Cooperative Diversity Coding Strategies Summer School on Communications and Information Theory, August 1st, 2006 Paul Lusina , Lutz Lampe, and Robert Schober {paull, lampe, rschober}@ece.ubc.ca Communication Theory Group Department of Electrical and Computer Engineering University of British Columbia Vancouver, Canada Cooperative Diversity Code Design – p.1/31
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Cooperative Diversity Coding Strategiespaull/teaching/eece_496/coop_div_codes.pdf · 2006-07-28 · Cooperative Diversity Coding Strategies Summer School on Communications and Information
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Cooperative Diversity Coding Strategies
Summer School on Communications and InformationTheory,
• The ideal code would have a weight distribution which wouldensure that αSD = αRD.
• Select an encoder that balances αSD and αRD.
Can ’good’ encoders be found based on this observation?
Cooperative Diversity Code Design – p.15/31
Balancing Technique 2: Finding ’good’ encoders
Control the information and transmission sequence mapping.
Selection of the finite field encoder polynomial• Controls the mapping between the information and codeword se-
quences.
Selection of the finite field primitive element• Controls the mapping between the information and codeword se-
quences.
Mapping to the signal constellation• Controls the mapping between the codeword and transmission se-
quences.
Cooperative Diversity Code Design – p.16/31
Challenging the theory:
’All encoders have the same performance’
Cooperative Diversity Code Design – p.17/31
Convolutional Code (1,7/5) and (1,5/7) Encoders
u(i)
c2(i)
c1(i)
u(i)
c2(i)
c1(i)
Code (1, 7/5) Code (1, 5/7)
• The Extended Weight Enumerator Polynomial gives theinformation and codeword weight distribution for all codewords.
• Assume the Relay repeats the redundancy bits of the source i.e.sSD = sRD
Cooperative Diversity Code Design – p.18/31
Minimum Distance Codeword Performance (high SNR)
Simultaneous decode and forward (Alamouti, ζ = 0.5)
Code dmin dheadmin dtail
min ζ αSD αRD
((αSDαRD)(1,7/5)
(αSDαRD)(1,5/7)
)
dB
(1, 7/5) 5 2 3 0.5 2.13 1.132.43
(1, 5/7) 5 3 2 0.5 2.75 0.50
Time division decode and forward (Min. Dist., MD)
Code dmin dheadmin dtail
min ζ αSD αRD
((αSDαRD)(1,7/5)
(αSDαRD)(1,5/7)
)
dB
(1, 7/5) 5 2 3 0.278 1.63 1.630.72
(1, 5/7) 5 3 2 0.000 2.25 1.00
Cooperative Diversity Code Design – p.19/31
Codeword Weight Distribution Ai,j
Encoder (1,7/5) Encoder (1,5/7)
12
34
56
78
910
12
34
56
78
910
0
10
20
30
40
50
Head Wt
Weight Distribution (1,7/5)
Tail Wt
Coe
f. (d
B)
12
34
56
78
910
12
34
56
78
910
0
10
20
30
40
50
Head Wt
Weight Distribution (1,5/7)
Tail WtC
oef.
(dB
)
• i → Head Weight j → Tail Weight• (1,7/5) encoder has more codewords dSD > dH .• Therefore a ζ exists for αSD = αRD.
Cooperative Diversity Code Design – p.20/31
The proof is in the pudding
Cooperative Diversity Code Design – p.21/31
Encoder Performance Evaluation
Simulation Environment
• Quasi-static independent Rayleigh block fading over all channels• Perfect avoidance of error propagation at the relay using a CRC code.• BPSK modulation with perfect receiver channel state information.
Theory Curves
• Calculation of the head and tail weight for codewords of length of 100.
• Union bound of the code averaged over n = 105 channel realizations.
Pbit ≤1
n
n∑
l
min
1
2,1
k
∑
i,j
Ai,j · Q
√
γ ·(
dist(si,j , s0, ζ,hl)
2
)2
Cooperative Diversity Code Design – p.22/31
Encoder comparison: Alamouti, ζ = 0.5
10 10.5 11 11.5 12 12.5 13 13.5 14 14.5 1510
−3
10−2
Eb/No
BE
R
th. (1,7/5)th. (1,5/7)sim (1,7/5)sim (1,5/7)
15 15.5 16 16.5 17 17.5 18 18.5 19 19.5 2010
−4
10−3
Eb/No
BE
R
th. (1,7/5)th. (1,5/7)
• (1,7/5) has a theoretical advantage of 0.1 dB which is maintainedat high SNR.
• Simulation results show almost equal performance at lower SNR.