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EN Data Communication and Networking Point-to-Point Protocols

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1 EN253203 Data Communication and Networking Point-to-Point Protocols
Asst. Prof. Nararat Ruangchaijatupon Electrical Engineering Program Faculty of Engineering, KKU Office: EN04325A,

2 What is PPP? A protocol in the Data Link Layer (Layer2)
Commonly used layer2 protocols: LANs – Ethernet (IEEE802.3) (CCNA 1, Chapter 5: Ethernet, WANs HDLC (High-Level Data Link) PPP (Point-to-Point Protocol) PPP comes after HDLC and SLIP (Serial Line IP) for improvement

3 HDLC What is HDLC? Let’s understand it a bit.
Watch -> PPP comes after HDLC to improve Authentication Compression Multilink PPP Error Detection Identify Contents

4 Point-to-Point Protocol (1)
Transmission between 2 devices over a serial link Synchronous/Asynchronous link Use over many types of physical networks serial cable, phone line, trunk line, cellular telephone, specialized radio links, and fiber optic links such as SONET Internet service providers (ISPs) - customer dial-up access to the Internet IP packets are encapsulated.

5 Point-to-Point Protocol (2)
ISPs commonly use 2 derivatives of PPP to establish a digital subscriber line (DSL) Internet service connection with customers Point-to-Point Protocol over Ethernet (PPPoE) ( Point-to-Point Protocol over ATM (PPPoA) (

6 3 Components of PPP Encapsulation component (to transmit datagrams over the physical layer) /Framing method Link Control Protocol (LCP) to establish, configure, test, negotiate, setting options, terminate Network Control Protocol (NCP) to negotiate optional configuration for the network layer

7 Multiple Network Layer Protocols
By using NCP Internet Protocol Control Protocol (IPCP) for IP OSI Network Layer Control Protocol (OSINLCP) AppleTalk Control Protocol (ATCP) for AppleTalk Internetwork Packet Exchange Control Protocol (IPXCP) for the Internet Packet Exchange (IPX) DECnet Phase IV Control Protocol (DNCP) for DNA Phase IV Routing protocol (DECnet Phase IV) NetBIOS Frames Control Protocol (NBFCP) for NetBIOS Frames protocol (or NetBEUI) IPv6 Control Protocol (IPV6CP) Source : Point-to-Point_Protocol

8 LCP Configuration Options (1)
Authentication – 2 authentication choices Password Authentication Protocol (PAP) Less secure Challenge Handshake Authentication Protocol (CHAP) Based on challenge-response, more secure Compression – reduce amount of data, improve link throughput Decompression the frames at the destination

9 LCP Configuration Options (2)
Error Detection Checksum and FCS (Frame Check Sequence) Identify fault Loop-data link (prevent loop-back condition) Multilink -> Multilink PPP Link aggregation / Load balancing number the fragments because frames may arrive out of order

10 Let’s Watch https://www.youtube.com/watch?v=7PtTn38f4os

11 PPP Frame (1) Resemble HDLC frame Start with 1-byte flag (01111110)
Source : Resemble HDLC frame Start with 1-byte flag ( ) Then the 1-byte address field (always ) : meaning – all stations are to accept the frame

12 PPP Frame (2) 1-byte control ( ) – unnumbered frame because PPP doesn’t have sequencing not retransmission Numbered mode can be used in case of unreliable transmission (such as wireless link) 1 or 2-byte protocol field What kind of packet is in the payload

13 PPP Frame (3) Payload field – variable length (default 1500 bytes)
Padding (optional) 2 or 4-byte FCS (Frame Check Sequence) Checksum CRC:16 bits (2 bytes) or 32 bits (4 bytes) Default:16 bits - Polynomial x16+x12+x5+1). End with a 1-byte flag ( )

14 Line Activation and Phase (1)
Source: Tanenbaum1996, p.233 Line Dead: No physical layer exists Link Establish: Physical connection established

15 Line Activation and Phase (2)
Authentication Phase LCP option negotiation Network Phase NCP is invoked to configure the network layer Open Phase Data transport Terminate Phase Close the connection (e.g. auth fail, FCS error)

16 Question & Discussion Assignment

17 Delay Models

18 PPP http://personal.sut.ac.th/paramate/files/compcom/compcomm11.pdf

19 Pope Francis, left, and his cousin, Sister Ana Rosa Sivori visit the Supreme Buddhist Patriarch at Was Ratchabophit Sathit Maha Simaram Temple, Thursday, Nov. 21, 2019, in Bangkok, Thailand. (AP Photo/Gregorio Borgia) Source:

20 OSI Model International Organization for Standardization (ISO) developed a reference model for Open System Interconnection (OSI). Because it deals with connecting open systems. Systems that are open for connection with other systems.

21 OSI Reference Model Fig. 1-16

22 OSI Reference Model (cont.)
OSI model does not specify the exact services and protocols to be used in each layer. It just tells what each layer should do. However, ISO has produced international standards for all the layers but they are not the part of the reference model.

23 OSI Reference Model

24 OSI Reference Model closest to the end user. determining resource availability, and synchronizing communication. HTTP,SSH,IE, MSN, Skype translating between application and network formats. formats and encrypts data to be sent across a network. MIME, HTML, CSS GIF. dialogues (connections) between computers, establishes, manages and terminates the connections. L2PT, PPTP,SSL,SQL. Transmission Control Protocol (TCP) and User Datagram Protocol (UDP), quality of service. IP address (IPv4, IPv6), Ipsec, IPX, Apple Talk, routing, subnet. Medium Access Control, Point-to-Point Protocol (PPP), ATM, Ethernet, IEEE the wireless LAN protocol. layout of pins, voltages, cable specifications, hubs, repeaters, modulation, coding, medium. EIA/TIA-232, RJ45, RJ11.

25 Physical layer Concern with transmitting raw bits over a communication channel Make sure when one side sends bit “1”, the other side receives “1”, not “0” How many volts, how many msec, how many pins in the connector and what each pin is used for Mechanical, electrical, interfaces

26 Data Link Layer (1) Take the raw transmission facilities, transform them into a line without transmission errors Apparent to the network layer Break input data into data frames Transmit frames sequentially Process the acknowledgement frames sent by the receiver

27 Data Link Layer (2) Recognize the frame boundary
Special bit pattern (must not be incorrectly interpreted) Since noise may destroy part of frame(s) or complete frame(s) Damaged/lost frames -> retransmit If the acknowledgement frame is lost -> Duplicated frames could be sent

28 Data Link Layer (3) Flow regulation Error handling
fast transmitter -> slow receiver (less buffer space, less speed/bandwidth) Error handling If the line can transmit in both directions Acknowledgement from B to A vs. Data from B to A -> piggybacking Broadcast network Multiple access control

29 Network Layer Control the operation of subnets
How packets are routed from the source to the destination Addressing Static route vs. Dynamic route The start of each conversion Network load Congestion control Different protocols/different packet size

30 Transport Layer Ultimate source and destination machines
Accept data from session layer split it into smaller units Host with several programs tell which message belongs to which connection If require high throughput create multiple network connection Multiplex several transport connections into the same connection to reduce cost Flow of information -> flow control

31 Session Layer (1) Establish sessions between different machines
Log in to remote timesharing systems Transfer a file between 2 machines Token management If traffic can go one way at a time Synchronization Provide checkpoints if transmission fail during operation

32 Presentation Layer (1) Concern with syntax and semantics of the information transmitted Encoding data into a standard way Different computers have different codes (ASCII, Unicode)

33 Application Layer (1) Contains a variety of protocols Example
Network virtual terminal File transfer from different file systems with different naming conventions

34 Data Transmission in OSI Model
Fig. 1-17 Actual data transmission is vertical Each layer is programmed as though it were horizontal Source: Tanenbaum1996, p.34

35 TCP/IP Reference Model
Fig. 1-18 ARPANET -> The Internet First defined: Carf and Kahn, 1974 Later perspective: Leiner et al., 1985 Because sponsor was Depart. of Defense Connections remain intact Some machines/transmission lines were put off Flexible architecture Transfer files vs. real-time speech transmission Source: Tanenbaum1996, p.36

36 Host-to-Network Layer
Host has to connect to the network using some protocol This protocol is not defined and varies from host-to-host, from network-to-network Source:

37 Internet Layer Packet-switching network -> connectionless
Permits hosts to input packets into network Have packets travel independently to destination (through different networks) Packets may not arrive in-order IP (Internet Protocol) specify packet format and protocol Packet routing

38 Transport Layer Allow peer entities on the source and the destination hosts to carry on conversation 2 end-to-end protocols TCP (Transport Control Protocol) Connection-oriented, fragmentation, flow-control -> accurate delivery UDP (User Datagram Protocol) Connectionless, prompt delivery : speech/VDO Do not want sequencing nor flow control

39 Application Layer TCP/IP model does not have session/presentation layers -> little use Application layers contains high-level protocols TELNET -> virtual terminal FTP -> file transfer SMTP -> electronic mail HTTP -> world wide web

40 OSI vs. TCP/IP models comparison (1)
Concept of a stack of independent protocols OSI separates service, interface, protocol TCP/IP does not clearly distinguish OSI model was created before the protocol was invented TCP/IP was created after the protocols (to describe the existing protocols) Does not fit other protocols

41 Question & Discussion Assignment

42

43 PPP http://personal.sut.ac.th/paramate/files/compcom/compcomm11.pdf

44 Delay Models

45 ข้อมูลรายวิชา รหัสวิชา : EN version : 1 ชื่อวิชา : การสื่อสารข้อมูลและระบบเครือข่าย คำอธิบายรายวิชา(ไทย) : การสื่อสารข้อมูลและระบบเครือข่ายขั้นแนะนำ สถาปัตยกรรมเครือข่ายแบบชั้น โปรโตคอลและลิงค์แบบจุดต่อจุด แบบจำลองดีเลย์ในระบบเครือข่ายข้อมูล โปรโตคอลควบคุมตัวกลางในการเข้าถึง การควบคุมการไหล การควบคุมข้อผิดพลาด ระบบเครือข่ายงานบริเวณเฉพาะที่ระบบเครือข่ายสลับ เส้นทางในระบบเครือข่ายข้อมูล ความปลอดภัยระบบเครือข่าย ระบบเครือข่ายก้อนเมฆ ระบบและสถาปัตยกรรมมาตรฐาน คำอธิบายรายวิชา(อังกฤษ) : Introduction to data communications and networks, layered network architecture, point-to-point protocols and links, delay models in data networks, medium-access control protocols, flow control, error control, local area network,switching network, routing in data networks, network security, cloud network, architecture and system, standards

46 2.Digital Transmission Fundamentals
Information can be represented in digital forms. For example, text, speech, audio, data, images and video. Serial and Parallel transmission. The transmission system uses pulses or sinusoids to transmit binary information over a physical transmission medium. The capability of transmission system is affected by several factors including: Amount of energy put into transmitting each signal. The distance that the signal has to transverse. The amount of noise. The bandwidth of the transmission medium

47 Digital Transmission Fundamentals: Channel Capacity
If channel has bandwidth W, then the narrowest pulse that can be transmitted over the channel has width T=1/2W seconds. Thus the fastest rate at which pulses can be transmitted into the channel is given by the Nyquist rate: rmax = 2W pulses/second. The Nyquist rate is the maximum signaling rate that is achievable through an ideal low-pass channel with no intersymbol interference. Question: what is bandwidth? Fourier? Why modulate signal?

48 Digital Transmission Fundamentals: Channel Capacity
Binary information can be transmitted by sending pulse with amplitude +A to send a 1 bit and –A to send a 0 bit. See fig The system has a bit rate of 2W pulse/sec x 1bit/pulse = 2W bps. Bit rate can be increased by sending pulses with more levels. For example, if pulse take on amplitudes from {-A,-A/3,A/3,A} to transmit {00,01,10,11}, then each pulse conveys two bits and bit rate is 4W bps.

49 Digital Transmission Fundamentals: Channel Capacity
If multilevel transmission is used, M=2m amplitude levels, the bit rate is 2Wm bits/second. In the absence of noise, the bit rate can be increase without limit by increasing the number of signal levels M. What is Baud? (some call Baud rate, symbol rate). In digital communication systems, the physical layer gross bitrate, raw bitrate, data signaling rate, gross data transfer rate or uncoded transmission rate is the total number of physically transferred bits per second over a communication link, including useful data as well as protocol overhead. Symbol rate ≤ Gross bit rate Gross bit rate = Symbol rate · m

50 Digital Transmission Fundamentals: cont’d
Signal-to-Noise Ratio (SNR) is defined to measures the relative amplitudes of the desired signal and the noise.

51 Digital Transmission Fundamentals: cont’d
Channel Capacity is the maximum rate at which bits can be transfer reliably. In 1948, C.E. Shannon derived an expression for channel capacity. The Shannon channel capacity is given by: where W is channel bandwidth. SNR is Signal-to-Noise Ratio See, C.E. Shannon, “A Mathematical Theory of Communication”, The Bell System Technical Journal, Vol. 27, pp , , July, October, 1948.

52 Digital Transmission Fundamentals: Shannon Channel Capacity
สายโทรศัพท์มี Bandwidth เท่ากับ 1 kHz และมี signal to noise ratio เท่ากับ 15/1 จงหาความสามารถในการส่งข้อมูลผ่านสายโทรศัพท์นี้ (Ans = 4000bps) If S/N were 30 dB and the bandwidth is 3000Hz, determine Shannon Channel Capacity (Ans ~ 30,000bps) สัญญาณดิจิตอลแบบ Worst case ที่มีขนาด 1 kbps จะมีความถี่เท่าใด กำหนดให้ช่องสื่อสารที่ปราศจากสัญญาณรบกวนมีแบนด์วิดท์ 1 kHz เมื่อนำมาส่งสัญญาณไบนารี จะได้อัตราบิตสูงสุดเท่าไร

53 Digital Transmission Fundamentals: Channel Capacity
Baseband, defined by IEEE, is “the band of frequencies occupied by the (data signal) before it modulates a carrier (or subcarrier) frequency to form the transmitted line or radio signal.

54 Digital Transmission Fundamentals: Line Coding
Line coding is the method used for converting a binary information sequence into a digital signal in a digital communication system. The selection of line encoding involves several considerations such as bandwidth, the ease to recover signal, error detection, immunity to noise and interference. Bipolar = Bipolar-AMI

55 Digital Transmission Fundamentals: Line Coding

56 Digital Transmission Fundamentals: Line Coding
AMI = Alternate Mark Inversion

57 Digital Transmission Fundamentals: Line Coding

58 Digital Transmission Fundamentals: Line Coding

59 Digital Transmission Fundamentals: Line Coding
Nonreturn to Zero (NRZ) NRZ is the easiest way to transmit digital signals and make efficient use of bandwidth. NRZI is an example of differential coding. One benefit of this scheme is that it may be more reliable to detect transition in the presence of noise than to compare a value of a threshold. The main limitation of NRZ signals are the presence of a DC component and the lack of synchronization capability. For example, consider that with a long strings of 1s or 0s for NRZ-L or a long string of 0s for NRZI, the output is a constant voltage over a long period of time. Any drift between the timing of transmitter and receiver will result in a loss of synchronization. NRZ codes are commonly used for digital magnetic recording. Limitations of NRZ make these code unattractive for signal transmission applications.

60 Digital Transmission Fundamentals: Line Coding
Multilevel Binary Mutilevel binary address some of the deficiencies of the NRZ codes. These code use more than two signal levels. (Bipolar-AMI, pseudoternary) There will be no loss of synchronization if a long string of 1s occurs. Because the 1 signals alternate in voltage from positive to negative, there is no net DC component. The bandwidth is considerably less than the bandwidth for NRZ. Simple error detection. A long string of 0s still presents a problem. Multilevel binary signal requires approximately 3dB more signal power than a two-valued signal for the same probability of bit error.

61 Digital Transmission Fundamentals: Line Coding
Biphase Manchester and Differential Manchester are in common use to overcome the limitations of NRZ codes. In the Manchester code, there is a transition at the middle of each bit period. The mid-bit transition serves as a clocking mechanism and also as a data. All of the biphase technique require at least one transition per bit time and may have as many as two transitions. Thus, the maximum modulation rate is twice that for NRZ; This means the greater bandwidth required, but advantages are; Syncrhonization: Because of predictable transition during each bit time, the receiver can synchronize on that transition. The biphase are known as self-clocking code. No DC component: Error Detection: the absence of an expected transition can be used to detect errors. The bulk of the energy in biphase codes is between one-half and one times the bit rate. Thus the bandwidth is reasonably narrow and contains no DC component; however, it is wider than the bandwidth for the multilevel binary codes. Biphase codes are popular technique for data transmission.

62 Digital Transmission Fundamentals: Line Coding
Block & Linear Codes Line coding techniques can be classified to linear code and block codes. Biphase and AMI are linear codes. 4B3T and 3B2T are block code. 2B1Q can be considered to either a block code, or a linear code. 2B1Q, two binary bits are converted to on of four symbols. 4B3T, 4 binary bits are converted to 3 ternary Bauds (3 level). LineCoding-Zarlink.pdf

63 Digital Transmission Fundamentals: Line Coding
4B/5B is block coding. Each 4-bit ‘nibbles’ has extra 5th bit added. As a result, the 5-bit patterns can always have two 1s. This enable clock synchronization required for reliable data transfer. The selection of the 5-bit code is such that each code contains no more than one leading 0 and no more than two trailing 0s. Therefore, when these 5-bit codes are sent in sequence, no more than three consecutive 0s are encountered.

64 Digital Transmission Fundamentals: Line Coding
5B/6B Encoding is the process of encoding the scrambled 5-bit data patterns into predetermined 6-bit symbols. This creates a balanced data pattern, containing equal numbers of 0's and 1's, to provide guaranteed clock transitions synchronization for receiver circuitry. 5B/6B encoding also provides an added error-checking capability. 8B/6T means send 8 data bits as six ternary (one of three voltage levels) signals. 8B/10B, Each octet of data is examined and assigned a 10 bit code group. The data octet is split up into the 3 most significant bits and the 5 least significant bits. This is then represented as two decimal numbers with the least significant bits first e.g. for the octet we get the decimal bits are used to create this code group and the naming convention follows the format /D6.5/. There are also 12 special code groups which follow the naming convention /Kx.y/.

65 Digital Transmission Fundamentals: Line Coding
Data Rate – data elements (bits) sent in 1 sec – unit: bps (gross bitrate, raw bitrate, data signaling rate, gross data transfer rate or uncoded transmission rate) Signal Rate – signal elements/pulses sent in 1 sec – unit: baud (symbol rate, modulation rate) The physical layer net bitrate, information rate, useful bit rate, payload rate, net data transfer rate, coded transmission rate, effective data rate or wire speed (informal language) of a digital communication channel is the capacity excluding the physical layer protocol overhead. Throughput denotes the achieved average useful bit rate in a computer network over a logical or physical communication link or through a network node, typically measured at a reference point above the datalink layer. The throughput often excludes data link layer protocol overhead. The throughput is affected by the traffic. Goodput or data transfer rate refers to the achieved average net bit rate that is delivered to the application layer, exclusive of all protocol overhead, data packets retransmissions, etc. For example, in the case of file transfer, the goodput corresponds to the achieved file transfer rate.

66 Digital Transmission Fundamentals: Line Coding
8B/10B encoding finds application are Fibre Channel, Gigabit Ethernet, InfiniBand, XAUI, and to modulate bytes of audio data on Digital Audio Tape The overhead of the 64b/66b encoding is 3.125%, which is considerably less than the 25% overhead of the previously used 8b/10b encoding scheme. Technologies that use 64b/66b encoding 10 Gigabit Ethernet (most varieties), Fibre Channel 10GFC and 16GFC, 100 Gigabit Ethernet, 10G-EPON, 10 Gbit/s Ethernet Passive Optical Network, Aurora from Xilinx, InfiniBand, Thunderbolt, Common Public Radio Interface 128b/130b encoding, as used by PCIe 3.0, and a very similar variant is the 128b/132b encoding used by USB 3.1.

67 Digital Transmission Fundamentals: Line Coding
Scrambling Techniques The biphase techniques have widespread use in LAN, but they have not widely used in long-distance applications, because these techniques require a high signaling rate relative to the data rate. This sort of inefficiency is more costly in long-distance applications. The idea behind the scrambling techniques is simple: sequences that would result in a constant voltage level on the line are replaced by filling sequences that will provide sufficient transitions for the receiver’s clock to maintain synchronization. The design goals are: No DC component No long sequences of zero-level line signals No reduction in data rate Error-detection capability

68 Digital Transmission Fundamentals: Line Coding
Scrambling Techniques Two techniques are commonly used in long-distance transmission services; Bipolar with 8-zeros substitution (B8ZS) is commonly used in North America High-Density Bipolar of order 3 (HDB3) code is commonly used in Europe and Japan. HDB3 code replaces any instance of 4 consecutive 0 bits with one of the patterns "000V" or "B00V" substitute 8 zeros substitute 4 zeros substitute 4 zeros

69 Digital Transmission Fundamentals: Digital Modulation
A band-pass channel is the channel that do not pass the lower frequencies and instead pass power in some frequency range from f1 to f2. W = f1 - f2 A modem is a device that carries out the function to produce a signal that contains the information sequence and that occupies frequencies in the range passed by the channel.

70 Digital Transmission Fundamentals: Digital Modulation
In Quadrature Amplitude Modulation (QAM), the original information is split into two sequences that consist of the odd and even symbols, Ak and Bk. Ak is called the in-phase component and Bk is called the quadrature-phase component.

71 Digital Transmission Fundamentals: Signal Constellations

72 Digital Transmission Fundamentals: MODEM standards
Most telephone channel have bandwidth in the range f1=500Hz to f2=2900Hz. This implies W=2400 and hence signaling rate of 1/T = W = 2400 pulses/sec. Trellis modulation systems are more complex in that they combine error-correcting coding with the modulation. V.34bis standard can operate at rate of 2400, 2743, 2800, 3000, 3200 or 3429 pulses/sec. A range of bit rates are 2400, 4800, 9600, 14400, 19200, 28800, and

73 Digital Transmission Fundamentals: MODEM standards
Baud, Bit rate? FDM, TDM? Simplex, Duplex? MODEM แบบ V.29 มีความเร็วในการส่งข้อมูล 9600 bps โดยใช้การ Modulation แบบ 16-QAM ที่มี 8 phase และ 2 ระดับสัญญาณ จะมี buad เท่าไร (2400)

74 Digital Transmission Fundamentals: MODEM
The Recommended Standard (RS) 232 is the serial line interface provides connection between computer and communication devices. Data Terminal Equipment (DTE), Data Communications Equipment (DCE); Data Circuit-terminating Equipment.

75 Digital Transmission Fundamentals: MODEM
RS232 is an Electronics Industries Association (EIA) standard specifies interface between DTE and DCE. CCITT recommended a similar standard called V.24. The connectors have 9 or 25 pins D-type connectors, DB-9 and DB-25.

76 Digital Transmission Fundamentals: Optics

77 Digital Transmission Fundamentals: Optics
Wave Division Multiplexing (WDM) The first WDM used two channels, consisting of Shortwave and Longwave. The boundary between these two wavelengths was defined at 1100 nm. The first two WDM wavelengths were chosen and became the de-facto standard : 850 nm for SW, 1310 nm for LW

78 Digital Transmission Fundamentals: Optics
Dense Wavelength-Division Multiplexing (DWDM) 16 or more channels (16 and 40 channel systems are now common).

79 Digital Transmission Fundamentals: Error Detection
Parity checks and Cyclic Redundancy Check (CRC). Error detection requires redundancy Every error-detection technique will fail to detect some errors. Parity checks Parity checks used in early transmission systems. There are two possible regimes for error detection: odd parity and even parity. For parity checking, count only 1’s in a bit sequence, ASCII code is 7-bit code, an eighth bit is added as a parity bit. has three 1s, thus add 0 for the eighth bit if the parity is odd parity. has three 1s, thus add 1 for the eighth bit if the parity is even parity. 8-N-1, 7-E-1, 7-O-1, 7-E-2. Parity check is called Vertical Redundancy Checking (VRC). Its error detection capacity is weak. Detect only 1-bit error.

80 Digital Transmission Fundamentals: Error Detection
The other type of parity checking is called Longitudinal Redundancy Checking (LRC). Generally, LRC was used in addition to VRC to provide a more robust error detection capability, two-dimensional parity check.

81 Digital Transmission Fundamentals: Error Detection
Cyclic Redundancy Check (CRC) CRC is the powerful error-detecting code. For a k-bit block of bits, or message, the transmitter generates an n-bit sequence, Frame Check Sequence (FCS). The frame length is k+n bits that is divisible by some number with no remainder. If the receiver divides the frame by the same divisor, no error occurs. CRC can be viewed in three ways: Modulo 2 Arithmetic Modulo 2 arithmetic uses binary addition with no carries, which is just exclusive-or operation. For example, 1111 eor 1010 = 0101

82 Digital Transmission Fundamentals: Error Detection
No error, if T/P has no remainder. It can be proved that FCS is the remainder, R, of 2nM/P. FCS->CRC

83 Digital Transmission Fundamentals: Error Detection
The pattern P is chosen to be one bit longer than the desired FCS. At minimum, both the high- and low-order bits of P must be 1. Polynomials A second way of viewing the CRC process is to express all values as polynomials in a dummy variable, with binary coefficients. For example, M=110011, M(X)= X5+X4+X1+1, P=11001, P(X)=X4+X3+1 Then T(X) = XnM(X) + R(X)

84 Digital Transmission Fundamentals: Error Detection
All following errors are not divisible by a suitably chosen P(X): All single-bit errors. All double-bit errors, as long as P(X) has at least three 1s. Any odd number of errors, as long as P(X) contains a factor (X+1) Any burst error for which the length of the burst is less than the length of the divisor polynomials. Most larger burst errors.

85 Digital Transmission Fundamentals: Error Detection
Digital Logic The CRC process can be represented by a dividing circuit consisting of exclusive-or gates and a shift register. ถ้าต้องการส่ง ข้อมูล ด้วยวิธีการ CRC และ Generator code x^3 + 1 จงหา CRC สำหรับการส่งข้อมูลชุดนี้ (100) ถ้าต้องการส่ง ข้อมูล ด้วยวิธีการ CRC และ Generator code x^3 + 1 จงหา bit stream ที่ส่งออกจากผู้ส่ง ( )


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