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TURBOTURBO--LIKE CODES FOR 4GLIKE CODES FOR 4G
Prof. Kyungwhoon Cheun (전 경 훈)
Communication Systems and Circuits Design (CSC) Labhttp://csc.postech.ac.kr
Pohang University of Science and Technology(POSTECH)
Work performed in part for Samsung Electronicsand in part for HY-SDR center
2003-4-21 The 5th Smart Antenna /SDR Workshop 2
Talk Outline
? Code Requirements
? State of the Art
? Code Options for 4G : Pros and Cons? Turbo, LDPC, RA
? Trade-off Decisions
? Design Example ? RP–Turbo Code
? Conclusions
2003-4-21 The 5th Smart Antenna /SDR Workshop 3
Code RequirementsCode Requirements? Performance? Performance approaching channel capacity
? Allow for high speed decoding approaching Gbps rates
? Complexity? Reasonable encoder/decoder gate count, memory
requirements and power consumption
? Flexibility ? Rate, Code length, Puncturing, Modulation, MA scheme
? ARQ? Allow for effective hybrid ARQ
2003-4-21 The 5th Smart Antenna /SDR Workshop 4
Code RequirementsCode Requirements
? The FEC design issue? Design a code that is an acceptable
compromise among the above 4 factors
Performance
Complexity Flexibility
ARQ
2003-4-21 The 5th Smart Antenna /SDR Workshop 5
State of the ArtState of the Art
Eb/No in dB
? So,… , where are we?
Mariner1969
OdenwalderConvolutionalCodes 1976
Turbo Code19930.7dB
N=65,536
Galileo:BVD1992Galileo:LGA
1996
Pioneer1968-72
Voyager1977
0 1 2 3 4 5 6 7 8 9 10-1-2
0.5
1.0 BPSK Capacity Boun
d
Cod
e R
ate
r
Shan
non
Cap
acity
Bou
nd
UncodedBPSK
Globalstar1999
Iridium1998
510 ??bP
Spe
ctra
l Effi
cien
cy
Irregular RA0.98dB
N=10,000
Irregular LDPC
0.95dBN=10,000
Vector LDPC ~1dB
N=8192
Irregular RA0.50dB
N=100,000
Irregular LDPC
0.48dBN=100,000
2003-4-21 The 5th Smart Antenna /SDR Workshop 6
Code Options : TurboCode Options : Turbo
1px
sx
RSCEncoder 1
Interleaver
RSCEncoder 2
N
N
N
n
N
N
2px
* RSC: Recursive Systematic Code* RSC: Recursive Systematic Code
* Invented by C. Berrou, et al., “Near Shannon limit error-correcting coding and decoding: Turbo codes,”Proc. 1993 Int. Conf. Commun., pp 1064-1070, 1993.
* Invented by C. Berrou, et al., “Near Shannon limit error-correcting coding and decoding: Turbo codes,”Proc. 1993 Int. Conf. Commun., pp 1064-1070, 1993.
Puncturer
N
2003-4-21 The 5th Smart Antenna /SDR Workshop 7
Code Options : TurboCode Options : Turbo? Parallel Concatenated Turbo Codes? Pros
? Proven scheme (3G)? Acceptable performance? Excellent flexibility – (trellis based / puncturing)
? Cons? There are now better performing codes? Rather complex decoding? Not suitable for very high data rates? Performance highly dependent on frame size? Not suitable for short frame sizes
? Possible Improvements?? Irregular parallel concatenated Turbo codes? Repeat-Puncture Turbo code (RP-TC)? We will later show an example of this scheme
2003-4-21 The 5th Smart Antenna /SDR Workshop 8
Code Options : LDPCCode Options : LDPCc1
m vcm cv
c2 c3 c4
v1 v2 v3 v4 v5 v6 v7
Checknodes
Variablenodes
mv
??
???
???
? ??
1,0,
}\{'
)('
)(ll
ll ifmmifm
mcCc
vcv
v
vc
v
Regular - Invented by R. G. Gallager (1962), “Low density parity check codes,” IRE Trans. Inform. Theory, vol. IT-8, pp. 21-28, Jan. 1962.
Irregular - Invented by T. J. Richardson, M. A. Shokrollahi, and R. L. Urbanke (2001), “Design of Capacity-Approaching Irregular Low-Density Parity-Check Codes,” IEEE Trans. Inform. Theory, vol. 47, no. 2, pp. 619-637, Feb. 2001.
? ? ? ?
? ? ? ???
??
??
??
??
??
???
????
}{\'}{\'
}{\'}{\')(
)1('
)1('
)1('
)1('
11
11log
vVv
m
vVv
m
vVv
m
vVv
m
cv
c
cv
c
cv
c
cv
c
cv
ee
eem
ll
ll
l
Low Density
2003-4-21 The 5th Smart Antenna /SDR Workshop 9
Code Options : LDPCCode Options : LDPC? LDPC (Low Density Parity Check) : Irregular? Pros
? Best known theoretical performance (0.0045dB)? But how close do we need to be within capacity?? These performance may only be obtained at the expense of very large
frame lengths and degree orders (complexity)
? Cons? Complex encoding? Moderate to complex decoding? Very low flexibility? Hmmm… How much of these are we willing to give up to get
a few tenth of a dB improvement? Flarion Vector-LDPCTM
? Approximately 2.3dB at 10-6 BER, N=1024? Not enough information for fair comparison.
2003-4-21 The 5th Smart Antenna /SDR Workshop 10
Code Options : RACode Options : RA
Regular - Invented by D. Divsalar, H. Jin and R. J. McEliece (1998)“Coding theorems for ‘Turbo-like codes,” in Proc. 36th Allerton Conf. On Commun., Control and Computing, Sept. 1998, pp.201-210.
Irregular - Invented by H. Jin, A. Kandekkar and R. J. McEliece (2000)“Irregular repeat-accumulative codes,” in Proc. 2nd Int. Symp. On Turbo Codes, Sept. 2000, pp.1-8.
2003-4-21 The 5th Smart Antenna /SDR Workshop 11
Code Options : RACode Options : RA
? RA (Repeat Accumulate) : Irregular? Pros? Performance very close to LDPC? Moderate encoding complexity
? Cons? Moderate to complex decoding? Flexibility better than LDPC but still low
2003-4-21 The 5th Smart Antenna /SDR Workshop 12
TradeTrade--Off DecisionsOff Decisions
? Strategy A? Start from LDPC? Accept ??dB loss in performance to gain code
“structure”? ? Reduce encoder/decoder complexity? ? Gain code flexibility
? In many cases this approach will lead to an equivalent “structured” code such as the RA code
2003-4-21 The 5th Smart Antenna /SDR Workshop 13
TradeTrade--Off DecisionsOff Decisions
? Strategy B? Start from Codes with Structure, i.e., Turbo/RA? Accept some loss in structure to gain ? dB in
performance? Loss in “structure” in some sense means “irregularity”or
“randomization”of the code
? There are ways to get code graph “irregularity”or “randomness”without significantly losing desirable code structure? An example will be shown shortly
2003-4-21 The 5th Smart Antenna /SDR Workshop 14
TradeTrade--Off DecisionsOff Decisions
? Our Choice?? We think that the second approach is the answer
? What about other “codes” for 4G at the CSC Lab? Space-time codes? QO-STBC for any number of antennas
? MIMO/BLAST? Combined space-time and Layered Space-Time? Efficient decoding for layered space-time codes
? The final decision for the selection of the FEC shall take into account ALL components and aspects of the system
2003-4-21 The 5th Smart Antenna /SDR Workshop 15
Design Example : RPDesign Example : RP--TCTC
? Repeat-Puncture Turbo Codes (RP-TC)? A simple improvement to traditional parallel
concatenated TCs? Enhanced performance due to increased
interleaver size for a fixed frame size? Enhanced performance due to resulting code
graph irregularity? All desirable characteristics of the parallel
concatenated Turbo code are retained, e.g, flexibility
? Slight increase in decoding complexity
2003-4-21 The 5th Smart Antenna /SDR Workshop 16
Design Example : RPDesign Example : RP--TCTC? Code Structure
RSCEncoder 1
Interleaver
Repeat‘L’
RSCEncoder 2
LN
N
N
LN
N
n
LN
Puncturer
N
1px
sx
2px
2003-4-21 The 5th Smart Antenna /SDR Workshop 17
Design Example : RPDesign Example : RP--TCTC? Weight Distribution
? Code rate=1/3
? Generator=(1+D2)/(1+D+D2)
? Information frame length N=128
? Uniform interleaver
??
???
????
??
freedd
bdb N
EdRQBP
0
2
2003-4-21 The 5th Smart Antenna /SDR Workshop 18
Design Example : RPDesign Example : RP--TCTC? Union Bound:
Packet Error Rate? Uniform interleaver
? Packet length:1024 Bytes
? Information frame length: N bits
? Code rate=1/3
★ Multiple code frames in a packet
2003-4-21 The 5th Smart Antenna /SDR Workshop 19
Design Example : RPDesign Example : RP--TCTC? Code Graph? Decoding by BCJR and Message Passing Algorithm (MPA)
Interleaver
RSC1
RSC2
Variable nodes forsystematicinformation
bits
Tail bits for terminationPunctured parity bit positions
yt2,1 yt2,m
yt1,1 yt1,mys,1 ys,2 ys,N
yp2,1 yp2,L+1 ytp2,1 ytp2,m
yp1,1 yp1,2 yp1,N ytp1,1 ytp1,m
Lbranches Variable node
Hidden variable node
Factor node
yp2,2 yp2,L+2 yp2,(L-1)N+2yp2,(L-1)N+1
← BCJR
← BCJR
2003-4-21 The 5th Smart Antenna /SDR Workshop 20
Design Example : RPDesign Example : RP--TCTC? Simulation :
Packet Error Rate? Uniform interleaver
? Packet length:256 Bytes
? Information frame length: N bits
? Code rate=1/3
? 30 decoder iterations
★ Multiple code frames in a packet
2003-4-21 The 5th Smart Antenna /SDR Workshop 21
Design Example : RPDesign Example : RP--TCTC? Simulation :
Packet Error Rate? Uniform interleaver
? Packet length:1024 Bytes
? Information frame length: N bits
? Code rate=1/3
? 30 decoder iterations
★ Multiple code frames in a packet
2003-4-21 The 5th Smart Antenna /SDR Workshop 22
ConclusionsConclusions
? No clear winner yet, but? Will clearly require codes outperforming current Turbo
codes
? Will require at least as much or more flexibility than 3G
? Different requirements for different environments? Mobile
? Nomadic
? MIMO
? The coming couple of years will be exciting
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