Turbo Codes and Turbo-Coded Modulation in CDMA Mobile Radio …ipd481/Papers varios/slides.pdf · 2018. 1. 15. · ä Performance of turbo-coded 8-PSK decreases dramatically ä Coded

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


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


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


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


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


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


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

}


CDMA Simulation Model: Downlink with pilot signalCDMA Simulation Model: Downlink with pilot signal


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


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


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


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

Turbo Codes and Turbo-Coded Modulation in CDMA Mobile Radio …ipd481/Papers varios/slides.pdf · 2018. 1. 15. · ä Performance of turbo-coded 8-PSK decreases dramatically ä Coded

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