ECEN5533 Modern Commo Theory Dr. George Scheets Lesson #19 29 October 2013

1. ECEN5533 Modern Commo TheoryDr. George Scheets Lesson #19 29 October 2013 • Read Section 9.1 - 9.5 • Problems: Chapter 5 #19, 22, 25, 26 • Reworked Design #1 due various dates • Late reworks accepted @ -1 per working day • Quiz #2 (Focuses on Chapters 2 – 4, 5 Digital) • <31 October (Remote) • Reworked Quiz #2 due various dates • Exam #2, 7 Nov (local), < 14 Nov (remote DL) • Design #2, 14 Nov (local), <21 Nov (remote DL)

2. ECEN5533 Modern Commo TheoryDr. George Scheets Lesson #20 31 October 2013 • Read Section 9.6 - 9.7 • Problems: 5.27 & Fiber Optics (on web) • Reworked Quiz #2 due various dates • Exam #2, 7 Nov (local), < 14 Nov (remote DL) • Design #2, 14 Nov (local), < 21 Nov (remote DL)

3. ECEN5533 Modern Commo TheoryDr. George Scheets Lesson #21 5 November 2013 • Read Section 6.1 – 6.3 • Problems: Old Exam #2 • Reworked Quiz #2 due various dates • Exam #2, 7 Nov (local), < 14 Nov (remote DL) • Focus on chapters 2-5 & 9 • Maybe a block FEC coder problem similar to classwork • Design #2, 14 Nov (local), < 21 Nov (remote DL

4. Point Spreads as of Today • Quiz #1 (20 points)Hi = 19.4, Low = 7.3, Ave = 14.35, σ = 3.64 • Exam #1 (100 points)Hi = 90, Low = 60, Ave = 73.80, σ = 10.46A > 87, B > 72, C > 62, D > 52 • Design #1 (70 points)Hi = 69, Low = 46, Ave = 59.30, σ = 6.88

5. Design a Digital Satellite Network • Use Digital Link Equation • Low Earth Orbiting Satellites • Specify # orbiting paths & satellites per path • Generate worst case distance → Uplink & Downlink • Main spec to meet is End-to-End P(Bit Error) • Design Options • fc, Pt, antennas, margin • modulation, compression, FEC, 16 or 32 TDM multiplexing MegaMoron

6. Iridium 6 Low Earth orbits, 11 satellites per polar orbit Not-so-miniature phone. image sources: Wikipedia & www.iridium.com

7. Eb/No versus C/W bps per Hz • As C/W ↓bps want to move per Hz of BW.Should be easier. • If Eb/No too low, Reliable commo impossible. • Required Eb/No > -1.6 dBa.k.a. Shannon Limit

8. BER for Coherent Orthogonal M-FSK • As M = 2k ↑, BER ↓ • BW required ↑ • Violating Shannon's Limit? Image Source: Bernard Sklar's Digital Communcations

9. BER for Coherent M-PSK • As M = 2k ↑, BER ↑ • BW required stays the same. • Baud rate same • Symbol shape same Image Source: Bernard Sklar's Digital Communcations

10. Linear Block Codes • Parity Bits add redundancy Move Legal Words to Higher Dimension • Transmitter can use G to generate Code words from Data words • Receiver can use H to generate Syndrome from received Code words • Syndrome provides clues as to underlying ‘illness’

11. Syndrome • "A complex of symptoms indicating the existence of an undesirable condition or quality." American Heritage Dictionary • Medical Conditions • Cough • Fever • Knife sticking out of side of the head • etc.

12. Linear Block Codes • When plotted in multi-dimensional space • Data words are adjacent • Code words are not adjacent • Hamming Distance, Minimum Distance • Guaranteed Error Detecting Capability = MinDistance - 1 • May detect other errors, but not guaranteed • Guaranteed Error Correcting Capability = (Error Detecting Capability)/2 • May correct other errors, but not guaranteed

13. Linear Block Codes • Minimum Distance Rule • Typically P(Code Bit Error) > P(Data Bit Error) • Linear Block Code Performance Compare P(uncoded data word is received correctly) versus P(code word is correctable) • Both of these word probabilities can be converted to recovered data P(Bit Error)

14. Communication System Source Data, Digitized audio or video. Outputs bits. Modulator Converts bits to a symbol suitable for channel. Channel Coder Adds extra FEC bits. Channel Decoder Examines blocks of bits. If possible, corrects or detects bit errors. Outputs estimate of source bit stream. Symbol Detector Examines received symbol & outputs 1 (binary) or more (M-Ary) bits. Channel Attenuates, distorts, & adds noise to symbols.

15. Channel Coder • FEC codes used in power-limited environments. Allows the designer to trade-off an increase in the bit rate as opposed to increasing the received signal power. • Cell Phones • Deep Space Probes • Compact Disk • FEC codes work best for random errors • Errors frequently occur in bursts • Interleaving used to make bursty errors appear random

16. Modulation • Copper Cable • Electrical pulses frequently used • Fiber Cable • Electrical pulses converted to optical pulses • RF Systems • Sinusoid symbols used • Center frequency impacts antenna size • Binary versus M-Ary • M-Ary packs more bits in the bandwidth • M-Ary more susceptible to decoding errors • M-Ary used when bandwidth is tight & SNR decent

17. Symbol Detector • Extremes: • Single Sample Not affected by increase in bit rate if SNR same • Infinite Sample (Matched Filter Detector)P(BE) gets worse as bit time decreasesAs T  0, P(BE)MFD P(BE)SSD • INPUT:Binary ASK, PSK, FSK, or PulseM-Ary Pulse or QAM (combo of ASK & PSK) • OUTPUT:Baseband (square pulses)

18. No Coding (In Class Example) Transmitter 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) = 107.0*10-6 11 BPSK Data bits in

19. 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

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

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

22. 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

23. Coding sometimes makes things worse P(BE) Coded System is usually unusable by time Eb/No drops this low. Uncoded Eb/No

24. FEC Examples • Matched Filter Detector (MFD) • 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 • Integration time becomes shorter • H(f) becomes wider, less of a low pass filter

25. 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) = 0.1 for SSD for all bit rates • 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)

26. Single Sample Detector & No coding: Block Diagram Source Channel Coder Symbol Detector: Single Sample Channel P(Data Bit Error) = .1

27. Matched Filter Detector & No coding: Block Diagram • Matched Filter shows reduced bit errors compared to SSD • Improvement decreases as symbol rate increases Source Channel Coder Symbol Detector: Matched Filter Channel P(Data Bit Error) = .02

28. 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 P(code bit error) = .03

29. 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 words00, 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 = .9409P(One code bit in error) = 2*.97*.03 = .0582P(Both code bits in error) = .03*.03 = .0009 • Decoder takes 2 code bits at a time and outputs 1 data bitIf illegal code word received, it can guess 0 or 1.94.09% + 5.82%(1/2) = 97% of time correct bit output .09% + 5.82%(1/2) = 3% of time the incorrect bit is output • FEC makes it worse: 3% data bit error vs 2% No Coding

30. 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 P(data bit error) = .03 P(code bit error) = .03 P(Data Bit Error) = .02 when FEC not used.

31. 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. Eb/No There generally always is a cross-over point. The max possible P(BE) = 1/2.

32. 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 P(code bit error) = .04

33. 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 words000, 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 = .884736P(One code bit in error) = 3*.962*.04 = .110592P(Two code bits in error) = 3*.96*.042 = .004608P(Three code bits in error) = .04*.04*.04 = .000064 • Decoder takes 3 bits at a time & outputs 1 bit. Majority Rules.88.4736% + 11.0592% = 99.5328% of time correct bit is output .0064% + .4608% = 0.4672% of time incorrect bit is output • FEC makes Data BER better (.5% vs 2%) @ thrice the bit rate