1. Submission Title: [Rate 1/4 code for TG4a]
Sep 2005
Project: IEEE P Working Group for Wireless Personal Area Networks (WPANs)
Submission Title: [Rate 1/4 code for TG4a]
Date Submitted: [22-Sep-2005]
Source: [Michael Mc Laughlin] Company [Decawave Ltd.]
Address [25 Meadowfield, Sandyford, Dublin 18, Ireland]
Voice:[+353−1− ], FAX: [What’s a FAX?], E−Mail:
Re: [ a.]
Abstract: [Proposes a FEC scheme for TG4a data]
Purpose: [To promote discussion in a.]
Notice: This document has been prepared to assist the IEEE P It is offered as a basis for discussion and is not binding on the contributing individual(s) or organization(s). The material in this document is subject to change in form and content after further study. The contributor(s) reserve(s) the right to add, amend or withdraw material contained herein.
Release: The contributor acknowledges and accepts that this contribution becomes the property of IEEE and may be made publicly available by P
Mc Laughlin, Decawave

2. FEC Options 1 – 5 FEC 1 FEC 2 FEC 3 FEC 4 FEC 5 Sep 2005 SOC
K= 3,4 or 5
R = ½ or ¼
Coherent Receiver: True Rate = ¼
Non Coherent Receiver: Equivalent to Rate = 1 or ½
(Rate ½ or ¼ before erasures)
FEC 1
Convolutional
Encoder
K= 3,4 or 5
R= 1/4
Coherent Receiver: True Rate = ¼
Non Coherent Receiver: Equivalent to Rate = ½
(Rate ¼ before erasures)
FEC 2
Systematic
Convolutional
Encoder
K= 3,4 or 5
R = 1/2
Convolutional
Encoder
K=3, R= 1/2
FEC 3
Coherent Receiver: Concatenated code, Rate = ¼
Non Coherent Receiver: Convolutional code, Rate = ½
Systematic
Convolutional
Encoder
K= 3,4 or 5
R = 1/2
BCH or RS
GF(28): RS(40,32)
GF(26): RS(43,53)
Coherent Receiver: Concatenated code Rate = 0.4
Non Coherent Receiver: RS code, Rate = 0.8
FEC 4
Systematic
Convolutional
Encoder
K= 3,4 or 5
R= 1/2
Coherent Receiver: Convolutional code Rate = ½
Non Coherent Receiver: Uncoded
FEC 5
Mc Laughlin, Decawave

3. Example FEC Option 3 XOR XOR Sign Pos’n data in XOR Sign Pos’n XOR
Sep 2005
Example FEC Option 3
XOR
XOR
Sign
data in
Pos’n
XOR
Sign
XOR
Pos’n
Inner code: K=3 g1=05, g2=02 (systematic)
Outer code: Rate ½ K=3 g1=07, g2=05
Mc Laughlin, Decawave

4. Same as FEC Option 2 Sign XOR data in Pos’n XOR XOR Sign XOR Pos’n
Sep 2005
Same as FEC Option 2
XOR
Sign
data in
XOR
Pos’n
XOR
Sign
XOR
Pos’n
Overall code: Rate ¼ K=5 g1=35, g2=16, g3=21, g4=12
Mc Laughlin, Decawave

5. Option 3 is subset of Option 2
Sep 2005
Option 3 is subset of Option 2
Option 2: Each coded bit is a generated by a combination of 2 polynomials
All Option 3 polynomial combinations can be generated by Option 2
Converse is not true
Best FEC 2 at least as good as Best FEC 3
Mc Laughlin, Decawave

6. Rate ¼ Coherent - Coherent receiver sees all 4 generators e.g.
Sep 2005
Rate ¼ Coherent
- Coherent receiver sees all 4 generators e.g.
g1=25, g2=12, g3=23, g4=16
k=5
dfree=15
# parallel paths=1
Mc Laughlin, Decawave

7. Sep 2005
Non Coherent Receiver
See rate ¼ convolutional code punctured to rate ½
g2=12, g4=16 => Rate ½ K=4
dfree = 5
about 3.0dBs performance improvement over uncoded at 10-2
8 state decoder
Mc Laughlin, Decawave

8. Rate ¼ K=5 Performance Sep 2005 Mc Laughlin, Decawave
AWGN PER for Rate 1/4 K=5 g=[25,12,23,16] (Blue) and Rate 1/2 K=5 10 10 -1
PER 10 -2
g = 33,02 non-antipodal (Option 3 coherent)
g = 33,02 non-antipodal (Option 3 non-coherent)
g = 35,23 antipodal (Option I) 10 -3
Coherent rate 1/4 K=5
Non-coherent rate 1/4 K=5 (Eff K=4) 10 -4 2 4 6 8 10 12 14
Eb/No
Mc Laughlin, Decawave

9. Lower Complexity K=4, Rate ¼ Code
Sep 2005
Lower Complexity K=4, Rate ¼ Code
g1=17, g2=04, g3=15, g4=06
Coherent Receiver sees all generators
k=4, dfree=13, # parallel paths=2
Exactly the same as best BPSK K=4 Rate ¼ code
Non-Coherent Receiver sees only g2 and g4
g2=04, g4=06
k=3, dfree=3, # parallel paths=1
Compare to best dfree of 5 for k=3
Mc Laughlin, Decawave

10. Sub Optimal K=4, Rate ¼ code
Sep 2005
Sub Optimal K=4, Rate ¼ code
g1=17, g2=04, g3=15, g4=07
Coherent Receiver sees all generators
dfree=12, k=4
# parallel paths=1
lose ~0.35dB for dfree, gain ~0.2dB for #parallel paths
overall lose ~0.15dB
Non-Coherent Receiver sees g2 and g4
g2=04, g4=07
k=3, dfree=4, # parallel paths=1
Compare to best dfree of 5 for k=3
Mc Laughlin, Decawave

11. Compare K=4, Rate ¼ and K=5, Rate ½
Sep 2005
Compare K=4, Rate ¼ and K=5, Rate ½
AWGN PER for K=4, Rate 1/4 and K=5 Rate 1/2 2 4 6 8 10 12 14 -4 -3 -2 -1
PER
[17,04,15,06] Coherent
[17,04,15,06] Non-coherent
[17,04,15,07] Non Coherent
[17,04,15,07] Coherent
g = 33,02 non-antipodal (Option 10 coherent)
g = 33,02 non-antipodal (Option 10 non-coherent)
g = 35,23 antipodal (Option I)
Eb/No
Mc Laughlin, Decawave

12. Rate ¼ K=4 and K=5 Performance
Sep 2005
Rate ¼ K=4 and K=5 Performance
AWGN PER for Rate 1/4 K=4, Rate 1/4 K=5 and and Rate 1/2 K=5 10 10 -1 -2
PER 10
K=4 Rate ¼ Optimal Coherent
K=4 Rate ¼ Opimal Non-Coh
K=5 Rate ¼ Non Coherent
K=5 Rate ¼ Coherent 10 -3
g = 33,02 non-antipodal (Option 10 coherent)
g = 33,02 non-antipodal (Option 10 non-coherent)
g = 35,23 antipodal (Option I) 10 -4 2 4 6 8 10 12 14
Eb/No
Mc Laughlin, Decawave

13. K=4 Optimal vs Sub Optimal
Sep 2005
K=4 Optimal vs Sub Optimal 2 4 6 8 10 12 14 -4 -3 -2 -1
AWGN PER for Rate 1/4 K=4 g=[17,04,15,06] and g=[17,04,15,07]
Eb/No
PER
[17,04,15,06] Coherent
[17,04,15,06] Non-coherent
[17,04,15,07] Coherent
[17,04,15,07] Non-coherent
Mc Laughlin, Decawave

14. Rate ¼ need 4 bits / uncoded bit
Sep 2005
Rate ¼ need 4 bits / uncoded bit
~1000ns
2 codes transmitted every microsecond
Mc Laughlin, Decawave

15. Original Option 1 Proposal
Sep 2005
Original Option 1 Proposal
~1000ns
2 codes transmitted every microsecond
Mc Laughlin, Decawave

16. Summary The K=4, rate ¼, sub-optimal code is recommended (17,04,15,07)
Sep 2005
Summary
The K=4, rate ¼, sub-optimal code is recommended (17,04,15,07)
Coherent performance as good or better than Rate ½ K=5
Non-Coherent performance also very good. 1% PER at ~10.5dB Eb/No
8 state, each state 2 possible outputs
=>low complexity decoder
Systematic code => allows receiver without viterbi
Mc Laughlin, Decawave