1. Union Bound Analysis of Bit Interleaved Coded Orthogonal Modulation with Differential Precoding
Shi Cheng and Matthew C. Valenti
Lane Dept. of CSEE
West Virginia University

2. Outline Review of BICM Results of turbo coded BICOM
Bit Interleaved Coded Modulation (BICM) (Caire 1998)
BICM with Iterative Decoding (BICM-ID) (Li and Ritcey 1997)
Results of turbo coded BICOM
Union bound for convolutional coded BICOM
Convolutional Coded BICOM with Differential Precoding(DP)
Conclusions
7/11/2006

3. BICM System Use the off-the-shelf binary codes
For Gray labeled constellations, BICM capacity is close to the Coded Modulation (CM) capacity
Examples: 8PSK, 16QAM with Gray labeling
Binary
Encoder
Bitwise
Interleaver
M-ary
Modulator
Channel
Soft
Decoder
Bitwise
Deinterleaver
Soft
Demodulator

4. Extrinsic Information
Not Gray Labeling?
For the labeling approach other than gray mapping, BICM capacity is worse than the CM capacity
Examples: 16QAM with set partition labeling, Orthogonal modulation
Use BICM with iterative decoding (BICM-ID)
Soft
Decoder
Bitwise
Deinterleaver
Soft
Demodulator
Channel
Bitwise
Interleaver
Extrinsic Information
feedback

5. BICM and CM Capacity of Orthogonal Modulation12 CM
Reference:
M.C.Valenti and S. Cheng, “Iterative demodulation and decoding of turbo coded M-ary noncoherent orthogonal modulation”
IEEE Journal on Selected Areas in Communications, Sept
AWGN Channel,
Noncoherent Detection
M: Modulation Alphabet Size
BICM 10
Minimum Eb/No (in dB) 8
M = 2 6
M = 4 4
M = 16 2
M = 64
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9 1
Code Rate R

6. Turbo Code Simulation Results10
Reference:
M.C.Valenti and S. Cheng, “Iterative demodulation and decoding of turbo coded M-ary noncoherent orthogonal modulation”
IEEE Journal on Selected Areas in Communications, Sept
AWGN Channel,
Noncoherent Detection
Simulation is collected for BER = 10-4, with CDMA 2000 turbo code of length 6138
BICM
BICM-ID 9 8
M = 2 7 6
Eb/No in dB 5
M = 4 4 3
M = 16
M = 64 2 1
M = 64
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.45
0.5
0.55
0.6
Code rate R

7. Summary
BICM-ID improves the performance up to 1dB against BICM without ID.
The gap between the CM capacity and the turbo code result is still large, for M=16 and 64.
Is there any better code?
7/11/2006

8. Preliminary Results of Convolutional Codes (rate = ½)10 10
C = 3
C = 3
C = 4
C = 4
C = 5
C = 5
C = 6
C = 6 10 -1
Turbo code
Turbo code 10 -1 10 -2 10 -2
BER
BER 10 -3 10 -3
Length
6138
Length
6138 10 -4 10 -4 1
1.5 2
2.5 3
3.5 4 1
1.2
1.4
1.6
1.8 2
2.2
2.4
2.6
2.8 3
Eb/No (dB)
Eb/No (dB)
M = 16
M = 64
7/11/2006

9. Union Bound Simple, asymptotically tight
Following Benedetto’s SCCC bound,
Channel coding -> outer code
Modulator and its precoding -> inner code
Uniform interleaving assumption
Outer code
Inner Code
Pairwise Error Probability (PEP)
Binary
Encoder
Bitwise
Interleaver
M-ary
Modulator
Precoding
7/11/2006

10. Symbol-wise Trellis (M=4)
Inner Code Trellis
Trellis of the modulator and its precoding
Allow parallel Transitions
Modulation Type
Precoding
Bit-wise
Trellis
Symbol-wise Trellis (M=4)
BICOM
BICOM-DP
1/1
1/1
10/e
11/e 2 3
0/0
0/0
00/e
01/e 1
0/1
0/1
00/e
11/e 3 2 1 / 1 1 / / e 1 1 1 D 3 / e / e 2 1 / 1 / 1 1 1 / e
0/0
0/0
00/e
11/e 1
7/11/2006

11. Tail Terminated Error Events
For a recursive code, the tail termination input bits could have a positive weight. W
(i)
l,h,j
... 1 2 3 j
Input weight l
Output weight h T
(i)
l',h,j
... 1 2 3 j
Input weight l’
Input weight
l>l’
Output weight h
7/11/2006

12. Example Outer Code: dodd=7, deven=10 Overall Effective Ouput Weight:
Outer Code:
dodd=7, deven=10
Overall Effective Ouput Weight:
hmin=4, with tail termination.
hmin=5, without tail termination. 5 6 7 8 9 10 11 12 13 14 15
-10 -9 -8 -7 -6 -5 -4
Bound no termination
Bound termination 10 -1
simulation 10 -2 -3
Rayleigh R
Noncoherent CSI E F
BICOM-DP
AWGN
Outer Code
Noncoherent g
(o)
= [
1+D 4
, D+D 3 +D 4 ]
Inner Code g
(i) =
1/(1+D) M
= 4, K
= 200
Eb/No (dB)
7/11/2006

13. Bound Results Rate ½ Outer Code g = [ 1+D ,1+D+D ] M = 8, AWGN10
K=300 Simulation
Rate ½ Outer Code
K=300 g
(o) = [
1+D 2
,1+D+D 2 ]
K=600
K=3000 M
= 8, AWGN
K=6000
Coherent Detection
EF bound -5 10 R E
BICOM B g
(i) =1
-10 10
BICOM-DP g
(i)
=1/(1+D)
-15 10 1 2 3 4 5 6 7 8 9 10
Eb/No (dB)

14. Pairwise Error Probability
Equivalent to the PEP of binary FSK, not a function of M (modulation alphabet size)
Channel: AWGN and Rayleigh fading
Detection:
Coherent
Noncoherent with known fading amplitude information.
Noncoherent with Rayleigh fading statistics only.
Use Gauss Chebyshev quadratures if necessary
7/11/2006

15. Bound Results BICOM-DP Rate ½ Outer Code g = [ 1+D +D , 1+D+D +D ] M10
BICOM-DP
Rayleigh Noncoherent noCSI
Rayleigh Noncoherent CSI
Rate ½ Outer Code
Rayleigh Coherent g
(o) = [
1+D 2 +D 3 ,
AWGN Noncoherent
1+D+D 2 +D 3 ]
AWGN Coherent M
= 16, K
=500 -5 10 R E F
Square Law
-10 10
Upper Bound
on AWGN
Noncoherent
Detection
-15 10 5 10 15
Eb/No (dB)

16. Convolutional Code Results10 1
1.5 2
2.5 3
3.5 4
4.5 5 10
-10 -9 -8 -7 -6 -5 -4 -3
C = 3
C = 4 10 -1
Turbo code 10 -2
BICOM-DP
Simulations
BICOM
Simulations
BER
BICOM
Bounds
Length 6138
Rate ½
M = 16
AWGN Channel
Noncoherent Detection
BICOM-DP
Bounds
Eb/No (dB)

17. Convolutional Code Results10
C = 3
C = 4 10 -1
Turbo code 10 -2
BICOM
Simulations 10 -3 10 -4
BER
BICOM
Bounds 10 -5
BICOM-DP
Simulations 10 -6 10 -7 10 -8
Length 6138
Rate ½
M = 64
AWGN Channel
Noncoherent Detection
BICOM-DP
Bounds 10 -9 10
-10 1
1.5 2
2.5 3
3.5 4
4.5 5
Eb/No (dB)

18. Conclusions
Union bound is a simple method to get the asymptotic performance of BICOM system.
Tail termination bits for recursive code need to be considered in the bound.
Interleaving gain is offered by the recursive structure of inner code. The simplest structure is 1/(1+D).
Using convolutional code with differential precoding for M = 16 or 64 orthogonal modulation, we can get better performance than the turbo coded BICOM system.
7/11/2006