ECE 4710: Lecture #11 1 Binary vs. Multi-Level Bit Message: t 5 V T s = 1 msec T 0 = 8 T s = 8 msec R = (8/8 ms) = 1 kbps FNBW = 1/T s = 1 kHz TsTs T0T0 Binary Waveform

ECE 4710: Lecture #11 2 Binary vs. Multi-Level 8-Bit Message: t 5 V 3 V 1 V T s = 2 msec T 0 = 4 T s = 8 msec D = (4/8 ms) = 500 sps R = (8/8 ms) = 1 kbps FNBW = 1/T s = 500 Hz TsTs T0T0 L =4 Multi-Level Waveform Symbol Key 00 = 0 V 01 = 1 V 10 = 3 V 11 = 5 V Same Data Rate, One-Half BW

ECE 4710: Lecture #11 3 Binary vs. Multi-Level 8-Bit Message: t 5 V 3 V 1 V T s = 1 msec T 0 = 4 T = 4 msec D = (4/4 ms) = 1 ksps R = (8/4 ms) = 2 kbps FNBW = 1/T s = 1 kHz TsTs T0T0 L =4 Multi-Level Waveform Symbol Key 00 = 0 V 01 = 1 V 10 = 3 V 11 = 5 V Same BW, 2  Data Rate

ECE 4710: Lecture #11 4 Binary vs. Multi-Level  Reduced BW OR increased data rate significant advantage for multi-level signal  Why not do this 100% of the time??  Why not increase to L = 8 or L = 16 levels??  Primary disadvantage: for same S/N ratio a multi- level signal will have higher probability of bit errors compared to binary signal  Reduced ability to accurately discriminate between different signal levels

ECE 4710: Lecture #11 5 Binary vs. Multi-Level t 5 V T VS. 5 V 3 V 1 V T t

ECE 4710: Lecture #11 6 Channel Capacity  Shannon’s capacity formula  Use multi-level signal to decrease BW  required S/N increases to maintain same capacity for same BER  User error coding to lower S/N requirement for same BER  required bandwidth increases to handle additional coding bits while maintaining same capacity (data rate)  BW for S/N tradeoff is ** fundamental ** for all communication systems

ECE 4710: Lecture #11 7 Binary Line Coding  Line Codes : Binary 1’s and 0’s represented by a variety of serial-bit signaling formats  Two Major Categories  Non Return-to-Zero (NRZ) »Signal waveform amplitude stays at one constant value for full duration of bit period  Return-to-Zero (RZ) »Signal waveform amplitude returns to zero volt level for a portion of the bit period  zero level portion is usually 0.5 T b for “1” t A TbTb t A TbTb 0

ECE 4710: Lecture #11 8 Binary Line Coding  Four major sub-classifications based on the rules used to assign voltage levels to binary data (1/0)  Unipolar Signaling : positive signaling has “1” = + A volts and “0” = 0 volts »Also called “On/Off Keying”  Polar Signaling : “1”= + A volts and “0” =  A volts  Bipolar (AMI) Signaling : binary “1” represented by alternating positive and negative values while binary “0” is represented by constant zero volt level »Also called “Alternate Mark Inversion” = AMI  Manchester Signaling : “1” represented by positive/negative cycle in one bit period while “0” represented by negative/positive cycle »Also called “Split Phase Coding”

ECE 4710: Lecture #11 9 Common Line Codes

ECE 4710: Lecture #11 10 Common Line Codes

ECE 4710: Lecture #11 11 Shorthand Names  Book adopts shorthand naming convention that is common in industry  Unipolar NRZ  Unipolar  Polar NRZ  Polar  Bipolar RZ  Bipolar  Bipolar vs. Polar  Polar NRZ is sometimes called Bipolar NRZ (Bipolar) »Common in satellite communications »Book does NOT use this convention  Book uses telephone industry convention »T1 Bipolar RZ = Bipolar

ECE 4710: Lecture #11 12 Properties  Various line codes have advantages and disadvantages  Signaling line code selected based on properties and intended application  Important properties  Self-synchronization »Enough timing information built-into code so bit synchronizers in Rx can be designed to extract timing/clock signal from the code itself  Clock signal needed to control sampling trigger in receiver »Long series of binary 1’s or 0’s should NOT cause problem in recovery of clock signal

ECE 4710: Lecture #11 13 Properties  Important properties (continued)  Probability of Bit Error »Rx designed so that BER is low when signal is corrupted by ISI or channel noise  Spectrum/Bandwidth »Signal BW should be small relative to channel BW so no ISI »Spectrum suitable for baseband channels with AC or DC coupling  AC coupled channels like phone lines require line code signal PSD to have little or no energy at DC ( f =0)  If PSD has significant energy at DC then AC channel will significantly attenuate signal, distort signal, and cause large amount of ISI

ECE 4710: Lecture #11 14 Properties  Important properties (continued)  Error Detection »Some line codes can have simple error detection built in »Channel codecs should be easy to implement for chosen line code  Transparency »Data protocol and line code designed so that every possible data sequence is faithfully and transparently received »Code is NOT transparent if certain data sequences are reserved for control purposes  Random data might accidentally generate control sequence »Code is NOT transparent if long string of 1’s or 0’s result in loss of synchronization signal  Bipolar format is not transparent since long string of 0’s will cause loss of clocking signal

ECE 4710: Lecture #11 15 Spectrum  PSD for deterministic waveform given previously as  Stochastic approach finds PSD for line code with random data sequence  more realistic  Digital signal represented by

ECE 4710: Lecture #11 16 Spectrum  For unipolar NRZ line code :  General expression for PSD of digital signal is  F(f ) is FT of f (t) and R(k) is autocorrelation of the binary data given by

ECE 4710: Lecture #11 17  Polar NRZ line code   Possible levels are + A and  A  If data are independent (uncorrelated from bit to bit)  FT of pulse shape is Polar NRZ Spectrum

ECE 4710: Lecture #11 18 Polar NRZ Spectrum  Substituting into Normalized A = 1 A2A2