Iterative Detection and Decoding for Wireless Communications. Matthew Valenti Dissertation Defense July 8, 1999 Advisor: Dr. Brian D. Woerner Mobile and Portable Radio Research Group Bradley Department of Electrical and Computer Engineering Virginia Tech Blacksburg, Virginia. Outline. - PowerPoint PPT Presentation
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V IRG IN IA PO LY TECH N IC IN ST IT U TE A N D STA TE U N IV ERSITY Tech V irginia 1 8 7 2 VIRGINIA POLYTECHNIC INSTITUTE & STATE UNIVERSITY MOBILE & PORTABLE RADIO RESEARCH GROUP MPRG Iterative Detection and Decoding for Wireless Communications Matthew Valenti Dissertation Defense July 8, 1999 Advisor: Dr. Brian D. Woerner Mobile and Portable Radio Research Group Bradley Department of Electrical and Computer Engineering Virginia Tech Blacksburg, Virginia
Transcript
VIRGINIA POLYTECHNIC INSTITUTEAND STATE UNIVERSITY
TechVirginia
1 8 7 2
VIRGINIA POLYTECHNIC INSTITUTE & STATE UNIVERSITY
MOBILE & PORTABLE RADIO RESEARCH GROUP
MPRG
Iterative Detection and Decoding for Wireless Communications
Matthew ValentiDissertation DefenseJuly 8, 1999
Advisor: Dr. Brian D. Woerner Mobile and Portable Radio Research Group Bradley Department of Electrical and Computer EngineeringVirginia TechBlacksburg, Virginia
Ou
tlin
e
Outline
Introduction and background Turbo codes Iterative decoding algorithms
Turbo codes for the wireless channel 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
Intr
od
ucti
on
Error Correction Coding Channel coding adds structured redundancy to a
transmission.
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
ChannelEncoder
m x
Power Efficiency of Coding Standards
Mariner1969
OdenwalderConvolutionalCodes 1976
Turbo Code1993
Galileo:BVD1992Galileo:LGA
1996
Pioneer1968-72
Voyager1977
0 1 2 3 4 5 6 7 8 9 10-1-2
0.5
1.0
Eb/No in dB
BPSK Capacity Bound
Cod
e R
ate
r
Sha
nnon
Cap
acity
Bou
nd
UncodedBPSK
Globalstar1999
Iridium1998
510bP
Spe
ctra
l Eff
icie
ncy
Convolutional Codes
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
Constraint Length Kc = 3
D Dim
)0(ix
)1(ix
Recursive Systematic Convolutional Encoding
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
Turbo codes get their name because the decoder uses feedback, like a turbo engine.
Itera
tive d
ecod
ing
Iterative Decoding
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
Decoder#1
Decoder#2
DeMUX
Interleaver
Interleaver
Deinterleaver
systematic data
paritydata
ExtrinsicInformation
ExtrinsicInformation
hard bitdecisions
Itera
tive d
ecod
ing
Trellis-Based Estimation Algorithms
ViterbiAlgorithm
SOVA
ImprovedSOVA
MAPAlgorithm
max-log-MAP
log-MAP
Sequence Estimation
Symbol-by-symbol Estimation
Soft-Input Soft-Output (SISO)Decoding Algorithms
Viterbi algorithm1967 Viterbi
SOVA1989 Hagenauer/Hoeher
Improved SOVA1996 Papke/Robertson/Villebrun
MAP algorithm1974 Bahl/Cocke/Jelinek/Raviv
max-log-MAP1990 Koch and Baier
log-MAP1994 Villebrun
0.5 1 1.5 210
-7
10-6
10-5
10-4
10-3
10-2
10-1
100
Eb/N
o in dB
BE
R
1 iteration
2 iterations
3 iterations6 iterations
10 iterations
18 iterations
Performance as a Function of Number of Iterations
Kc = 5 r = 1/2 K = 65,536 Log-MAP algorithm AWGN
Turb
o C
od
es
Summary of Performance Factors
and Tradeoffs Latency vs. performance
Frame/interleaver size Complexity vs. performance
Decoding algorithm Number of iterations Encoder constraint length
Spectral efficiency vs. performance Overall code rate
Other factors Interleaver design Puncture pattern Trellis termination
Fad
ing
ch
an
nels
Turbo Codes for Fading Channels
Many channels of interest can be modeled as a frequency-flat fading channel. Fading: channel is time-varying Flat: all frequencies experience same attenuation
Because of the time-varying nature of the channel, it is necessary to estimate and track the channel. 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.
Fad
ing
ch
an
nels
im lx lx nv )(tsturbo
encoderchannel
interleaversymbolmapper
pulse shapingfilter
)(ts )(ty)(tn)(tc
fading AWGN
im
ny)(tymatched
filterchannel
estimator
channeldeinterl.
turbodecoder
*2
ˆˆ2
nc
symboldemapper
lr lr
transmitter
channelreceiver
nz
System ModelInput data
Decoded data
Fad
ing
ch
an
nels
Fading Channel Types
. X(t), Y(t) are Gaussian random processes.
Represents the scattering component Autocorrelation: Rc()
A is a constant. 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, =A2/22
Correlated fading: Fully-interleaved fading:
)()()( tjYtXAtc
)2()( 0 dc fJR
)()( cR
0 2 4 6 8 10
10-6
10-4
10-2
100
Eb/N
o in dB
BER
fd T
s = .0025
fd T
s = .005
fd T
s = .01
no interleaving block interleavingfully interleaved
The turbo decoding algorithm requires accurate estimates of channel parameters. Branch metric:
Noise variance: Fading amplitude: Phase: (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.
pi
pi
si
siiii xzxzmPss ˆˆ][ln)( 1
*2
2iii cyz
nn ca
nn c
b
o
rE
N
22
Fad
ing
ch
an
nels
Case 1:Known Phase
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:
SOVA: Estimated SI SOVA: Perfect SI Log-MAP: Estimated SILog-MAP: Perfect SI
0 1 2 3 4 5 610
-6
10-5
10-4
10-3
10-2
10-1
100
Eb/N
o in dB
BE
R
SOVA: Estimated SI SOVA: Perfect SI Log-MAP: Estimated SILog-MAP: Perfect SI
Fad
ing
ch
an
nels
Case 2:Unknown Phase
Now assume that the receiver is unable to obtain accurate estimates of the phase n. 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
Fad
ing
ch
an
nels
Pilot Symbol Assisted Modulation (PSAM)
Pilot symbols: 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#Mp
symbol#1
symbol#Mp
pilot symbol
segment #2
symbol#1
symbol#Mp
symbol#1
symbol#Mp
pilot symbol
pilot symbols added here
Fad
ing
ch
an
nels
)(ˆ q
im
ny)(ty matchedfilter
channelestimator
channeldeinterl
.
turbodecoder
)(*
2ˆ
ˆ2 q
nc
symboldemapper
)(q
lr )(q
lr
channelinterleaver
symbolmapper
)(ˆ qnv )(ˆ q
lx
)(ˆ q
lx
Pilot Symbol Assisted Decoding
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.
Tentativeestimates of the code bits
Finalestimates of
the data
0 1 2 3 4 5 6 7 8 9 1010
-6
10-5
10-4
10-3
10-2
10-1
100
101
Eb/N
o in dB
BE
R
DPSK conventional PSAM, unknown fadesturbo-PSAM, unknown fades BPSK, perfect SI
Performance of Pilot Symbol Assisted Decoding
Simulation parameters: 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
Pilot symbol spacing: Mp = 8 Wiener filtering: Nc = 30
At Pb = 10-5
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.
Fad
ing
ch
an
nels
Performance Factors for Pilot Symbol Assisted Decoding
Performance is more sensitive to errors in estimates of the fading process than estimates in noise variance.
Pilot symbol spacing Want symbols close enough to track the channel. However, using pilot symbols reduces the energy available
for the traffic bits. Type of channel estimation filter
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.
Performance in Rapid Fading Rayleigh fading channel
fdTs = .02
Turbo code Kc = 4, r = 1/2 L=4140 bit interleaver
Turb
o p
rin
cip
le
Other Applications of the 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.
Seri
al C
on
cate
nate
d T
urb
o C
od
es
Serial Concatenated Codes
OuterConvolutional
Encoder
Datan(t)
AWGN
InnerDecoder
OuterDecoder
EstimatedData
TurboDecoder
interleaver
deinterleaver
interleaver
InnerConvolutional
Encoder
Extrinsic Information
Turb
o E
Q
Turbo Equalization
(Outer)Convolutional
Encoder
n(t)AWGN
SISOEqualizer
(Outer)SISO
DecoderEstimated
Data
TurboEqualizer
interleaver
deinterleaver
interleaver
ISIChannel
Extrinsic Information
Data
Can model intersymbol interferencechannel as an FIR filter
Turb
o M
UD
Turbo Multiuser Detection
ConvolutionalEncoder
#K
n(t)AWGN
SISOMUD
Bank ofK SISO
DecodersEstimated
Data
TurboMUD
interleaver #K
multiuserdeinterleaver
multiuserinterleaver
MAIChannelModel
Extrinsic Info
ConvolutionalEncoder
#1interleaver #1
Parallelto
Serial
“multiuser interleaver”
1b
b
y
1d
KbuKd
)(ˆ qd
Channel
Time-varying FIR filter
Turb
o M
UD
Direct Sequence CDMA
CDMA: Code Division Multiple Access The users are assigned distinct waveforms.
Spreading/signature sequences
All users transmit at same time/frequency. Use a wide bandwidth signal
Processing gain Ns
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.
1
0, )()(
sN
jccjkk jTtptg
Performance of Turbo-MUD for CDMA in AWGN
K = 5 users Spreading gain Ns = 7 Convolutional code: Kc = 3, r=1/2
Eb/No = 5 dB 1 K 9
0 1 2 3 4 5 6 710
-5
10-4
10-3
10-2
10-1
100
Eb/N
o in dB
BE
R
Matched Filter Turbo-MUD: iter 1Turbo-MUD: iter 2Turbo-MUD: iter 3Single User Bound
1 2 3 4 5 6 7 8 910
-5
10-4
10-3
10-2
10-1
100
Number of users
BE
R
Matched Filter Turbo-MUD: iter 1Turbo-MUD: iter 2Turbo-MUD: iter 3
0 2 4 6 8 10 12 14 1610
-6
10-5
10-4
10-3
10-2
10-1
100
Eb/N
o in dB
BE
R
Matched Filter Turbo-MUD: iter 1Turbo-MUD: iter 2Turbo-MUD: iter 3Single User Bound
1 2 3 4 5 6 7 8 910
-6
10-5
10-4
10-3
10-2
10-1
100
Number of users
BE
R
Matched Filter Turbo-MUD: iter 1Turbo-MUD: iter 2Turbo-MUD: iter 3
Performance of Turbo-MUD for CDMA in Rayleigh Flat-fading
K = 5 users Fully-interleaved fading
Eb/No = 9 dB 1 K 9
Turb
o M
UD
Time Division Multiple Access TDMA: Time Division Multiple Access
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, with 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.
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
K = 3 users Convolutional code: Kc = 3, r=1/2 Observations at 1 base station
Eb/No = 5 dB 1 K 9
0 1 2 3 4 5 6 7 8 9 1010
-6
10-5
10-4
10-3
10-2
10-1
100
Eb/No in dB
BE
R
Matched Filter Turbo-MUD: iter 1Turbo-MUD: iter 2Turbo-MUD: iter 3Turbo-MUD: iter 4Single-user bound
1 2 3 4 5 6 7 8 910
-6
10-5
10-4
10-3
10-2
10-1
100
101
Number of users
BE
R
Matched Filter Turbo-MUD: iter 1Turbo-MUD: iter 2Turbo-MUD: iter 3Turbo-MUD: iter 4
0 2 4 6 8 10 12 14 16 18 2010
-6
10-5
10-4
10-3
10-2
10-1
100
Eb/No in dB
BE
R
Matched Filter Turbo-MUD: iter 1Turbo-MUD: iter 2Turbo-MUD: iter 3Turbo-MUD: iter 4Single-user bound
1 2 3 4 5 6 7 8 910
-6
10-5
10-4
10-3
10-2
10-1
100
Number of users
BE
R
Matched Filter Turbo-MUD: iter 1Turbo-MUD: iter 2Turbo-MUD: iter 3Turbo-MUD: iter 4
Performance of Turbo-MUD for TDMA in Rayleigh Flat-Fading
K = 3 users Fully-interleaved fading
Eb/No = 9 dB 1 K 9
Turb
o M
UD
Extension: Multiuser Detection for TDMA Networks
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.
MultiuserDetector
#1
MultiuserDetector
#M
Bank ofK SISOChannelDecoders
1y
My
)(ˆ qd
Extrinsic Info
EstimatedData
Turb
o M
UD
Distributed Multiuser Detection First, consider the case where each user is uncoded. Each base station has a multiuser detector.
Implemented with the Log-MAP algorithm. Produces LLR estimates of the users’ symbols.
Sum the LLR outputs of each MUD.
MultiuserDetector
#1
MultiuserDetector
#M
1y
My
)(ˆ qd
F2
F1
F3
F4
F5
F6
F7
F2
F1
F3
F4
F5
F6
F7
F2
F1
F3
F4
F5
F6
F7
Cellular Network Topology
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
MF at closest BS MF with MRC MUD at closest BSDistributed MUD
Performance of Distributed MUD
Eb/No = 20 dB 1 K 9 For conventional receiver:
Performance degrades quickly with increasing K.
Only small benefit to using observations from multiple BS.
With multiuser detection: 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.
Turb
o M
UD
Cooperative Decoding for the TDMA Uplink
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.
MultiuserDetector
#1
MultiuserDetector
#M
Bank ofK SISOChannelDecoders
1y
My
)(ˆ qd
Extrinsic Info
EstimatedData
0 2 4 6 8 10 12 1410
-6
10-5
10-4
10-3
10-2
10-1
100
Eb/No in dB
BE
R Matched Filter MF w/ MRC Turbo-MUD: iter 1Turbo-MUD: iter 2Turbo-MUD: iter 3Turbo-MUD: iter 4Single-user bound
Performance of Cooperative Decoding
K = 3 transmitters Randomly placed in cell.
M = 3 receivers (BS’s) Corners of cell path loss ne = 3
Fully-interleaved Rayleigh flat-fading
Convolutional code Kc = 3, r = 1/2
1 2 3 4 5 6 7 8 910
-6
10-5
10-4
10-3
10-2
10-1
100
Number of users
BE
R
Matched Filter MRC Turbo-MUD: iter 1Turbo-MUD: iter 2Turbo-MUD: iter 3Turbo-MUD: iter 4
Performance of Cooperative Decoding
Eb/No = 5 dB 1 K 9
Randomly placed in cell.
M = 3 receivers For conventional receiver:
Performance degrades quickly with increasing K.
Only small benefit to using observations from multiple BS.
With multiuser detection: Performance degrades
gracefully with increasing K. No benefit after third iteration.
Could allow an increase in TDMA system capacity.
Con
clu
sio
n
Conclusion Turbo code advantages:
Remarkable power efficiency in AWGN and flat-fading channels for moderately low BER.
Turbo code disadvantages: 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.
Con
clu
sio
n
Future Work
Turbo codes for wireless communications. We have addressed the issue of carrier synchronization.
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.
Pu
blicati
on
s
Contributions/Publications Turbo codes for the wireless channel
Use of pilot symbols for channel estimation Combined pilot symbol-assisted and decision-directed decoding
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 flat-fading 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.
Pu
blicati
on
s
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 Mini-conference, 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.
Web Page
For more information visit: http:/www.ee.vt.edu/valenti/turbo.html
Intr
od
ucti
on
Goals of Error Correction Coding
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. The Hamming distance between two code words should be as
large as possible. Minimum distance: smallest Hamming distance between
two code words. 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.
Turb
o M
UD
Turbo Multiuser Detection
The “inner code” of a serial concatenation could be a multiple-access interference (MAI) channel. 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.
Intr
od
ucti
on
Low Power Communications
Goal for modern communication system design: 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
Intr
od
ucti
on
How to Achieve Low Power Communications 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. Shannon showed that as N approaches infinity, random
codes require the theoretical minimum SNR. However, random codes are not feasible.
The code must contain enough structure so that decoding can be realized with actual hardware.
Coding dilemma: “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.
Turb
o C
od
es
Turbo Codes
Background: 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
Union bound for maximum likelihood soft-decision decoding:
Or:
The minimum-distance asymptote is the first term of the sum:
K
i o
bi
ib N
rEdQ
K
wP
2
1
2
N
dd o
bddb N
rEdQ
K
wNP
min
2~
o
bb N
rEdQ
K
wNP
2~min
minmin
Performance of Turbo Equalizer
M=5 independent multipaths Symbol spaced paths Stationary channel Perfectly known channel.
Convolutional code: Kc=5 r=1/2
C. Douillard,et al “Iterative Correction of Intersymbol Interference: Turbo-Equalization”, 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 Ku =3 asynchronous users Identical pulse shapes Each user has its own interleaver
Convolutionally coded Kc = 3 r = 1/2
Iterative decoder M. Moher, “An iterative algorithm for asynchronous
