SNR, channel
estimation and tracking is a critical issue.
The principle of iterative or “turbo” processing can be
applied to other problems.


Turbo-multiuser detection can improve performance of
coded multiple-access systems.
When applied to TDMA networks, can allow multiple users
per time/frequency slot.
Future Work

Turbo codes for wireless communications.

We have addressed the issue of carrier synchronization.
Conclusion





Multiple-symbol DPSK could be a viable alternative.
Symbol and frame synchronization should also be considered.
Adaptive turbo codes
ARQ schemes for turbo codes.
Distributed multiuser detection.



Reduced complexity implementations.
Methods for performing channel estimation.
Study the impact on network architecture/control.

Multiuser detection at a network level.
Contributions/Publications

Turbo codes for the wireless channel

Use of pilot symbols for channel estimation

Performance curves for Rician channels
 Wireless multimedia applications
Valenti and Woerner, “Refined channel estimation for coherent detection of turbo
codes over flat-fading channels,” IEE Electronics Letters, Aug. 1998.
Valenti and Woerner, “Pilot symbol assisted detection of turbo codes over flatfading channels," IEEE Journal on Selected Areas in Communications, in review.
Valenti and Woerner, “A bandwidth efficient pilot symbol technique for coherent
detection of turbo codes over fading channels,” in Proc. MILCOM, Atlantic City,
Oct./Nov. 1999, to appear.
Valenti, “Turbo codes and iterative processing,” in Proc. IEEE New Zealand
Wireless Communications Symposium, Auckland, New Zealand, Nov. 1998,
invited paper.
Valenti and Woerner, “Performance of turbo codes in interleaved flat fading
channels with estimated channel state information,” in Proc., IEEE VTC, Ottawa,
Canada, May 1998.
Valenti and Woerner, “Variable latency Turbo-codes for wireless multimedia
applications,” in Proc. International Symposium of Turbo Codes and Related
Topics, Brest, France, Sept. 1997.

Publications






Combined pilot symbol-assisted and decision-directed decoding
Contributions/Publications

Multiuser detection for coded multiple-access networks
Log-MAP multiuser detection algorithm.
 Distributed multiuser detection using observations from multiple receivers.
 Application to TDMA networks.
Valenti and Woerner, “Distributed multiuser detection for the TDMA cellular
uplink, IEE Electronics Letters, in review.
Valenti and Woerner, “Combined multiuser detection and channel decoding
with receiver diversity,” in Proc. GLOBECOM, Communications Theory Miniconference, Sydney, Australia, Nov. 1998.
M.C. Valenti and Woerner, “Multiuser detection with base station diversity,” in
Proc. ICUPC, Florence, Italy, Oct. 1998.
M.C. Valenti and Woerner, “Iterative multiuser detection for convolutionally
coded asynchronous DS-CDMA,” in Proc. PIMRC, Boston, MA, Sept. 1998.
Valenti and Woerner, “Performance of turbo codes in interleaved flat fading
channels with estimated channel state information,” in Proc. VTC, Ottawa,
Canada, May 1998.
Publications






Web Page

For more information visit:

http:/www.ee.vt.edu/valenti/turbo.html
Goals of Error Correction Coding

Introduction

When the channel induces an error, the decoder chooses
the “closest” code word.
Therefore “distinct” code words are desired.

Hamming distance: the number of bit positions that two
code words differ.


Minimum distance: smallest Hamming distance between
two code words.


The Hamming distance between two code words should be as
large as possible.
Traditional code design seeks to maximize the minimum
distance.
(Hamming) weight: the number of ones in a code word.

In a linear code the minimum distance is the smallest
Hamming weight of all non-zero code words.
Turbo Multiuser Detection

The “inner code” of a serial concatenation could be a
multiple-access interference (MAI) channel.
Turbo MUD




MAI channel describes the interaction between K
nonorthogonal users sharing the same channel.
MAI channel can be interpreted as a time varying ISI
channel.
MAI channel is a rate 1 code with time-varying coefficients
over the field of real numbers.
The input to the MAI channel consists of the encoded and
interleaved sequences of all K users in the system.
Low Power Communications

Goal for modern communication system design:
Introduction


Reduce the minimum signal-to-noise power ratio (SNR)
required by the receiver
Benefits:

Allows more design flexibility

The transmitted signal can be less powerful
•
•
•
•



Extended battery life
Allows use of smaller transmit antennas
Produces less interference
Reduced adverse biological effects
More robust against noise, fading, and interference
Increased range of transmission
Allows use of smaller receive antennas
How to Achieve
Low Power Communications

Introduction

P = EbRb
Lower the data rate Rb

Source coding:




Compression
Compaction
Vocoding
Lower the energy per bit Eb required at the receiver

Signal processing:




Equalization
Multiuser detection
“Smart” antennas
Channel coding
Random Codes

Random codes achieve the best performance.


However, random codes are not feasible.


The code must contain enough structure so that decoding
can be realized with actual hardware.
Coding dilemma:


Shannon showed that as N approaches infinity, random
codes require the theoretical minimum SNR.
“All codes are good, except those that we can think of.”
With turbo codes:


The codes appear random to the channel.
Yet, they contain enough structure so that decoding is
feasible.
Turbo Codes

Background:
Turbo Codes



Turbo codes were proposed by Berrou and Glavieux in the
1993 International Conference in Communications.
Performance within 0.5 dB of the channel capacity limit for
BPSK was demonstrated.
Features of turbo codes:




Recursive convolutional encoders
Parallel code concatenation
Nonuniform or “Pseudo-random” interleaving
Iterative decoding
Performance Bounds for
Linear Block Codes

Union bound for maximum likelihood soft-decision
2
decoding:
w 
2rE 
K
Turbo Codes
Pb  
i 1

Or:
Pb 

b 
Q d i
K 
N o 
N

d  d min
i
~ 
Nd w
2rEb
d
Q d
K
No





The minimum-distance asymptote is the first term of
the sum:
~
Pb 
2rEb
N min wmin 
Q d min
K
No





Performance of Turbo Equalizer

M=5 independent
multipaths




Convolutional code:



Symbol spaced paths
Stationary channel
Perfectly known channel.
Kc=5
r=1/2
C. Douillard,et al “Iterative Correction of
Intersymbol Interference: TurboEqualization”, European Transactions
on Telecommuications, Sept./Oct. 97.
Performance of Serial
Concatenated Turbo Code





Rate r=1/3
Interleaver size K = 16,384
Kc = 3 encoders
Serial concatenated codes
do not seem to have a bit
error rate floor
S. Benedetto, et al “Serial Concatenation
of Interleaved Codes: Performance
Analysis, Design, and Iterative Decoding”
Proc., Int. Symp. on Info. Theory, 1997.
Performance of Turbo MUD

Generic MAI system




Convolutionally coded




Ku =3 asynchronous users
Identical pulse shapes
Each user has its own interleaver
Kc = 3
r = 1/2
Iterative decoder
M. Moher, “An iterative algorithm for asynchronous
coded multiuser detection,” IEEE Comm. Letters,
Aug.1998.