1. ECEN5533 Modern Commo Theory Dr. George Scheets. Lesson #34
ECEN5533 Modern Commo Theory Dr. George Scheets Lesson # April 2016
Read 6.4 – 6.5
Problems: 9.2, 4, & 7
Design #2 due Friday, 8 April
Corrected tests due Friday, 15 April

2. ECEN5533 Modern Commo Theory Dr. George Scheets. Lesson #35
ECEN5533 Modern Commo Theory Dr. George Scheets Lesson # April 2016
Skim 6.6 – 6.9
Problems: 5.8, 6.2, & 6.3
Design #2 due Friday, 8 April
Corrected tests due Friday, 15 April

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5. No Coding Transmitter Receiver Modulator 11 Data bits in 11 BPSK
Data bits out
Receiver
Matched
Filter
Detector
Data bits out
P(Data BE) = 9.730*10-6
P(Data Word Error)
= 107.4*10-6
BPSK
11 Data bits in

6. Detects and/or corrects
FEC Coding
Transmitter
FEC Coder
Adds extra
parity bits.
11 Data bits in
15 Code bits out
From Receiver
Matched Filter
Detector
FEC Decoder
Removes parity bits.
Detects and/or corrects
errors.
15 Code bits in
P(Code BE) = 127.6*10-6
11 Data bits out
P(Data Word Error)
≈ 1.707*10-6
P(Data BE) ≈ .2278*10-6
(was 9.720*10-6)
Equation 6.46

7. FEC Example Uncoded (15,11) Code Bit Rate 4800 bps 6545 bps
P(BE) out of (10-6) (10-6)
Matched Filter
detector
P(11 bit Data (10-6) ≈ 1.708(10-6)
Word Error)
P(data BE) (10-6) ≈ (10-6)
(using Eqn 6.46)

8. FEC Examples Coding can make things worse
MFD P(BE) gets worse as bit rate increases
h(t) = 1; 0 < t < T, for an integrator
H(f) = sinc with a phase shift Main lobe BW = 1/T Hz
Integration time becomes shorter
H(f) becomes wider, less of a low pass filter

9. FEC Examples In the limit, as bit interval T approaches zero
# of independent samples approaches 1
MFD P(BE) approaches SSD P(BE)
Suppose you have a system where
P(BE) = 0.02 for MFD at bit rate R (no FEC)
P(BE) = 0.03 for MFD at bit rate 2R (2:1 FEC)
P(BE) = 0.04 for MFD at bit rate 3R (3:1 FEC)

10. Matched Filter Detector & No coding: Block Diagram
Source
Channel Coder
Symbol Detector:
Matched Filter
Channel
Suppose P(Data Bit Error) = .02

11. Suppose P(code bit error) = .03
MFD 2:1 FEC 2R
code
bps
Source Coder:
Input = 1 bit.
Output =
Input + Parity
bit.
Source
Channel Coder R
application
bps R
app.
bps
2R code bps
Source Decoder:
Looks at blocks of
2 bits. Outputs
1 bit.
Symbol
Detector:
Matched
Filter
Channel
Suppose P(code bit error) = .03

12. Example) MFD 2 bit code words
Suppose you transmit each bit twice, smaller bit width will cause P(Code Bit Error) to increase to, say 0.03
Legal Transmitted code words; 00, 11
Possible received code words 00, 11 (appears legal, 0 or 2 bits in error) 01, 10 (clearly illegal, 1 bit in error) P(No code bits in error) = .97*.97 = P(One code bit in error) = 2*.97*.03 = P(Both code bits in error) = .03*.03 = .0009
Decoder takes 2 code bits at a time and outputs 1 data bit If illegal code word received, it can guess 0 or % %(1/2) = 97% of time correct bit output .09% %(1/2) = 3% of time the incorrect bit is output
FEC makes it worse: 3% data bit error vs 2% No Coding

13. MFD 2:1 FEC 2R code bps Source Coder: Input = 1 bit. Source
Output =
Input + Parity
bit.
Source
Channel Coder R
application
bps R
app.
bps
2R code bps
Source Decoder:
Looks at blocks of
2 bits. Outputs
1 bit.
Symbol
Detector:
Matched
Filter
Channel
P(data bit error) = .03
P(code bit error) = .03

14. Matched Filter Detector & No coding: Block Diagram
Source
Channel Coder
Symbol Detector:
Matched Filter
Channel
P(Data Bit Error) = .02
FEC coding can make things worse.

15. Typical FEC Performance
Coded
Plot changes as type of symbol, type of
detector, and type of FEC coder change.
P(BE)
Uncoded
Plot changes as type
of symbol, and
type of detector change.
Last example is
operating here.
There generally always is a cross-over point.
The max possible P(BE) = 1/2.
Eb/No

16. MFD 2:1 FEC 2R code bps Source Coder: Input = 1 bit. Source
Output =
Input + Parity
bit.
Source
Channel Coder R
application
bps R
app.
bps
2R code bps
Source Decoder:
Looks at blocks of
2 bits. Outputs
1 bit.
Symbol
Detector:
Matched
Filter
Channel
P(app. bit error) = .03
P(code bit error) = .03

17. Suppose P(code bit error) = .04
MFD 3:1 FEC 3R
code
bps
Source Coder:
Input = 1 bit.
Output =
Input + two
parity bits.
Source
Channel Coder R
application
bps R
app.
bps
3R code bps
Source Decoder:
Looks at blocks of
3 bits. Outputs
1 bit.
Symbol
Detector:
Matched
Filter
Channel
Suppose P(code bit error) = .04

18. Example) MFD 3 bit code words
Transmit each bit thrice, P(Bit Error) again increases to, say 0.04, due to further increase in the bit rate.
Legal Transmitted code words; 000, 111
Possible received code words 000, 111 (appears legal, 0 or 3 bits in error) 001, 010, 100 (clearly illegal, 1 or 2 code bits in error) 011, 101, 110 (clearly illegal, 1 or 2 code bits in error) P(No code bits in error) = .96*.96*.96 = P(One code bit in error) = 3*.962*.04 = P(Two code bits in error) = 3*.96*.042 = P(Three code bits in error) = .04*.04*.04 =
Decoder takes 3 bits at a time & outputs 1 bit. Majority Rules % % = % of time correct bit is output % % = % of time incorrect bit is output
FEC makes Data BER better (.5% vs thrice the bit rate

19. MFD 3:1 FEC 3R code bps Source Coder: Input = 1 bit. Source
Output =
Input + two
parity bits.
Source
Channel Coder R
application
bps R
app.
bps
3R code bps
Source Decoder:
Looks at blocks of
3 bits. Outputs
1 bit.
Symbol
Detector:
Matched
Filter
Channel
P(app. bit error) = .005
P(code bit error) = .04

20. Matched Filter Detector & No coding: Block Diagram
Source
Channel Coder
Symbol Detector:
Matched Filter
Channel
P(Data Bit Error) = .02

21. Trellis Decoding
source: 1991 IEEE Communications Magazine

22. Coding Gain
P(BE)
Coded
Uncoded
Eb/No

23. Coding Gain
P(BE)
Coded
Uncoded
Target
Data
P(BE)
Eb/No
Required Eb/No

24. Coding Gain with using coder P(BE) Coded Uncoded Target Data P(BE)
Eb/No
Eb/No you can get by
with using coder

25. Coding Gain Link Analysis using FEC: 1) Increase Bit Rate R
2) Include Coding Gain
3) Use Uncoded P(BE) equation.
P(BE)
Coded
Uncoded
Target
Data
P(BE)
Coding Gain
Eb/No

26. Rate 1/2 Turbo Coder
uk (data) & vk (parity bits) are transmitted to far side
vk = v1k 1/2 of the time & v2k other half
Source: Figure 8.26 from Sklar's Digital Communications

27. Rate 1/2 Turbo Decoder ←
Matched
Filter ←
Matched
Filter
xk (corrupted data) & yk (corrupted parity bits)
yk = y1k 1/2 of the time & y2k other half
Source: Figure 8.27 from Sklar's Digital Communications

28. Rate 1/2 Turbo Coding Performance
P(data bit error) = when Eb/No = 0.7 dB & 18 reps
P(bit error) = for BPSK when Eb/No = 0.7 dB
Source: Figure 8.28 from Sklar's Digital Communications