--- 2
TURBO LDPC
--- / / /
(dbm) -20-40 -60-80 0-100 0 4 8 12 16 d
2 2
d>>dc dc
---
f2-f1 >> Bc
RAKE ARQ
α 1 α 2 α 3 α M
Selective Combining SNR Equal-Gain Combining maximal Ratio Combining SNR
10-1 5 2 10-2 5 2 10-3 5 2 10-4 5 2 10-5 5 2 10-6 5 P b M = 4 99.5 98.0 M = 2 M = 1 10 15 20 25 30 35 40 γ b, SNR/bit, db 99.99 99.9 90.0 80.0 70.0 60.0 50.0 40.0 30.0 20.0 10.0 5.0 2.0 1.0 0.5 0.2 0.1 0.05 0.02 0.01-40 M = 1 P out -30-20 -10 0 10 10log 1 ( ) M = 2
1 SNR 10dB SNR M
DSSS / RAKE
DSSS DSSS + / RAKE Bs>>Bc
Bluetooth 1600 79MHz 1Ms/s IEEE 802.11 FHSS 2.5 GSM
GSM
FDD
OTD TSTD Time Switched Transmit Diversity STTD Space Time block coding based Transmit Diversity STTD
cdma2000 OTD
OTD
TSTD WCDMA SCH PSC SSC cdma2000 Walsh PN
WCDMA STTD b0 b1 b2 b3 1 b0 b1 b2 b3 STTD -b2 b3 b0 -b1 2 STTD P-CCPCH S- CCPCH DPCH PICH PDSCH AICH CPICH
STTD STTD 1 STTD 2 TPC TFCI STTD
cdma2000 STTD
1 WCDMA TPC TFCI w1 2 w2 DPCCH (FBI )
WCDMA 1 90 2 Bits
WCDMA 2 Bit 4 4 Bits 3 Bits 8 1 Bit
cdma2000 STD TXAA WCDMA 2 Walsh
TURBO LDPC
n, k k n n-k k BCH Fire RS n, k, m k n n k m l = m+1 GSM IS-95 TURBO
1 [1 1 0 1 0] 1 + x + x 3 [1 1 1] 1 + x + x 2
2 Conv ( [1 1 0 1 0], [1 1 1] ) = (1 + x + x 3 )(1 + x + x 2 ) = 1 + x + x 2 x + x 2 + x 3 x 3 + x 4 + x 5 -------------------------------------------------------------------- 1 + 2x + 2x 2 +2x 3 +x 4 + x 5 [ mod-2 ] 1 + x 4 + x 5. [1 0 0 0 1 1]
k bits, n-bits 3 Conv( [1 1 0 1 0 0 0], [1 1 1] ) = [1 0 0 0 1 1 0] k/n = 1 k/n = 1/2
4 [1 0 1]* Conv( [1 1 0 1 0 0 0], [1 0 1] ) = [1 1 1 0 0 1 0] [1 1 0 1 0 1 0 0 1 0 1 1 0 0] [1 1 1], [1 0 1] ½ known good
bit m+1 bits m =
? [1 1 0 1 0 1 0 0 1 0 1 1 0 0] [1 1 0 1 0] LUT
00 [1 1 0 1 0 0 0] [11 01 01 00 10 11 00]
Viterbi + = Viterbi
Viterbi 1 00 10 11 01 11 01 01 00 10 11
Viterbi 2 00 1/11 10 11 01 11 01 01 00 10 11
Viterbi 3 00 10 11 1 1/01 01 11 01 01 00 10 11
00 10 11 01 Viterbi 4 1 1 0/01 11 01 01 00 10 11
Viterbi 5 00 10 11 01 1 1 0 1/00 11 01 01 00 10 11
Viterbi 6 00 10 11 01 1 1 0 1 0/10 11 01 01 00 10 11
Viterbi 7 00 10 11 01 1 1 0 1 0 0/11 11 01 01 00 10 11
Viterbi 8 00 10 11 01 1 1 0 1 0 11 01 01 00 10 11 0 0/00 00
Viterbi 9 00 10 11 01 1 1 0 1 0 11 01 01 00 10 11 0 0 00 1 1 0 1 0 0 0 [ ] k 00
00 10 11 01 Viterbi 0 inf inf inf Viterbi 00
00 10 11 01 Viterbi 0 inf inf inf 11 01 01 00 10 11 00 h(11, 00) = 2 h(11, 11) = 0 2 0 inf inf max(2,0) + 2 11 11 4 2 1 1!
00 0 10 inf 11 inf 01 inf 2 0 inf inf 4 2 1 1 2 2 1 3 3 1 3 3 4 4 1 3 1 3 4 4 11 01 01 00 10 11 00 11 11 01 00 10 11 00
00 10 11 01 1 0 inf inf inf 2 0 inf inf 4 2 1 1 11 01 01 00 10 11 00 11 11 01 00 10 11 00 2 2 1 3 3 1 3 3 4 4 1 3 1 3 4 4
00 10 11 01 2 0 inf inf inf 1 1 0 1 0 2 0 inf inf 4 2 1 1 11 01 01 00 10 11 00 11 11 01 00 10 11 00 2 2 1 3 3 1 3 3 4 4 1 3 1 3 4 4
2,1,2 5,7
d free d min d free <(5.8)*m m=
2,1,2 2 1 2 5,7 [1 0 1] [1 1 1] d free 5
E b /N 0
Viterbi Viterbi 10 10 bits
Viterbi 1967 Pe Pe BSC DMC 1.5~2dB
1 1 2 3 5 6 7 9 10 11 4 8 12 1,5,9,2,6,10,3,7, 11,4,8,12 1, 2,3,4,5, 6,7,8, 9, 10,11,12 1 2 3 5 6 7 9 10 11 4 8 12 1,5,9, 2, 6,10,3,7,11, 4,8,12 f D = 10 Hz, = 10 Mb/s, = 330,000 bits
P b Turbo
ICC 93 C. Berrou Turbo
Turbo Turbo
RSC U X X U
Turbo ( Z ) 0 = 0 ( X) 0 ( Y) 0 ( ˆd ) ( ) 1 ˆd 2 ( Z) 1 ( X) 1 ( Y) 1 ( Z) 2 ( X) 2 ( Y) 2 L L L ( Z) P 1 ( X) P 1 ( Y) P 1 ( dˆ ) P
Turbo MAP ( Z ) 2 k p 1 (y ) 1 k p 1 Z 1k L 1k (y ) 2 k p 1 L 2k ( Z 2k ) p d (x ) 1 k p 1 (y 2k ) p (x 1k ) p (y 1k ) p
Turbo
Berrou 0.5-1dB
10-1 10-2 Uniform random reverse berrou 10-3 BER 10-4 10-5 10-6 10-7 0 0.5 1 1.5 2 2.5 3 Eb/N0(dB)
RSC helical 0.5dB
10-1 10-2 Helical Berrou Reverse 10-3 BER 10-4 10-5 10-6 10-7 0 0.5 1 1.5 2 2.5 3 Eb/N0(dB)
Turbo Turbo
Turbo 10 0 10-1 EGCfad EGCconv 10-2 BER 10-3 10-4 10-5 0 1 2 3 4 5 6 7 8 Eb/N0(dB)
Turbo 10-1 10-2 MRCconv MRCnew BER 10-3 10-4 10-5 0 2 4 6 8
AWGN Turbo Turbo Turbo
LDPC 1 1962 Gallager Low Density Parity Check Code LDPC 1962 1995 1975 Zyablov Pinsker 1982 Margulis 1981 Tanner
LDPC 2 20 90 Turbo LDPC MacKay Neal Spiser Spielman LDPC LDPC LDPC LDPC LDPC
LDPC 1 LDPC 0 j 0 k 0 j 3 0 LDPC 0 1 GF(q) 0 q-1
LDPC 2 Gallager n j,k LDPC j 1 1 i 1 i- 1 k+1 ik 1 2 MacKay 2 Tanner
LDPC 3 LDPC LDPC Tanner 6 LDPC LDPC 4 0
LDPC LDPC Gallager BP Sipser Spielman
LDPC