Recent Progress in Mobile Transmission Joachim Hagenauer Institute for Communications Engineering () Munich University of Technology (TUM) D-80290 München, Germany State University of Telecommunications (SUT) St. Petersburg, Russia, April 6th, 2004
Outline The turbo principle approaches Shannon s limits MIMO systems allow high data rates in mobile systems Analog VLSI chips allow higher speed and low power consumption
History: Introduction 1948: Shannon s absolute limits in communications, e.g. 0.2 db in Eb/N0 for binary codes with rate 1/2 on AWGN channel 1962: Gallager s low density parity check codes with iterative decoding 1966: Forney: Concatenated codes before 1993: Concatenated codes (Viterbi plus RS codes) approach Shannon s limit by by 2.5 db and with iterations by 1.5 db. 1993: Berrou, Glavieux and Thitimajshima: Turbo decoding approaches Shannon s limit by 0.5 db. 1995: Douillard, Glavieux, Berrou et al: Turbo equalization 1997: Turbo principle recognized as general method in communications systems 2001: Chung, Forney, Richardson, Urbanke :Iterative decoding of Irregular LDPC Codes within 0.0045 db of Shannon limit
Introduction The Turbo Principle comprises...... a communication system with serial and/or parallel concatenations of components... a posteriori probability (APP) symbol-by-symbol decoders/detectors... soft-in/soft-out decoders/detectors... interleavers between the components... exchange of extrinsic information between components in the form of probabilities or log-likelihood ratios
The Turbo Principle...... in mechanics
... in communications Decoder 1 Decoder 2... in mechanics The Turbo Principle...
Examples for serial concatenation in communications systems data Transmitter Encoder Inter Encoder I leaver II Receiver Decoder Deinter Decoder II leaver I data estimate AWGN Inter leaver configuration en-/decoder I (outer code) en-/decoder II (inner code) serial code concat. FEC en-/decoder FEC en-/decoder turbo equalization FEC en-/decoder Multipath channel/detector turbo BiCM FEC en-/decoder Mapper/demapper turbo MIMO FEC en-/decoder Mapper & MIMO detector turbo multiuser FEC en-/decoder SISO multiuser detector turbo source-channel source encoder FEC en-/decoder LDPC code/decoder check nodes variable nodes
" )( * 0 +, " $ %& ' " +-,!#" )( * 1 *2!. / %& ' Exchange of extrinsic information between horizontal and vertical decoding Principle of Turbo Decoding for a parallel concatenated scheme.
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 E b /N 0 in db 10 4 it. 3 9 it. 2 it. 1 10 3 BER 10 2 it. 0 10 1 uncoded R=1/2 parallel concatenated code Shannon limit 10 0 Rate 1/2, constituent code: rate 2/3, memory 2, interleaver size 1024 Performance of Decoder of a PCC Turbo Code
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 E b /N 0 in db 10 4 10 3 BER 10 2 10 1 Shannon limit uncoded R=1/2, M=2, interleaver of size: 1024, it. 9 R=1/2, M=4, interleaver of size: 1024, it. 9 R=1/2, M=4, interleaver of size: 65536, it. 18 10 0 Influence of the Interleaver Size for a PCC Turbo Code
Low Density Parity Check (LDPC) codes and their Turbo decoder A low density parity check code of rate k/n can be described as a serial concatenation of n variable nodes as inner repetition codes with n k check nodes as outer single parity check nodes.
4 3 3 = D G 5 5 8 : C 9 4 5 data estimate FEC decoder 4<; 7 E 8 D 7 5 8 D 7FE LISS > @A? >? data FEC encoder Mapper 6 7 5 8 > B System with Multipath Channel and Receiver with Turbo Feedback
H TP R Q K PO R Q U V V W H Q Q LSM data estimate outer decoder HJI LNM P/S demodulator channel data outer encoder S/P modulator V Turbo applications: QAM with channel codes
MIMO systems allow high data rates in mobile systems Classical Multiplex and Diversity Systems: A new dimension is opened by space (multiple transmit and receive antennas: MIMO) Method yields costs Time Div. and rate gain bandwidth Frequency Div. and rate gain bandwidth Code Div. and rate gain bandwidth, complexity and interference Space Div. and rate gain complexity and interference
Beamforming antenna scenario Beam can be made adaptive
Multiple antenna scenario aiming for rate gain Multiple antennas needed at transmitter and receiver
X ^ X _ X `[ X Y X Z X [ \ \ X [ ` X X \ \ ` X X a X [ \ \ X [ X c X \ \ \ \ []\ Y \ b \ d \ \ Example of V-BLAST for NT = 4 and rate gain 4 if NR 4. The Bell Lab Layered Space Time architecture (Foschini 1996 BLAST): Systems aiming for rate gain
Multiple antenna scenario aiming for diversity gain Transmit Diversity: Receiver (i.e. cellphone) needs only one and simple antenna
k k k k k k k k k y = Hx + n. o fil n j q fil m j k t fil j n e fil ml n j o fp j q fsr j k t fp j o fih j euf r p j q fih j k t fih j egfih h j The multiple-antenna (MIMO) channel model
Channel capacities of SISO and MIMO systems (Telatar 1995) The channel capacity for a single-input/single-output (SISO) fading channel with complex signaling and perfect channel knowledge at the receiver C = log 2 (1 + h (11) 2E s ) and for the multiple-input/multiple-output MIMO channel C = log 2 det IN R + E s N0 NTN0 HH H Both capacities measured in bits/channel use are random variables. Therefore the average (ergodic) capacity C = E H{C}. and the outage capacity P (C < Cx) = x 100, 0 < x < 100, are of interest.
10% outage capacity of different MIMO channels Gaussian channel input
0 0 5 10 15 20 25 E /N in db S 0 2 N T =N R =1 4 12 10 8 6 N T =N R =4 C 10 in bits/channel use 14 16 Gaussian input QPSK 16 QAM 18 Discrete (QPSK, 16-QAM) and Gaussian channel input 10% outage capacity of different MIMO channels
v Ž { Ž x ˆ Œ v w Ž data estimate APP Decoder vzy Detector Š ƒ ƒ ˆ Encoder data w~} Space Time Mapper FEC-MIMO Scheme with Turbo detector/decoder
MIMO Turbo Detector Inner MIMO channel with Sequential detector (LISS) Simulation results: outer PCC code r = 1/2, QPSK, NT = NR = 4,
Introduction to analog decoders and receivers Receivers and decoders (especially turbo decoders) use soft (real and not binary) values (probabilities, log-likelihood values) They still operate in discrete time and with discrete operations Can we do decoding in continuous time and values: analog? Are receivers in analog VLSI possible? First Proposals: JH (ITW 98,ISIT 98), Loeliger (ISIT 98) High speed receivers in digital VLSI implementation are area and power consuming FEC decoders for high speed communications should work in the Gbit/s range Analog VLSI Implementations of functions like Viterbi, APP, Turbo algorithm should be faster smaller and less power consuming
Realization of an 8-state trellis section
Memory one tailbiting convolutional code
The analog decoder outperforms 6 digital iterations E b /N 0 in db 10 5 1 0 1 2 3 4 5 6 10 4 10 3 BER 10 2 10 1 uncoded (32,16) analog (32,16) MAP 16x16 analog turbo 16x16 1st it. 16x16 2nd it. 16x16 3rd it. 16x16 6th it. 10 0 Simulation measurement results Building a Turbo code from memory two tailbiting convolutional code
High Speed Implementation of the (16,8,3) Tailbiting Code (2001) by TUM/Lucent
Comparison of Several Implementations TUM ETH University Universities Lucent Endora of Utah Padova, Torino code (16,8,3), m=1 (18,9,5), m=2 (8,4,4) ext. Hamming UMTS, 1/3, mem. 3 process 0.25µm BiCMOS IBM6HP 0.8µm BiCMOS 0.5µm CMOS 0.35mum CMOS chip area 1.68mm 2 1.64mm 2 7.28mm 2 2.25mm 2 9mm 2 transistor # bipolar 441 940 - - # nmos 356 - n.a. n.a. # pmos - 650 n.a. n.a. total # per inf.bit&state 49.8 54.4 44.17 n.a. n.a. supply 3.3V 3.3V 5V n.a. 3.3 V bias 80µA (nmos) per block 200µA (bipolar) 400µA 200µA or 50µA 10µA 10µA power 20mW 150mW 98mW @ 200µA est. 3.8mW 5.6mW consumption 50mW @ 50µA power per 2.72mW @ 200µA inf.bit&state 1.25mW 9.4mW 1.38mW @ 50µA 0.32mW 0.028mW measurements channel AWGN AWGN BSC AWGN speed 160Mbit/s 10 Gbit/s 100Mbit/s 10Mbit/s 2Mbit/s BER yes tbd. n.a. n.a. n.a. year chip worked? 1999 Yes 2002 Yes 2001? 2001 2003?
Conclusions The Turbo Principle is a very general principle Approaching the capacity limits of mobile systems is possible Analog FEC Decoders are possible and have many advantages especially for tailbiting convolutional codes (TBCC) and turbo decoding Proof of concept prototype analog VLSI of TUM/Lucent with TBCC works at up to 10 Gbit/s. Worldwide nine groups currently working on analog decoder design There are many more applications for the Turbo Principle: Turbo source compression Joint source channel coding Interference cancellation Papers can be downloaded from WWW..EI.TUM.DE