Ch 10
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This document discusses error detection and correction techniques used at the data link layer. It covers parity checks, cyclic redundancy checks (CRC), checksums, and Hamming codes. Parity checks, CRC, and checksums are used for error detection, while Hamming codes can detect and correct errors. The document provides examples of how these techniques work and compares their abilities to detect single-bit and burst errors.
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Networks must be able to transfer data from one device to another with acceptable
accuracy. For most applications, a system must guarantee that the data received are
identical to the data transmitted. Any time data are transmitted from one node to the
next, they can become corrupted in passage. Many factors can alter one or more bits of
a message. Some applications require a mechanism for detecting and correcting errors.
Some applications can tolerate a small level of error. For example, random errors
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a very high level of accuracy.
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corrected before it continues its journey to other nodes. However, most link-layer protocols
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This chapter is divided into five sections.
❑ The first section introduces types of errors, the concept of redundancy, and distinguishes
between error detection and correction.
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using block coding and also introduces the concept of Hamming distance.
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Download to View - Animated Examples
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Error detection uses the concept of redundancy, which means adding extra bits for detecting error at the destination.
Parity Check is one of the Error Correcting Codes.
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Ch 28
This document discusses multimedia and interactive audio/video technologies on the internet. It covers topics like digitizing audio and video, compression standards like JPEG and MPEG, streaming stored and live content, and protocols for interactive audio/video like RTP, RTCP, SIP, and H.323. Diagrams are included to illustrate concepts like frame construction, streaming approaches using web servers or media servers, and protocols for real-time communication and signaling.
Ch 24
This document provides an overview of chapters in a book about application layer networking. It discusses the client-server model and socket interface. Chapter 24 focuses on the client-server relationship and model, and how sockets work for connectionless iterative and connection-oriented concurrent servers. The document outlines topics covered in each chapter relating to application layer protocols like DNS, SMTP, FTP, HTTP and multimedia.
Parity bits
Parity bits are used to detect single bit errors during data transmission. There are two common types of parity - even and odd. Even parity means the total number of 1s in the transmitted bits including the parity bit should be even. Odd parity means the total should be odd. The receiving device calculates parity and compares it to the received parity bit to check for errors. While parity can detect single bit errors, it cannot detect errors if an even number of bits are corrupted.
Ch 18
This document discusses virtual circuit switching technologies including Frame Relay and ATM. It covers the phases of virtual circuit switching including setup, data transfer, and teardown. Frame Relay architecture is examined including its layers and use of DLCIs to identify virtual circuits. ATM is also summarized, including its use of fixed-size cells, multiplexing techniques, and architecture using virtual paths and connections defined by VPI and VCI numbers. The layers of both Frame Relay and ATM are depicted along with their addressing and encapsulation methods.
Lecture 20
This document discusses error detection methods for data transmission. It covers parity checks, which add redundant bits to detect errors. Simple parity check can detect single-bit errors and odd-length burst errors by making the number of 1s in each data unit even or odd. Two-dimensional parity check arranges bits in a table, calculates parity for each row and column, and sends this frame. It can detect burst errors up to the length of redundant bits with very high probability. The lecture provides examples to illustrate how parity checks work to detect errors.
Ch 23
This chapter discusses congestion control and quality of service techniques for data networks. It covers topics like traffic profiling, congestion and its effects on network performance, open and closed loop congestion control, examples of TCP and Frame Relay congestion control, flow characteristics and classes, scheduling algorithms, traffic shaping using leaky and token buckets, integrated services and differentiated services quality of service models, and quality of service in Frame Relay and ATM networks. The chapter also includes various figures illustrating related concepts.
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Computer Networks- Introduction and Data Link Layer
Computer Networks- Introduction and Data Link Layer
Error Checking and Correction (Parity Bit, Majority Voting, Check Digit)
Error Checking and Correction (Parity Bit, Majority Voting, Check Digit)
Similar to Ch 10
network
The document discusses error detection and correction techniques used in data link layers. It covers different types of errors like single-bit and burst errors. It then explains various error detection methods like parity checks, cyclic redundancy checks (CRC), and checksums which work by adding redundant bits. CRC is more advanced than parity checks as it can detect all burst errors up to a certain length as well as most longer bursts. Forward error correction techniques like Hamming codes are also covered, which allow both detection and correction of errors by adding even more redundant bits in specific positions.
Errror Detection and Correction
This document discusses error detection and correction in digital communication. It covers the types of errors like single-bit and burst errors. It then explains various error detection techniques like parity checks, checksums, and cyclic redundancy checks (CRC) that work by adding redundant bits. Finally, it discusses Hamming codes that can not only detect errors but also correct single-bit errors through the strategic placement of redundant bits.
Lecture 5
This document discusses error detection and correction in digital communication. It covers the types of errors like single-bit and burst errors. It then explains various error detection techniques like parity checks, longitudinal redundancy checks, and cyclic redundancy checks which work by adding redundant bits. Finally, it discusses Hamming codes, which can not only detect errors but also correct single-bit errors through the strategic placement of redundant bits.
Data Link Layer Numericals
Here is the presentation for Data Link Layer Numericals from the book Andrew S. Tanenbaum (Computer Networks) and B A Forouzan ( Data Communication and Networking)
Data link layar
The document discusses the functions of the data link layer, including framing data, error detection and correction, and flow control. Specifically, it describes how the data link layer:
1. Organizes the physical layer bit stream into frames and applies error detection techniques like checksums.
2. Uses flow control methods like acknowledgments and windowing to prevent fast senders from overwhelming slow receivers and ensure reliable transmission.
3. Provides an interface between the physical layer and network layer, allowing network layer packets to be reliably transmitted over a communication channel.
Data link layar
The document discusses various functions and protocols of the data link layer, including:
1. Framing of data, error detection using checksums, and flow control to prevent faster senders from overwhelming slower receivers.
2. Common data link layer protocols like stop-and-wait and sliding window protocols using go-back-N and selective repeat to allow multiple frames to be transmitted.
3. Error detection techniques like parity bits, checksums, and cyclic redundancy checks to detect errors in transmitted frames.
Data link layar
The document discusses various functions and protocols of the data link layer, including:
1. Framing of data, error detection using checksums, and flow control to prevent faster senders from overwhelming slower receivers.
2. Common data link layer protocols like stop-and-wait and sliding window protocols using go-back-N and selective repeat to allow multiple frames to be transmitted.
3. Error detection techniques like parity bits, checksums, and cyclic redundancy checks to detect errors in transmitted frames.
Skr+3200+chapter+3+(kweh)
This document discusses computer network error detection and correction. It begins by defining single-bit errors and burst errors. It then explains three common error detection techniques: parity check, cyclic redundancy check (CRC), and checksum. Parity check uses a redundant bit to make the total number of 1s even or odd. CRC performs binary division to generate redundant bits. Checksum adds data bits and compares the sum. For error correction, it describes Hamming codes, which add redundant bits in specific positions to detect and correct single-bit errors.
Computer Networks Module II
Error detection and correction
Data link control and protocols
Point-to-Point access (PPP)
Multiple Access
Local Area Networks: Ethernet
Wireless LANS
Virtual Circuit Switching: Frame Relay and ATM
Data linklayer
The document discusses various aspects of data link layer protocols. It describes the services provided by the data link layer, including framing, error control, and flow control. It then discusses different types of framing, error detection techniques like CRC codes, and elementary data link protocols including stop-and-wait and sliding window protocols. It also covers topics like pipelining, error recovery methods for noisy channels, and the use of finite state machines to model protocols.
Computer Networks/Computer Engineering.pdf
This document discusses error detection and correction in data transmission. It begins with an introduction to types of errors like single-bit and burst errors. It then discusses key concepts like error detection, correction, and forward error correction versus retransmission. The document focuses on block coding techniques for error detection and correction. It explains linear block codes and provides examples of parity-check codes and Hamming codes. Parity-check codes can detect single and odd number of errors while Hamming codes can detect and correct errors.
ch10.ppt
This document discusses error detection and correction techniques for digital data transmission. It covers various types of errors that can occur like single-bit and burst errors. It also describes different coding schemes used for error detection and correction including block coding, linear block codes, cyclic codes, and checksums. Specific codes discussed include parity-bit codes, Hamming codes, and cyclic redundancy checks (CRCs). The techniques are evaluated based on their error detection and correction capabilities as defined by concepts like minimum Hamming distance.
Error Detect and Correct.ppt
This document summarizes key concepts around error detection and correction techniques. It discusses how data can be corrupted during transmission and the need for redundancy to detect and correct errors. Specific techniques covered include cyclic redundancy checks (CRCs), checksums, and cyclic codes. CRCs treat data as polynomials and divide by a generator polynomial to get a remainder that is sent with the data for error checking. Checksums involve sending the sum of data values to check against at the receiver. Cyclic codes allow for cyclic shifts of codewords without changing the meaning. Examples are provided to illustrate these error detection and correction methods.
ERROR_DETECTION.pptx
Error detection refers to the process of identifying and detecting errors or inconsistencies in data or transmitted signals. It is an essential aspect of ensuring data integrity and reliability in various communication systems, computer networks, and storage systems.
The purpose of error detection is to determine if errors have occurred during data transmission or storage and to provide a mechanism to identify and correct these errors. Errors can occur due to various factors such as noise, interference, hardware failures, or software issues. By detecting errors, corrective measures can be taken to ensure the accuracy and integrity of the transmitted or stored data.
There are several techniques and algorithms commonly used for error detection. Here are a few notable ones:
Parity Check: Parity check is a simple and widely used error detection method. It involves adding an extra bit, called a parity bit, to a group of bits being transmitted. The parity bit is set to 1 or 0 based on whether the total number of 1s in the data is even or odd. At the receiving end, the parity bit is recalculated and compared to the received parity bit. If they do not match, an error is detected.
Checksum: Checksum is a technique that involves calculating a numerical value, often a sum or a hash, based on the data being transmitted. This value is then appended to the data. At the receiving end, the checksum is recalculated and compared to the received value. If they do not match, it indicates the presence of an error.
Cyclic Redundancy Check (CRC): CRC is a more sophisticated error detection algorithm widely used in networking protocols and storage systems. It involves generating a cyclic redundancy code based on the data being transmitted. This code is appended to the data, and at the receiving end, the code is recalculated and compared to the received code. A mismatch indicates the presence of errors.
Forward Error Correction (FEC): FEC is an error detection and correction technique that involves adding redundant information to the transmitted data. This redundancy allows the receiver to not only detect errors but also correct them without the need for retransmission. FEC is commonly used in applications where retransmission is expensive or not feasible, such as satellite communications and wireless networks.
Error detection techniques play a crucial role in ensuring data integrity and reliable communication. They provide a mechanism to detect errors and trigger appropriate actions, such as requesting retransmission or performing error correction. By implementing effective error detection mechanisms, data integrity can be maintained, and the overall quality and reliability of communication systems can be improved.
Chapter 10
This document discusses error detection and correction techniques for digital data transmission. It introduces different types of errors that can occur, such as single-bit and burst errors. It describes how redundancy is used to detect and correct errors using block coding techniques. Specific examples are provided to illustrate how block codes are constructed and used to detect and correct errors. Key concepts discussed include linear block codes, Hamming distance, minimum Hamming distance, and how these relate to the error detection and correction capabilities of different coding schemes.
Ch10
This document discusses error detection and correction techniques for digital data transmission. It introduces different types of errors that can occur, such as single-bit and burst errors. It describes how redundancy is used to detect and correct errors using block coding techniques. Specific examples are provided to illustrate how block codes are constructed and used to detect and correct errors. Key concepts discussed include linear block codes, Hamming distance, minimum Hamming distance, and how these relate to the error detection and correction capabilities of different coding schemes.
Ch10
This document discusses error detection and correction techniques for digital data transmission. It introduces different types of errors that can occur, such as single-bit and burst errors. It describes how redundancy is used to detect and correct errors using block coding techniques. Specific examples are provided to illustrate how block codes are constructed and used to detect and correct errors. Key concepts discussed include linear block codes, Hamming distance, minimum Hamming distance, and how these relate to the error detection and correction capabilities of different coding schemes.
Ch10 2 v1
This document discusses error detection and correction techniques using Hamming codes and cyclic codes. It provides examples of calculating Hamming distance between words and finding the minimum Hamming distance of coding schemes. Linear block codes are introduced where the XOR of two codewords results in another valid codeword. Simple parity check codes that can detect single bit errors are examined. Hamming codes that can detect up to two errors and correct single errors are analyzed. Cyclic codes are discussed as a special type of linear block code where cyclically shifting a codeword results in another valid codeword. Polynomial representations and cyclic redundancy checks are presented.
Ch10
This document discusses error detection and correction in digital communications. It begins with an introduction to different types of errors that can occur like single-bit errors and burst errors. It explains that redundancy is needed to detect or correct errors. It then discusses various block coding techniques used for error detection and correction including linear block codes, cyclic codes, and cyclic redundancy checks. Specific error correcting codes like Hamming codes and parity checks are explained through examples. The key aspects of error detection capability, minimum Hamming distance, and generator polynomials in cyclic codes are covered.
10 Error Detection_and_Correction
This document discusses error detection and correction in digital communications. It begins by introducing different types of errors that can occur during data transmission and explains the need for redundancy to detect and correct errors. It then covers various block coding techniques used for error detection and correction, including linear block codes, Hamming codes, and cyclic codes such as cyclic redundancy checks (CRCs). Key concepts discussed include single-bit and burst errors, minimum Hamming distance, encoding and decoding processes, and the properties and advantages of different coding schemes.
Similar to Ch 10 (20)
More from soumya ranjan mohanty
Ch 30
This document discusses message security, user authentication, and key management. It covers digital signatures, symmetric and asymmetric encryption, authentication using keys or nonces, key distribution methods like Diffie-Hellman, and public key infrastructure including the X.500 standard and certificate fields. Kerberos is introduced as a network authentication system using ticket-granting servers. Diagrams illustrate privacy, signatures, authentication approaches, man-in-the-middle attacks, key distribution centers, and the Kerberos process.
Ch 26
The document discusses electronic mail (email) and file transfer protocols.
It provides an overview of email components like mail addresses, user agents, mail transfer agents, and mail access protocols. It also describes the format of emails and common data types in MIME.
For file transfer, it explains that FTP uses TCP connections and ports 20 and 21. It gives examples of transferring files between an FTP client and server by issuing commands over the control connection and transferring data over the data connection. Anonymous FTP is also demonstrated.
Ch 25
The document discusses the domain name system (DNS) which provides a hierarchical and distributed naming system that translates human-friendly domain names to IP addresses. DNS uses a system of name servers that are organized into zones to distribute the mapping of domain names to IP addresses globally. Resolvers use recursive or iterative resolution processes to map names to addresses by querying name servers in the DNS hierarchy.
Ch 22
The document discusses transport layer protocols, focusing on TCP and UDP. It provides details on:
1) The responsibilities of the transport layer, including process-to-process delivery and the connectionless and connection-oriented nature of UDP and TCP.
2) An overview of UDP, including that it is unreliable and uses port numbers for demultiplexing. Common UDP applications and ports are listed.
3) An overview of TCP, including that it is reliable, uses sequencing, acknowledgments and establish connections. TCP segments, flags, and the three-way and four-way handshakes are described.
4) TCP congestion control using sliding windows, and how timeouts and retransmissions handle lost
Ch 21
The document describes various unicast and multicast routing protocols. It discusses Interior Gateway Protocols (IGPs) like RIP, OSPF, and IS-IS that are used for unicast routing within an autonomous system. It also discusses the Border Gateway Protocol (BGP) used for unicast routing between autonomous systems. For multicast routing, it covers protocols like DVMRP, MOSPF, CBT, and PIM that utilize concepts like reverse path forwarding, shared trees, and source trees to efficiently deliver packets to multiple receivers. Key multicast protocols like IGMP are also explained which help multicast routers track group memberships.
Ch 20
This document discusses network layer protocols including ARP, IPv4, ICMPv4, IPv6, and ICMPv6. It provides examples of how ARP maps IP addresses to physical addresses, how IPv4 handles packet fragmentation, and the types of ICMP messages. It also covers IPv6 addressing formats, the IPv6 packet format, and methods for transitioning from IPv4 to IPv6 such as tunneling and header translation.
Ch 17
The document discusses cellular telephone and satellite networks. It covers cellular systems including analog cellular (AMPS), digital cellular (D-AMPS and GSM), CDMA cellular (IS-95), and 3G cellular. It also discusses satellite networks including different types of orbits (GEO, MEO, LEO), examples of satellite systems (Iridium, Teledesic), and applications of satellite communication. Diagrams and figures are included to illustrate key concepts.
Ch 19
The document discusses network layer concepts including addressing, routing, and protocols. It covers IP addressing schemes like classful addressing and subnetting. It also describes routing techniques like next-hop, network-specific, host-specific, and default routing. Examples are provided to illustrate how routers use routing tables to forward packets based on the destination IP address.
Ch 14
This document discusses the evolution of Ethernet technology over three generations from traditional Ethernet to Fast Ethernet to Gigabit Ethernet. It describes the MAC and physical layers of each generation and shows diagrams of their frame formats, implementations, and encoding techniques. Key aspects covered include Ethernet addressing, connection methods, bandwidth sharing, bridging, switching, full-duplex operation, and standards such as 802.3.
Ch 13
The document discusses multiple access protocols for wireless networks. It describes random access methods like ALOHA, CSMA, and CSMA/CA. It also covers controlled access methods using reservation, polling, and token passing. Finally, it examines channelization techniques for dividing bandwidth like FDMA, TDMA, and CDMA. It provides examples checking properties of orthogonal codes used in CDMA.
Ch 15
Wireless LANs use the IEEE 802.11 standard which defines the physical and MAC layers. The physical layer uses either frequency hopping spread spectrum or direct sequence spread spectrum to transmit over radio frequencies. The MAC layer uses CSMA/CA for channel access and defines frame formats for addressing between devices in a basic service set or extended service set. Bluetooth uses a piconet topology with a master-slave relationship between devices for communication at the baseband layer, and supports both single-slave and multiple-slave communication through its L2CAP layer.
Ch 11
The document discusses various data link control protocols and HDLC frame formats. It covers topics like flow control, error control using automatic repeat request (ARQ), and different ARQ protocols including stop-and-wait, go-back-N, and selective repeat. It provides examples of how these protocols operate and calculates link utilization for different scenarios. It also discusses HDLC frame structures, types and fields, and the use of bit stuffing to ensure reliable data transmission.
Ch 09
The document discusses three high-speed digital access technologies: DSL, cable modem, and SONET. It provides details on ADSL technology for DSL, including that it is designed for residential users. For cable modem, it describes how a hybrid fiber-coaxial (HFC) network allows for bidirectional communication over coaxial cable using DOCSIS standards. SONET is introduced as a synchronous TDM system controlled by a master clock that transmits signals using frames and virtual tributaries to provide higher data rates.
Ch 08
This document discusses circuit switching and telephone networks. It describes different types of circuit switches used in telephone networks like space-division, time-division, and crossbar switches. It also describes the major components of telephone networks including local access and transport areas (LATAs), local exchange carriers, switching offices, and points of presence. It notes how telephone networks have transitioned from analog to digital services over time.
Ch 06
This document discusses multiplexing techniques including frequency division multiplexing (FDM), wavelength division multiplexing (WDM), and time division multiplexing (TDM). FDM combines signals by allocating different frequency bands to different channels. WDM combines optical signals using different wavelengths of light. TDM combines data by dividing the transmission time into intervals and allocating each time slot to a different data channel in sequence. The document provides examples of applying these multiplexing techniques and calculating data rates and time intervals.
Ch 05
This document discusses various analog and digital modulation techniques used to transmit digital and analog signals. It provides examples of calculating bit rates, baud rates, and bandwidth requirements for different modulation schemes including ASK, FSK, PSK, QAM, AM, and FM. Key modulation techniques covered are the modulation of a digital signal using digital-to-analog conversion and modulation of an analog signal using amplitude, frequency, or phase modulation.
Ch 04
The document discusses various topics related to digital transmission including line coding schemes, block coding, pulse amplitude modulation, pulse code modulation, sampling, and transmission modes. It provides examples of calculating bit rates for different line coding schemes. It also explains the Nyquist sampling theorem and gives an example of calculating the necessary sampling rate for a signal. Finally, it describes parallel and serial transmission and the differences between asynchronous and synchronous transmission modes.
Ch 03
The document discusses key concepts related to physical layer signals in data communication systems. It covers topics such as analog versus digital signals, signal characteristics like frequency and phase, signal impairments including attenuation and noise, and limits on data transmission rates based on channel bandwidth and signal-to-noise ratio. Examples are provided to illustrate concepts like calculating bandwidth, attenuation in decibels, and transmission rate limits. The document contains diagrams to supplement the explanatory text.
Ch 02
The document discusses network models and layers. It describes a layered model with physical, data link, network, transport, and application layers. The physical layer transmits individual bits between nodes. The data link layer transmits frames between nodes and uses physical addresses. The network layer delivers packets from source to destination, using network addresses. The transport layer delivers messages between processes, using port addresses. The application layer provides services to users. Figures are included to illustrate examples of how data is encapsulated and transmitted across each layer.
Ch 1
This document provides an overview of data communication and networking concepts. Chapter 1 introduces the basic components of data communication including data representation, direction of data flow, and network models. It describes different types of networks including LANs, MANs, and WANs. The chapter also discusses protocols, standards, and the history and structure of the Internet.
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Ch 10
- 1. Data Link Layer PART III
- 2. Position of the data-link layer
- 3. Data link layer duties
- 4. LLC and MAC sublayers
- 5. IEEE standards for LANs
- 6. Chapters Chapter 10 Error Detection and Correction Chapter 11 Data Link Control and Protocols Chapter 12 Point-To-Point Access Chapter 13 Multiple Access Chapter 14 Local Area Networks Chapter 15 Wireless LANs Chapter 16 Connecting LANs Chapter 17 Cellular Telephone and Satellite Networks Chapter 18 Virtual Circuit Switching
- 7. Chapter 10 Error Detection and Correction
- 8. Data can be corrupted during transmission. For reliable communication, errors must be detected and corrected. Note :
- 9. 10.1 Types of Error Single-Bit Error Burst Error
- 10. In a single-bit error, only one bit in the data unit has changed. Note :
- 11. 10.1 Single-bit error
- 12. A burst error means that 2 or more bits in the data unit have changed. Note :
- 13. 10.2 Burst error of length 5
- 14. 10.2 Detection Redundancy Parity Check Cyclic Redundancy Check (CRC) Checksum
- 15. Error detection uses the concept of redundancy, which means adding extra bits for detecting errors at the destination. Note :
- 16. 10.3 Redundancy
- 17. 10.4 Detection methods
- 18. 10.5 Even-parity concept
- 19. In parity check, a parity bit is added to every data unit so that the total number of 1s is even (or odd for odd-parity). Note :
- 20. Example 1 Suppose the sender wants to send the word world . In ASCII the five characters are coded as 1110111 1101111 1110010 1101100 1100100 The following shows the actual bits sent 1110111 0 1101111 0 1110010 0 1101100 0 1100100 1
- 21. Example 2 Now suppose the word world in Example 1 is received by the receiver without being corrupted in transmission. 11101110 11011110 11100100 11011000 11001001 The receiver counts the 1s in each character and comes up with even numbers (6, 6, 4, 4, 4). The data are accepted.
- 22. Example 3 Now suppose the word world in Example 1 is corrupted during transmission. 11111110 11011110 11101100 11011000 11001001 The receiver counts the 1s in each character and comes up with even and odd numbers (7, 6, 5, 4, 4). The receiver knows that the data are corrupted, discards them, and asks for retransmission.
- 23. Simple parity check can detect all single-bit errors. It can detect burst errors only if the total number of errors in each data unit is odd. Note :
- 24. 10.6 Two-dimensional parity
- 25. Example 4 Suppose the following block is sent: 10101001 00111001 11011101 11100111 10101010 However, it is hit by a burst noise of length 8, and some bits are corrupted. 1010 0011 1000 1001 11011101 11100111 10101010 When the receiver checks the parity bits, some of the bits do not follow the even-parity rule and the whole block is discarded. 10100011 10001001 11011101 11100111 1 0 101 0 1 0
- 26. In two-dimensional parity check, a block of bits is divided into rows and a redundant row of bits is added to the whole block. Note :
- 27. 10.7 CRC generator and checker
- 28. 10.8 Binary division in a CRC generator
- 29. 10.9 Binary division in CRC checker
- 30. 10.10 A polynomial
- 31. 10.11 A polynomial representing a divisor
- 32. Table 10.1 Standard polynomials x 32 + x 26 + x 23 + x 22 + x 16 + x 12 + x 11 + x 10 + x 8 + x 7 + x 5 + x 4 + x 2 + x + 1 x 16 + x 12 + x 5 + 1 x 10 + x 9 + x 5 + x 4 + x 2 + 1 x 8 + x 2 + x + 1 Polynomial LANs ITU-32 HDLC ITU-16 ATM AAL CRC-10 ATM header CRC-8 Application Name
- 33. Example 5 It is obvious that we cannot choose x (binary 10) or x 2 + x (binary 110) as the polynomial because both are divisible by x. However, we can choose x + 1 (binary 11) because it is not divisible by x, but is divisible by x + 1. We can also choose x 2 + 1 (binary 101) because it is divisible by x + 1 (binary division).
- 34. Example 6 The CRC-12 x 12 + x 11 + x 3 + x + 1 which has a degree of 12, will detect all burst errors affecting an odd number of bits, will detect all burst errors with a length less than or equal to 12, and will detect, 99.97 percent of the time, burst errors with a length of 12 or more.
- 35. 10.12 Checksum
- 36. 10.13 Data unit and checksum
- 39. Example 7 Suppose the following block of 16 bits is to be sent using a checksum of 8 bits. 10101001 00111001 The numbers are added using one’s complement 10101001 00111001 ------------ Sum 11100010 Checksum 00011101 The pattern sent is 10101001 00111001 00011101
- 40. Example 8 Now suppose the receiver receives the pattern sent in Example 7 and there is no error. 10101001 00111001 00011101 When the receiver adds the three sections, it will get all 1s, which, after complementing, is all 0s and shows that there is no error. 10101001 00111001 00011101 Sum 11111111 Complement 00000000 means that the pattern is OK.
- 41. Example 9 Now suppose there is a burst error of length 5 that affects 4 bits. 10101 111 11 111001 00011101 When the receiver adds the three sections, it gets 10101111 11111001 00011101 Partial Sum 1 11000101 Carry 1 Sum 11000110 Complement 00111001 the pattern is corrupted.
- 42. 10.3 Correction Retransmission Forward Error Correction Burst Error Correction
- 43. Table 10.2 Data and redundancy bits 11 4 7 7 3 4 9 4 5 10 4 6 3 3 2 Number of redundancy bits r 6 3 5 2 3 1 Total bits m + r Number of data bits m
- 44. 10.14 Positions of redundancy bits in Hamming code
- 45. 10.15 Redundancy bits calculation
- 46. 10.16 Example of redundancy bit calculation
- 47. 10.17 Error detection using Hamming code
- 48. 10.18 Burst error correction example