J.Tiberghien - VUB09-07-K.Steenhaut & J.Tiberghien - VUB 1 Telecommunications Concepts Chapter 1.4 Communications Theory

J.Tiberghien - VUB09-07-K.Steenhaut & J.Tiberghien - VUB 2 Contents Data transmission fundamentals –Parallel vs. serial transmission –Synchronous vs. asynchronous communications –Analog vs. digital communications –Shannon’s theorem –Eye diagrams Transmission error correction –Redundant encoding –Sliding window error correction Encoding and modulation

J.Tiberghien - VUB09-07-K.Steenhaut & J.Tiberghien - VUB 3 Contents Data transmission fundamentals –Parallel vs. serial transmission –Synchronous vs. asynchronous communications –Analog vs. digital communications –Shannon’s theorem –Eye diagrams Transmission error correction –Redundant encoding –Sliding window error correction Encoding and modulation

J.Tiberghien - VUB09-07-K.Steenhaut & J.Tiberghien - VUB 4 Parallel Transmission Disadvantages : Differences in propagation delay Cost of multiple communication channels Clock

J.Tiberghien - VUB09-07-K.Steenhaut & J.Tiberghien - VUB 5 Serial Transmission Clock Serial Data

J.Tiberghien - VUB09-07-K.Steenhaut & J.Tiberghien - VUB 6 Serial Transmission with clock/data multiplexing + ClockSerial Data

J.Tiberghien - VUB09-07-K.Steenhaut & J.Tiberghien - VUB 7 Contents Data transmission fundamentals –Parallel vs. serial transmission –Synchronous vs. asynchronous communications –Analog vs. digital communications –Shannon’s theorem –Eye diagrams Transmission error correction –Redundant encoding –Sliding window error correction Encoding and modulation

J.Tiberghien - VUB09-07-K.Steenhaut & J.Tiberghien - VUB 8 Synchronous Transmission Clock + Serial Data Modem DCE DTE Data is carried by the clock signal Tx clock in DTE or DCE Rx clock extracted by DCE

J.Tiberghien - VUB09-07-K.Steenhaut & J.Tiberghien - VUB 9 Synchronous Transmission Clock

J.Tiberghien - VUB09-07-K.Steenhaut & J.Tiberghien - VUB 10 Asynchronous Transmission + Clock synchronization Serial Data Modem DCE DTE The DCE’s just transmit data bits. Provisions for Clock synchronization need to be included in data

J.Tiberghien - VUB09-07-K.Steenhaut & J.Tiberghien - VUB 11 Start-stop synchronization Designed for electro-mechanical terminals Still used in modern electronic terminals ! clock

J.Tiberghien - VUB09-07-K.Steenhaut & J.Tiberghien - VUB 12 External PC modems Synchronous link Modem DTE DCE μPμP Modem DTE DCE μPμP Asynchronous links (serial port or USB) Most external PC modems use an asynchronous link between the PC and the modem and a synchronous link between the modems. The modem contains a microcomputer that buffers the data

J.Tiberghien - VUB09-07-K.Steenhaut & J.Tiberghien - VUB 13 Contents Data transmission fundamentals –Parallel vs. serial transmission –Synchronous vs. asynchronous communications –Analog vs. digital communications –Shannon’s theorem –Eye diagrams Transmission error correction –Redundant encoding –Sliding window error correction Encoding and modulation

J.Tiberghien - VUB09-07-K.Steenhaut & J.Tiberghien - VUB 14 Digital Data Communications TX RX Analog communication channel

J.Tiberghien - VUB09-07-K.Steenhaut & J.Tiberghien - VUB 15 Encoding and Decoding digital signals Transmitter (Tx) –Input : stream of binary numbers –Output : stream of analog signals suitable for transmission over long distances Receiver (Rx) –Input : stream of analog signals »generated by transmitter »distorted by transmission channel –Compares each input signal with all signals which could have been transmitted and decides from which one the input is a distorted image. –Output : stream of binary numbers, preferably identical to the input of the transmitter

J.Tiberghien - VUB09-07-K.Steenhaut & J.Tiberghien - VUB 16 Contents Data transmission fundamentals –Parallel vs. serial transmission –Synchronous vs. asynchronous communications –Analog vs. digital communications –Shannon’s theorem –Eye diagrams Transmission error correction –Redundant encoding –Sliding window error correction Encoding and modulation

J.Tiberghien - VUB09-07-K.Steenhaut & J.Tiberghien - VUB 17 Analog Transmission Channel Bandwidth –Difference between highest and lowest frequency of sine waves which can be transmitted –Number of possible state changes per second Signal to Noise ratio –S/N = (signal power) / (noise power) –S/N determines number of distinct states which can be distinguished within a given observation interval Characterized by : Frequency Received power

J.Tiberghien - VUB09-07-K.Steenhaut & J.Tiberghien - VUB 18 Binary vs. Multi-bit encoding Modulation rate = 1/t (in Baud) Data rate = (1/t) Log 2 n (in b/s) t 1 0 0V +8V -8V +4V -4V t 0V +8V -8V V +2V -2V -6V Noise margin = +/- 4 V Noise margin = +/- 2 V

J.Tiberghien - VUB09-07-K.Steenhaut & J.Tiberghien - VUB 19 Shannon’s Theorem DataRate <= B.Log 2 (1+S/N) B : Channel Bandwidth (in Hertz) S/N : Signal to Noise ratio Examples: Telephone channel, B = 3000 Hz, S/N = 1000 DataRate <= b/s Optical fiber B = 25 THz, S/N >= 1 DataRate <= 25 Tb/s

J.Tiberghien - VUB09-07-K.Steenhaut & J.Tiberghien - VUB 20 Contents Data transmission fundamentals –Parallel vs. serial transmission –Synchronous vs. asynchronous communications –Analog vs. digital communications –Shannon’s theorem –Eye diagrams Transmission error correction –Redundant encoding –Sliding window error correction Encoding and modulation

J.Tiberghien - VUB09-07-K.Steenhaut & J.Tiberghien - VUB 21 Eye Diagrams 101 Clock The incoming waveforms are displayed on an oscilloscope, synchronized by the recovered clock t

J.Tiberghien - VUB09-07-K.Steenhaut & J.Tiberghien - VUB 22 Multi-bit eye diagrams Good signal/noise ratioPoor signal/noise ratio Modern communication channels use phase and amplitude shifts, best displayed in polar eye diagrams

J.Tiberghien - VUB09-07-K.Steenhaut & J.Tiberghien - VUB 23 Communications in degraded mode Same baud rate Half bit/s rate

J.Tiberghien - VUB09-07-K.Steenhaut & J.Tiberghien - VUB 24 Contents Data transmission fundamentals –Parallel vs. serial transmission –Synchronous vs. asynchronous communications –Analog vs. digital communications –Shannon’s theorem –Eye diagrams Transmission error correction –Redundant encoding –Sliding window error correction Encoding and modulation

J.Tiberghien - VUB09-07-K.Steenhaut & J.Tiberghien - VUB 25 Error detection and correction Length of messages : Informative message: Redundancy: # Messages send: # Messages received: Hamming Distance (X-Y): k + r <= LMax k bits r bits, f(inf.mess.) 2 k 2 k+r  |X i -Y i | k+r i=1

J.Tiberghien - VUB09-07-K.Steenhaut & J.Tiberghien - VUB 26 Error Detection Example Belgian Bank Account Numbers Bank account number structure –Bank identification : 3 digits –Account number : 7 digits –Error detection : 2 digits The ten first digits modulo 97 are appended for error detection purposes. This algorithm allows detection of all single digit errors Example : – MOD 97 = 08 – MOD 97 = 01

J.Tiberghien - VUB09-07-K.Steenhaut & J.Tiberghien - VUB 27 Error detecting codes k = 1; r = 1; red.bit = inf.bit Single bit errors are detected if hamming distance between legitimate messages > 1. No guessing is possible as erroneous messages are at equal distances from several correct ones Hd = 2

J.Tiberghien - VUB09-07-K.Steenhaut & J.Tiberghien - VUB 28 Error correcting codes k = 1; r = 2; red.bits = inf.bit Hamming distance between legitimate messages > 2. This implies that each erroneous message is closer to one correct message than to any other Hd = 3

J.Tiberghien - VUB09-07-K.Steenhaut & J.Tiberghien - VUB 29 Error correcting codes Required Overhead for single bit error correction k+r < 2 r information redundancyOverhead 1 <= 4 <= 11 <= 26 <= 57 <= 120 <= % 75 % 36 % 19 % 11 % 6 % 3 %

J.Tiberghien - VUB09-07-K.Steenhaut & J.Tiberghien - VUB 30 Error correction with a 4+3 bit code The three redundant bits are a function of the four data bits

J.Tiberghien - VUB09-07-K.Steenhaut & J.Tiberghien - VUB 31 Error Correction Error detecting codes –Correction by retransmission of erroneous blocks –If few errors, very low overhead –Most common approach to error correction in data communications Error correcting codes –Very high overhead with short data blocks –Longer data blocks can have multiple errors –Used when retransmission impossible or impractical –Also used when error rate rather high. –Error correcting codes for long blocks, with multiple errors exist and are used (trellis encoding)

J.Tiberghien - VUB09-07-K.Steenhaut & J.Tiberghien - VUB 32 Contents Data transmission fundamentals –Parallel vs. serial transmission –Synchronous vs. asynchronous communications –Analog vs. digital communications –Shannon’s theorem –Eye diagrams Transmission error correction –Redundant encoding –Sliding window error correction Encoding and modulation

J.Tiberghien - VUB09-07-K.Steenhaut & J.Tiberghien - VUB 33 Error Correction by Retransmission Time-out Data Ack A B time 12344

J.Tiberghien - VUB09-07-K.Steenhaut & J.Tiberghien - VUB 34 Error Correction by Retransmission Data Ack A B time Inefficient unless round-trip delay << transmission time of a datablock

J.Tiberghien - VUB09-07-K.Steenhaut & J.Tiberghien - VUB 35 Error Correction with sliding window Data Ack A B time Data blocks in sliding window can be transmitted without waiting for an acknowledgment. Receiving acknowledgments pushes window forward.

J.Tiberghien - VUB09-07-K.Steenhaut & J.Tiberghien - VUB 36 Error Correction with sliding window Data Ack A B time Data blocks in sliding window can be transmitted without waiting for an acknowledgment. Receiving acknowledgments pushes window forward.

J.Tiberghien - VUB09-07-K.Steenhaut & J.Tiberghien - VUB 37 Error Correction with sliding window Data Ack A B time Data blocks in sliding window can be transmitted without waiting for an acknowledgment. Receiving acknowledgments pushes window forward.

J.Tiberghien - VUB09-07-K.Steenhaut & J.Tiberghien - VUB 38 Error Correction with sliding window Data Ack A B time Data blocks in sliding window can be transmitted without waiting for an acknowledgment. Receiving acknowledgments pushes window forward.

J.Tiberghien - VUB09-07-K.Steenhaut & J.Tiberghien - VUB 39 Error Correction with sliding window Data Ack A B time Data blocks in sliding window can be transmitted without waiting for an acknowledgment. Receiving acknowledgments pushes window forward.

J.Tiberghien - VUB09-07-K.Steenhaut & J.Tiberghien - VUB 40 Error Correction with sliding window Data Ack A B time Data blocks in sliding window can be transmitted without waiting for an acknowledgment. Receiving acknowledgments pushes window forward. Time-out

J.Tiberghien - VUB09-07-K.Steenhaut & J.Tiberghien - VUB 41 Error Correction with sliding window Data Ack A B time Data blocks in sliding window can be transmitted without waiting for an acknowledgment. Receiving acknowledgments pushes window forward. Time-out

J.Tiberghien - VUB09-07-K.Steenhaut & J.Tiberghien - VUB 42 Error Correction with sliding window Data Ack A B time Data blocks in sliding window can be transmitted without waiting for an acknowledgment. Receiving acknowledgments pushes window forward. 6 Go Back n window management

J.Tiberghien - VUB09-07-K.Steenhaut & J.Tiberghien - VUB 43 Error Correction with sliding window Data Ack A B time Data blocks in sliding window can be transmitted without waiting for an acknowledgment. Receiving acknowledgments pushes window forward. 6 34

J.Tiberghien - VUB09-07-K.Steenhaut & J.Tiberghien - VUB 44 Error Correction with sliding window Data Ack A B time Data blocks in sliding window can be transmitted without waiting for an acknowledgment. Receiving acknowledgments pushes window forward. 8 Buffering required in receiver

J.Tiberghien - VUB09-07-K.Steenhaut & J.Tiberghien - VUB 45 Contents Data transmission fundamentals –Parallel vs. serial transmission –Synchronous vs. asynchronous communications –Analog vs. digital communications –Shannon’s theorem –Eye diagrams Transmission error correction –Redundant encoding –Sliding window error correction Encoding and modulation

J.Tiberghien - VUB09-07-K.Steenhaut & J.Tiberghien - VUB 46 Characterization of random signals* Rvtvtdt()lim().(             1 Autocorrelation function Fourier Spectrum SRd()().cos().     * Students with inadequate mathematical background may skip this slide

J.Tiberghien - VUB09-07-K.Steenhaut & J.Tiberghien - VUB 47 Straight Binary Code v t 0 a Freq Power Frequency spectrum : Maximum at f = 0 important DC component due to voltage asymetry No energy at clock frequency Amplitude of maxima decreases as 1/f

J.Tiberghien - VUB09-07-K.Steenhaut & J.Tiberghien - VUB 48 Manchester Code Frequency spectrum : Nothing at f = 0 High energy at clock frequency Amplitude of maxima decreases as 1/f v t Freq Power

J.Tiberghien - VUB09-07-K.Steenhaut & J.Tiberghien - VUB 49 Asymptotic Behavior of Spectra Both studied codes have energy spectra decreasing as 1/f 2, meaning that the voltage or current spectra decrease as 1/f. This is a consequence of the instantaneous state transitions tn n  sin 1,5,3,1 

J.Tiberghien - VUB09-07-K.Steenhaut & J.Tiberghien - VUB 50 Asymptotic Behavior of Spectra The smoother the waveforms are, the lesser energy will be found in the spectrum at higher frequencies In actual transmission systems, rounded waveforms, such as parts of sine waves will be used. tn n  cos 1,5,3,1 2 

J.Tiberghien - VUB09-07-K.Steenhaut & J.Tiberghien - VUB 51 Modulation Techniques Amplitude Frequency Phase

J.Tiberghien - VUB09-07-K.Steenhaut & J.Tiberghien - VUB 52 Introduced concepts Parallel vs. Serial transmission systems Transmission channel –characterized by bandwidth & signal to noise ratio –puts upper limit on the information throughput Error correction by using redundant coding of information –with error correcting codes –with error detecting codes and retransmission Throughput close to the upper limit requires specific coding of the information (modulation/demodulation)

J.Tiberghien - VUB09-07-K.Steenhaut & J.Tiberghien - VUB 53 Bibliography To know More about Communication Theory I.A.Glover P.M.Grant Digital Communications, Prentice Hall 1998 ISBN Recommended for this chapter