Turbo Codes and Turbo-Coded Modulation in CDMA Mobile Radio …ipd481/Papers varios/slides.pdf ·...
Transcript of Turbo Codes and Turbo-Coded Modulation in CDMA Mobile Radio …ipd481/Papers varios/slides.pdf ·...
Volker Kühn: Turbo Codes and Turbo-Coded Modulation in CDMA Mobile Radio ... 1University of Bremen
Turbo Codes and Turbo-Coded Modulationin CDMA Mobile Radio Systems for
Short Frame Transmission
Turbo Codes and Turbo-Coded Modulationin CDMA Mobile Radio Systems for
Short Frame Transmission
ä Introductionä Short description of turbo codesä Turbo-coded modulationä CDMA simulation model and simulation resultsä Conclusions
Volker Kühn, University of Bremen, Germany
Volker Kühn: Turbo Codes and Turbo-Coded Modulation in CDMA Mobile Radio ... 2University of Bremen
IntroductionIntroduction
ä Turbo codes reach near Shannon limit performance
ä Amazing results obtained with extremely large interleavers causingtremendous transmission delays
Question 1: Are turbo codes with small interleavers still superior toconvolutional codes at a comparable decoding effort?
ä Wideband CDMA as multiplex technique for third generation mobile radiosystems (Europe: UMTS)
Question 2: Trade-off between Direct-Sequence spreading,channel coding and modulation
Embedding turbo codes and turbo-coded modulation in a DS-CDMA system
Volker Kühn: Turbo Codes and Turbo-Coded Modulation in CDMA Mobile Radio ... 3University of Bremen
Turbo Codes: Structure of Encoder and DecoderTurbo Codes: Structure of Encoder and Decoder
ä Encoder
u Parallel concatenation of constituentcodes
u Encoders connected through aninterleaver
u Conventional block interleaver withN = 400 bits
u Optimization possible, but only smallgains expected due to short interleaver
ä Decoder
u D1 and D2 arranged seriallyu Inner decoder D1 and outer decoder D2u Decoding by Max-Log-MAP algorithmu Best compromise between robustness,
performance and decoding effort
Volker Kühn: Turbo Codes and Turbo-Coded Modulation in CDMA Mobile Radio ... 4University of Bremen
Turbo Codes: Constituent CodesTurbo Codes: Constituent Codes
ä Recursive, systematic convolutional codes
ä Parameter to be optimized: effective distance
è Maximize weight of redundancy bits c1 and c2 forinput weight w = 2
ä Recursive generator polynomial has to be prime
ä Other polynomials should maximize Hammingweight of redundancy bits for w = 2 sequences
ä Purpose:
u Comparison with convolutional codes(constraint length Lc = 9)
è Approximately same decoding effort
d zeff = + ⋅2 2 min
Rc g P
Rc = 12
238358
1 00 1
Rc = 14
238358258
1 11 01 10 1
Rc = 23
238358
1 00 00 00 1
Codes used in simulations
Volker Kühn: Turbo Codes and Turbo-Coded Modulation in CDMA Mobile Radio ... 5University of Bremen
Turbo-Coded Modulation: TransmitterTurbo-Coded Modulation: Transmitter
ä Demultiplexer collects n unpunctured code words c(k)ä 2n redundancy bits are punctured to m-n bitsä m bits are mapped to one of 2m possible symbols (Gray coding)ä Different error probabilities for bits ujè Assign bits processed by inner decoder to most reliable uj
Example:
ä 8-PSK modulation: m = 3
ä Code rate Rc = 2/3:u n = 2 info bits / symbolum-n = 1 parity bit / symbol
ä 2 information bits assigned to most reliable bits u1 and u2
Volker Kühn: Turbo Codes and Turbo-Coded Modulation in CDMA Mobile Radio ... 6University of Bremen
Turbo-Coded Modulation: ReceiverTurbo-Coded Modulation: Receiver
ä Coherent detection and soft outputdemodulation of received symbol x(l)
ä Reliability information for each bit uj of a symbol by optimal MAP algorithm:
{ } { }{ }
( )[ ]( )
( )[ ]( )
L uP u
P u
x s 2
x s 2j
j
j
i 2
N2
s u
i 2
N2
s u
ij
ij
===
=− −
− −∈ =
∈ =
∑
∑ln
1 x
0 xln
exp
exp
1
0
σ
σS
S
Volker Kühn: Turbo Codes and Turbo-Coded Modulation in CDMA Mobile Radio ... 7University of Bremen
Soft-Output Demodulation: Pragmatic approachSoft-Output Demodulation: Pragmatic approach
ä Soft-output values show large symmetryè Pragmatic approach:
{ }{ }{ }
( ) { } { }( )L u
2a x j2a x j
a a x x jj ≈
− ⋅ =− ⋅ =
− ⋅ − =
1
1
2 1
Im for 1Re for 2
Im Re for 3
Re{x} Im{x}
L{u 1
}
Re{x} Im{x}
L{u 2
}
Im{x}Re{x}
L{u 3
}
Volker Kühn: Turbo Codes and Turbo-Coded Modulation in CDMA Mobile Radio ... 8University of Bremen
CDMA Simulation Model: Downlink with pilot signalCDMA Simulation Model: Downlink with pilot signal
Volker Kühn: Turbo Codes and Turbo-Coded Modulation in CDMA Mobile Radio ... 9University of Bremen
Simulation Results: Comparison with convolutional codesSimulation Results: Comparison with convolutional codes
ä Approximately same bit error ratesfor convolutional codes with ratesRc = 1/2 and Rc = 1/4
ä Turbo code with Rc = 1/4 has sameperformance as CC’s
ä Turbo code with Rc = 1/2 loses0.5 dB
ä Turbo-coded 8-PSK losesapproximately 1 dB
ä Turbo codes do not outperform CC’sin case of short interleavers and samedecoding costs
ä Only small differences betweenRc = 1/2 and Rc = 1/4
93 610
-5
10-4
10-3
10-2
10-1
100
Eb / N0
TC, Rc = 1/4
TC, Rc = 2/3
CC, Rc = 1/4CC, Rc = 1/2
TC, Rc = 1/2
BE
R
Volker Kühn: Turbo Codes and Turbo-Coded Modulation in CDMA Mobile Radio ... 10University of Bremen
Simulation Results: Influence of channel estimationSimulation Results: Influence of channel estimation
ä Conventional channel estimationvia pilot signalu Only small differences between
Rc = 1/2 and Rc = 1/4u Loss of 4 dB in comparison to
perfectly known channel
ä Improved channel estimation byaveraging 10 estimated channelcoefficientsu Gain of 3 dB over conventional
estimationu Gain of 1 dB for Rc = 1/4 over
Rc = 1/2
ä Accurate channel estimationnecessary in order to exploitpotential of powerful codes
90 3 610
-5
10-4
10-3
10-2
10-1
100
Eb / N0
BE
Rperfectlyknown
averaged
non-averaged
Rc = 1/4Rc = 1/2
Volker Kühn: Turbo Codes and Turbo-Coded Modulation in CDMA Mobile Radio ... 11University of Bremen
Simulation Results: 10 additional usersSimulation Results: 10 additional users
ä Loss of 1 dB due to additional usersfor Rc = 1/2 and Rc = 1/4
ä Gap between Rc = 1/2 andRc = 1/4 slightly decreases due tobetter interference suppression forlonger DS-spreading
ä Code with Rc = 1/4 still superior toRc = 1/2
ä Performance of turbo-coded 8-PSKdecreases dramatically
ä Coded modulation scheme as usedin this work is not suitable for CDMAsystems
3 6 12Eb / N0
10-5
10-4
10-3
10-2
10-1
100
Rc = 1/4Rc = 1/2Rc = 2/3
9B
ER
add. usersno add. users
Volker Kühn: Turbo Codes and Turbo-Coded Modulation in CDMA Mobile Radio ... 12University of Bremen
ConclusionsConclusions
ä Turbo codes are no longer superior to convolutional codes for shortinterleavers and same decoding costs
ä Accurate channel estimation necessary in order to exploit high codinggains
ä Pilot signal aided estimation with averaging gains 3 dB overconventional estimation
ä Low rate coding with low DS-spreading is better than high rate codingand high DS-spreading for coherent demodulation
ä Turbo-coded modulation is not suitable for an implementation in DS-CDMA systems
ä Performance improvement for turbo-coded modulation due tomultiphase spreading sequences may be possible