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 Kühn, University of Bremen, Germany � Introduction � Short description of turbo codes � Turbo-coded modulation � CDMA simulation model and simulation results � Conclusions University 1 Volker Kühn: Turbo Codes and Turbo-Coded Modulation in CDMA Mobile Radio ... of Bremen
Introduction Introduction � Turbo codes reach near Shannon limit performance � Amazing results obtained with extremely large interleavers causing tremendous transmission delays Question 1: Are turbo codes with small interleavers still superior to convolutional codes at a comparable decoding effort? � Wideband CDMA as multiplex technique for third generation mobile radio systems (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 University 2 Volker Kühn: Turbo Codes and Turbo-Coded Modulation in CDMA Mobile Radio ... of 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 � D 1 and D 2 arranged serially � Inner decoder D 1 and outer decoder D 2 � Decoding by Max-Log-MAP algorithm � Best compromise between robustness, performance and decoding effort University 3 Volker Kühn: Turbo Codes and Turbo-Coded Modulation in CDMA Mobile Radio ... of Bremen
Turbo Codes: Turbo Codes: Constituent Codes Constituent Codes Codes used in simulations � Recursive, systematic convolutional codes � Parameter to be optimized: effective distance g P R c eff = + ⋅ d 2 2 z 23 8 1 0 R c = 1 min 2 35 8 0 1 � Maximize weight of redundancy bits c 1 and c 2 for 1 1 input weight w = 2 23 8 1 0 � Recursive generator polynomial has to be prime R c = 1 35 8 4 1 1 � Other polynomials should maximize Hamming 25 8 0 1 weight of redundancy bits for w = 2 sequences 1 0 � Purpose: 23 8 0 0 R c = 2 � Comparison with convolutional codes 3 35 8 0 0 (constraint length L c = 9) 0 1 � Approximately same decoding effort University 4 Volker Kühn: Turbo Codes and Turbo-Coded Modulation in CDMA Mobile Radio ... of Bremen
Turbo-Coded Modulation: Turbo-Coded Modulation: Transmitter Transmitter Example: � 8-PSK modulation: m = 3 � Code rate R c = 2/3: � n = 2 info bits / symbol � m - n = 1 parity bit / symbol � 2 information bits assigned to most reliable bits u 1 and u 2 � Demultiplexer collects n unpunctured code words c ( k ) � 2 n redundancy bits are punctured to m - n bits � m bits are mapped to one of 2 m possible symbols (Gray coding) � Different error probabilities for bits u j � Assign bits processed by inner decoder to most reliable u j University 5 Volker Kühn: Turbo Codes and Turbo-Coded Modulation in CDMA Mobile Radio ... of Bremen
Turbo-Coded Modulation: Turbo-Coded Modulation: Receiver Receiver � Coherent detection and soft output demodulation of received symbol x ( l ) � Reliability information for each bit u j of a symbol by optimal MAP algorithm: [ ] ( ) ∑ 2 − − σ i 2 exp x s 2 { } = N { } P u 1 x ( ) ∈ = i s S u 1 = j = [ ] j L u ln { } ln ( ) = ∑ j 2 P u 0 x − − σ i 2 exp x s 2 j N ( ) i ∈ = s S u 0 j University 6 Volker Kühn: Turbo Codes and Turbo-Coded Modulation in CDMA Mobile Radio ... of Bremen
Soft-Output Demodulation: Soft-Output Demodulation: Pragmatic approach Pragmatic approach L { u 2 } L { u 3 } L { u 1 } Re{ x } Im{ x } Im{ x } Re{ x } Im{ x } Re{ x } � Soft-output values show large symmetry � Pragmatic approach: { } − ⋅ = 2a Im x for j 1 1 { } { } ≈ − ⋅ = L u 2a Re x for j 2 j 1 ( ) ( ) { } { } − ⋅ − = a a Im x Re x for j 3 2 1 University 7 Volker Kühn: Turbo Codes and Turbo-Coded Modulation in CDMA Mobile Radio ... of Bremen
CDMA Simulation Model: CDMA Simulation Model: Downlink with pilot signal Downlink with pilot signal University 8 Volker Kühn: Turbo Codes and Turbo-Coded Modulation in CDMA Mobile Radio ... of Bremen
Simulation Results: Simulation Results: Comparison with convolutional codes Comparison with convolutional codes 0 � Approximately same bit error rates 10 for convolutional codes with rates R c = 1/2 and R c = 1/4 -1 10 � Turbo code with R c = 1/4 has same performance as CC’s -2 BER 10 � Turbo code with R c = 1/2 loses 0.5 dB -3 CC, R c = 1/4 10 � Turbo-coded 8-PSK loses CC, R c = 1/2 approximately 1 dB TC, R c = 1/4 -4 10 TC, R c = 1/2 � Turbo codes do not outperform CC’s TC, R c = 2/3 in case of short interleavers and same -5 10 decoding costs 3 6 9 � Only small differences between E b / N 0 R c = 1/2 and R c = 1/4 University 9 Volker Kühn: Turbo Codes and Turbo-Coded Modulation in CDMA Mobile Radio ... of Bremen
Simulation Results: Simulation Results: Influence of channel estimation Influence of channel estimation 0 � Conventional channel estimation 10 R c = 1/4 via pilot signal R c = 1/2 � Only small differences between -1 10 R c = 1/2 and R c = 1/4 � Loss of 4 dB in comparison to -2 non-averaged perfectly known channel 10 BER � Improved channel estimation by averaging 10 estimated channel -3 10 coefficients � Gain of 3 dB over conventional -4 10 estimation averaged � Gain of 1 dB for R c = 1/4 over perfectly -5 R c = 1/2 known 10 0 3 6 9 � Accurate channel estimation E b / N 0 necessary in order to exploit potential of powerful codes University 10 Volker Kühn: Turbo Codes and Turbo-Coded Modulation in CDMA Mobile Radio ... of Bremen
Simulation Results: Simulation Results: 10 additional users 10 additional users � Loss of 1 dB due to additional users 0 10 for R c = 1/2 and R c = 1/4 add. users R c = 1/4 no add. users � Gap between R c = 1/2 and -1 R c = 1/2 10 R c = 2/3 R c = 1/4 slightly decreases due to better interference suppression for -2 10 longer DS-spreading BER � Code with R c = 1/4 still superior to -3 10 R c = 1/2 � Performance of turbo-coded 8-PSK -4 10 decreases dramatically � Coded modulation scheme as used -5 10 in this work is not suitable for CDMA 3 6 9 12 systems E b / N 0 University 11 Volker Kühn: Turbo Codes and Turbo-Coded Modulation in CDMA Mobile Radio ... of Bremen
Conclusions Conclusions � Turbo codes are no longer superior to convolutional codes for short interleavers and same decoding costs � Accurate channel estimation necessary in order to exploit high coding gains � Pilot signal aided estimation with averaging gains 3 dB over conventional estimation � Low rate coding with low DS-spreading is better than high rate coding and high DS-spreading for coherent demodulation � Turbo-coded modulation is not suitable for an implementation in DS- CDMA systems � Performance improvement for turbo-coded modulation due to multiphase spreading sequences may be possible University 12 Volker Kühn: Turbo Codes and Turbo-Coded Modulation in CDMA Mobile Radio ... of Bremen
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