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Volker Kühn: Turbo Codes and Turbo-Coded Modulation in CDMA Mobile Radio ...
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University
- f Bremen
Volker Kühn: Turbo Codes and Turbo-Coded Modulation in CDMA Mobile Radio ...
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University
- f Bremen
Turbo Codes and Turbo-Coded Modulation Turbo Codes and Turbo-Coded - - PowerPoint PPT Presentation
Turbo Codes and Turbo-Coded Modulation Turbo Codes and Turbo-Coded - - PowerPoint PPT Presentation
Turbo Codes and Turbo-Coded Modulation Turbo Codes and Turbo-Coded Modulation in CDMA Mobile Radio Systems for in CDMA Mobile Radio Systems for Short Frame Transmission Short Frame Transmission Volker Khn, University of Bremen, Germany
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Volker Kühn: Turbo Codes and Turbo-Coded Modulation in CDMA Mobile Radio ...
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University
- f Bremen
Turbo Codes:
Structure of Encoder and Decoder
Turbo Codes:
Structure of Encoder and Decoder
Encoder
Parallel concatenation of constituent
codes
Encoders connected through an
interleaver
Conventional block interleaver with
N = 400 bits
Optimization possible, but only small
gains expected due to short interleaver
Decoder
D1 and D2 arranged serially Inner decoder D1 and outer decoder D2 Decoding by Max-Log-MAP algorithm Best compromise between robustness,
performance and decoding effort
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Volker Kühn: Turbo Codes and Turbo-Coded Modulation in CDMA Mobile Radio ...
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University
- f Bremen
Turbo Codes:
Constituent Codes
Turbo Codes:
Constituent Codes
Recursive, systematic convolutional codes Parameter to be optimized: effective distance Maximize weight of redundancy bits c1 and c2 for input weight w = 2 Recursive generator polynomial has to be prime Other polynomials should maximize Hamming weight of redundancy bits for w = 2 sequences Purpose:
Comparison with convolutional codes
(constraint length Lc = 9)
Approximately same decoding effort
d z
eff =
+ ⋅ 2 2
min
Rc g P Rc = 1 2 238 358 1 1
Rc = 1 4 238 358 258 1 1 1 1 1 1
Rc = 2 3 238 358 1 1
Codes used in simulations
SLIDE 5
Volker Kühn: Turbo Codes and Turbo-Coded Modulation in CDMA Mobile Radio ...
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University
- f Bremen
Turbo-Coded Modulation:
Transmitter
Turbo-Coded Modulation:
Transmitter
Demultiplexer collects n unpunctured code words c(k) 2n redundancy bits are punctured to m-n bits m bits are mapped to one of 2m possible symbols (Gray coding) Different error probabilities for bits uj Assign bits processed by inner decoder to most reliable uj Example: 8-PSK modulation: m = 3 Code rate Rc = 2/3:
n = 2 info bits / symbol m-n = 1 parity bit / symbol
2 information bits assigned to most reliable bits u1 and u2
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Volker Kühn: Turbo Codes and Turbo-Coded Modulation in CDMA Mobile Radio ...
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University
- f Bremen
Turbo-Coded Modulation:
Receiver
Turbo-Coded Modulation:
Receiver
Coherent detection and soft output demodulation of received symbol x(l) Reliability information for each bit uj of a symbol by optimal MAP algorithm:
{ } { } { }
( )
[ ]
( )
( )
[ ]
( )
L u P u P u x s 2 x s 2
j j j i 2 N 2 s u i 2 N 2 s u
i j i j
= = = = − − − −
∈ = ∈ =
∑ ∑
ln 1 x 0 x ln exp exp
1
σ σ
S S
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Volker Kühn: Turbo Codes and Turbo-Coded Modulation in CDMA Mobile Radio ...
7
University
- f Bremen
Soft-Output Demodulation:
Pragmatic approach
Soft-Output Demodulation:
Pragmatic approach
Soft-output values show large symmetry Pragmatic approach:
{ }
{ } { } ( ) { } { }
( )
L u 2a x j 2a x j a a x x j
j
≈ − ⋅ = − ⋅ = − ⋅ − =
1 1 2 1
Im for 1 Re for 2 Im Re for 3
Re{x} Im{x} L{u1} Re{x} Im{x} L{u2} Im{x} Re{x} L{u3}
SLIDE 8
Volker Kühn: Turbo Codes and Turbo-Coded Modulation in CDMA Mobile Radio ...
8
University
- f Bremen
CDMA Simulation Model:
Downlink with pilot signal
CDMA Simulation Model:
Downlink with pilot signal
SLIDE 9
Volker Kühn: Turbo Codes and Turbo-Coded Modulation in CDMA Mobile Radio ...
9
University
- f Bremen
Simulation Results:
Comparison with convolutional codes
Simulation Results:
Comparison with convolutional codes
Approximately same bit error rates for convolutional codes with rates Rc = 1/2 and Rc = 1/4 Turbo code with Rc = 1/4 has same performance as CC’s Turbo code with Rc = 1/2 loses 0.5 dB Turbo-coded 8-PSK loses approximately 1 dB Turbo codes do not outperform CC’s in case of short interleavers and same decoding costs Only small differences between Rc = 1/2 and Rc = 1/4 9 3 6 10
- 5
10
- 4
10
- 3
10
- 2
10
- 1
10 Eb / N0
TC, Rc = 1/4 TC, Rc = 2/3 CC, Rc = 1/4 CC, Rc = 1/2 TC, Rc = 1/2
BER
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Volker Kühn: Turbo Codes and Turbo-Coded Modulation in CDMA Mobile Radio ...
10
University
- f Bremen
Simulation Results:
Influence of channel estimation
Simulation Results:
Influence of channel estimation
Conventional channel estimation via pilot signal
Only small differences between
Rc = 1/2 and Rc = 1/4
Loss of 4 dB in comparison to
perfectly known channel
Improved channel estimation by averaging 10 estimated channel coefficients
Gain of 3 dB over conventional
estimation
Gain of 1 dB for Rc = 1/4 over
Rc = 1/2
Accurate channel estimation necessary in order to exploit potential of powerful codes
9 3 6
10
- 5
10
- 4
10
- 3
10
- 2
10
- 1
10 Eb / N0 BER
perfectly known averaged non-averaged Rc = 1/4 Rc = 1/2
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Volker Kühn: Turbo Codes and Turbo-Coded Modulation in CDMA Mobile Radio ...
11
University
- f Bremen
Simulation Results:
10 additional users
Simulation Results:
10 additional users
Loss of 1 dB due to additional users for Rc = 1/2 and Rc = 1/4 Gap between Rc = 1/2 and Rc = 1/4 slightly decreases due to better interference suppression for longer DS-spreading Code with Rc = 1/4 still superior to Rc = 1/2 Performance of turbo-coded 8-PSK decreases dramatically Coded modulation scheme as used in this work is not suitable for CDMA systems
3 6 12 Eb / N0 10
- 5
10
- 4
10
- 3
10
- 2
10
- 1
10
Rc = 1/4 Rc = 1/2 Rc = 2/3
9
BER
- add. users
no add. users
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Volker Kühn: Turbo Codes and Turbo-Coded Modulation in CDMA Mobile Radio ...
12
University
- f Bremen