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COE 341: Data & Computer Communications (T062) Dr. Marwan Abu-Amara

COE 341: Data & Computer Communications (T062) Dr. Marwan Abu-Amara. Chapter 6: Digital Data Communications Techniques. Contents. Asynchronous and Synchronous Transmission Types of Errors Error Detection Parity Check Cyclic Redundancy Check (CRC).

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COE 341: Data & Computer Communications (T062) Dr. Marwan Abu-Amara

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  1. COE 341: Data & Computer Communications (T062)Dr. Marwan Abu-Amara Chapter 6: Digital Data Communications Techniques

  2. Contents • Asynchronous and Synchronous Transmission • Types of Errors • Error Detection • Parity Check • Cyclic Redundancy Check (CRC) COE 341 – Dr. Marwan Abu-Amara

  3. Asynchronous and Synchronous Transmission: • To communicate meaningful data serially between TX and RX, signal timing should be the same at both • Timing considerations include: • Rate • Duration • Spacing • Need to synchronize RX to TX • Two ways to achieve this: • Asynchronous Transmission • Synchronous Transmission • RX needs to sample the received • data at mid-points • So it needs to establish: • - Bit arrival time • - Bit duration COE 341 – Dr. Marwan Abu-Amara

  4. Transmitter Receiver RX Clock TX Clock Tb Need for RX and TX Synchronization: • Clock drift (example): • If the receiver clock drifts by 1% every sample time, • For Tb = 1 msec, total drift after 50 bit intervals = 50 X 0.01 = 0.5 msec • i.e. instead of sampling at the middle, the receiver will sample bit # 50 at the edge of the bit • RX and TX clocks are out-of-synch  Communication Error! • In general, # of correctly sampled bits = 0.5 Tb/(n/100)Tb = 50/n, where n is the % timing error between TX and RX • Two approaches for correct reception: • Send only a few bits (e.g. a character) at a time (that RX can sample correctly before losing sync)  Asynchronous Transmission • Keep receiver clock synchronized with the transmitter clock  Synchronous Transmission COE 341 – Dr. Marwan Abu-Amara

  5. Asynchronous Transmission: Character-Level Synchronization • Avoids the timing problem by NOT sending long, uninterrupted streams of bits. • So data is transmitted one character at a time: • Has a distinct start bit • Consists of only 5 to 8 bits (so drift will not be a serious problem) • Has a distinct stop bit • Character is delimited (at start & end) by known signal elements: start bit – stop element • Sync needs to be maintained only for the duration of a character • The receiver has a new opportunity to resynchronize at the beginning of next character  Timing errors do not accumulate from character to character COE 341 – Dr. Marwan Abu-Amara

  6. S1 Receive Stop element S2 Receive Start bit Receive Stop element Asynchronous Transmission (Min) Binary 1 Binary 1 RX waits for a character following the end of the previous character • The ‘stop’ element confirms end of character  otherwise: Framing Error • Stop elements continue (idling) • until next character RX “knows” how many bits To expect in a character, and keeps counting them following the ‘start’ bit Parity bit: Even or Odd parity? S1: receiver in idling state S2: receive in receiving state COE 341 – Dr. Marwan Abu-Amara

  7. Asynchronous Transmission Framing error • Erroneous detection of end/start of a character • Can be caused by: • Noise: (1 is the idling ‘stop’ bit) 1 1 1 1 0 1 1 1 1 1 … • Incorrect timing of bit sampling due to drift of RX clock affects bit count Erroneous ‘Start’ bit due to noise COE 341 – Dr. Marwan Abu-Amara

  8. (Timing for ideal sampling at RX) 100 ms 94 ms 47 ms Half the bit interval from the ‘start’ rising edge Asynchronous Transmission Errors due to lack of sync for an 8-bit system • Let data rate = baud rate = 10 kbps • Bit interval = 1/10k = 100 ms • Assume RX’s clock is faster than TX by 6% (i.e. RX thinks the bit interval is 94 ms) • RX checks mid-bit data at 47 ms and then at 94 ms intervals • Bit 8 is wrongly sampled within bit 7 (bit 7 read twice!) • Possibility of a framing error at the end 893 COE 341 – Dr. Marwan Abu-Amara

  9. Asynchronous Transmission: Efficiency • Uses 1 start bit & 2 stop bits: (i.e. 3 non-data bits) with 8-bit characters and no parity:  Efficiency = 8/(8+3) = 72%  Overhead = 3/(8+3) = 28% COE 341 – Dr. Marwan Abu-Amara

  10. Asynchronous Transmission – Pros & Cons Advantages: • Simple • Cheap • Good for data with large gaps (keyboard) Cons: • Overhead of 2 or 3 bits per character (~20%) • Timing errors accumulate for large character sizes COE 341 – Dr. Marwan Abu-Amara

  11. Synchronous Transmission: Bit-Level Synchronization • Allows transmission of large blocks of data (frames) • TX and RX Clocks must be synchronized to prevent timing drift • Ways to achieve bit-level sync: • Use a separate clock line between TX and RX • Good over short distances • Subject to transmission impairments over long distances • Embed clock signal in data • e.g. Manchester or Differential Manchester encoding • Or carrier frequency for analog signals COE 341 – Dr. Marwan Abu-Amara

  12. Data field: data to be exchanged Preamble bit pattern: Indicates start of frame Postamble bit pattern: Indicates end of frame Control fields: convey control information between TX and RX data field 8-bit flag 8-bit flag control field control field Synchronous Frame Format Typical Frame Structure Preamble/Postamble flags ensure frame-level synchronization COE 341 – Dr. Marwan Abu-Amara

  13. Synchronous Transmission: Efficiency • Example: HDLC scheme uses a total of 48 bits for control, preamble, and postamble fields per frame: With a data block consisting of 1000 characters (8-bits per character),  Efficiency = 8000/(8000+48) = 99.4%  Overhead = 48/8048 = 0.6% • Higher efficiency and lower overhead compared to asynchronous COE 341 – Dr. Marwan Abu-Amara

  14. Errors in Digital Transmission • Error occurs when a bit is altered between transmission and reception (0  1 or 1  0) • Two types of errors: • Single bit errors • One bit altered • Isolated incidence, adjacent bits not affected • Typically caused by white noise • Burst errors • Contiguous sequence of B bits in which first, last, and any number of intermediate bits are in error • Caused by impulse noise or fading (in wireless) • More common, and more difficult to handle • Effect is greater at higher data rates • What to do about these errors: • Detect them (at least, so we can ask TX to retransmit!) • Correct them (if we can) COE 341 – Dr. Marwan Abu-Amara

  15. 1 2 3 4 … … F-2 F-1 F 1 0 1 0 1 0 0 0 1 0 1 0 … 0 0 1 Error Detection & Correction: Motivation • Assume NO error detection or correction: Number of erroneous frames received would be unacceptable • Hence, for a frame of F bits, Prob [frame is correct] = (1-BER)F : Decreases with increasing BER & F • Prob [frame is erroneous] = 1 - (1-BER)F = Frame Error Rate (FER) A frame of F bits All bits must be Correct! Prob [1st bit in error] = BER Prob [1st bit correct] = 1-BER Prob [2nd bit in error] = BER Prob [2nd bit correct] = 1-BER Prob [Fth bit in error] = BER Prob [Fth bit correct] = 1-BER All bits must be Correct! COE 341 – Dr. Marwan Abu-Amara

  16. Motivation for Error Detection & Correction: Example • ISDN specifies a BER = 10-6 for a 64kbps channel • Frame size F = 1000 bits • What is the FER? • FER = 1 – (1 – BER)F = 1 – (0.999999)1000 = 10-3 • Assume a continuously used channel • How many frames are transmitted in one day Number of frames/day = (64,000/1000) × 24 × 3600 = 5.5296 × 106 • How many erroneous frames/day? • 5.5296 × 106 × 10-3 = 5.5296 × 103 • Typical requirement: Maximum of 1 erroneous frame /day! • i.e. frame error rate is too high! We definitely need error detection & correction COE 341 – Dr. Marwan Abu-Amara

  17. Frame Error Probabilities: 1 0 1 0 1 0 0 0 1 0 1 0 … 0 0 1 • P1 + P2 + P3 = 1 • Without error detection facility: P3 = 0, and: P2 = 1 – P1 P1 1 - P1 1000 Correct Erroneous With an error detection facility 900 100 Errors, Undetected Errors, Detected P2 P3 20 80 COE 341 – Dr. Marwan Abu-Amara

  18. Error Detection Techniques • Two main error detection techniques: • Parity Check • Cyclic Redundancy Check (CRC) • Both techniques use additional bits that are added to the “payload data” by the transmitter for the purpose of error detection COE 341 – Dr. Marwan Abu-Amara

  19. Error Detection: Implementation Mismatch: Error Detected COE 341 – Dr. Marwan Abu-Amara

  20. Parity Check • Simplest error-detection scheme • Appending one extra bit: • Even Parity: Will append “1” such that the total number of 1’s is even • Odd Parity: Will append “1” such that the total number of 1’s is odd • Example: If an even-parity is used, RX will check if the total number of 1’s is even • If it is not  error occurred • Note: even number of bit errors go undetected COE 341 – Dr. Marwan Abu-Amara

  21. Cyclic Redundancy Check (CRC) • Burst errors will most likely go undetected by a simple parity check scheme • Instead, a more elaborate technique called Cyclic Redundancy Check (CRC) is typically implemented • CRC appends redundant bits to the frame trailer called Frame Check Sequence (FCS) • FCS is later utilized at RX for error detection • In a given frame containing n bits, we define: • k = number of original data bits • (n – k) = number of bits in the FCS field (i.e. additional bits) • So, that the total frame length is k + (n – k) = n bits D (k) FCS (n-k) 1 0 1 0 0 0 1 1 0 1 01110 T(n) COE 341 – Dr. Marwan Abu-Amara

  22. CRC Generation • CRC generation is all about finding the FCS given the data (D) and a divisor (P) • There are three equivalent ways to generate the CRC code: • Modulo-2 Arithmetic Method • Polynomial Method • Digital Logic Method D (k) FCS or F (n-k) 1 0 1 0 0 0 1 1 0 1 01110 T (n) 110101 P (n-k+1) COE 341 – Dr. Marwan Abu-Amara

  23. 1010 +1010 ___________ 0000 Modulo 2 Arithmetic • Binary arithmetic without carry • Equivalent to XOR operation • i.e: • 0  0 = 0; 1  0 = 1; 0  1 = 1; 1  1 = 0 • 1  0 = 0; 0  1 = 0; 1  1 = 1 • Examples: COE 341 – Dr. Marwan Abu-Amara

  24. CRC Error Detection Process • Given k-bit data (D), the TX generates an (n – k)-bit FCS field (F) such that the total n-bit frame (T) is exactly divisible by some (n-k+1)-bit predetermined devisor (P) (i.e. gives a zero remainder) • In general, the received frame may or may not be equal to the sent frame • Let the received frame be (T’) • In error-free transmission T’ = T • The RX then divides (T’) by the same known divisor (P) and checks if there is any remainder • If division yields a remainder then the frame is erroneous • If the division yields zero remainder then the frame is error-free unless many erroneous bits in T’ resulted in a new exact division by P • (This is very unlikely but possible, causing an undetected error!) COE 341 – Dr. Marwan Abu-Amara

  25. CRC Generation T = 2 (n – k) D + F (n-k) left shifts (multiplications by 2) Data D: ? LSB • P is 1-bit longer than F COE 341 – Dr. Marwan Abu-Amara

  26. CRC Generation • T = 2(n – k) D + F, What is F that makes T divides Pexactly ? • Claim: F is the remainder obtained from dividing {2(n – k) D} by divisor P where Q is the quotient and F is the remainder • If this is the correct F, T should now divide P with Zero remainder • Note: For F to be a remainder when dividing by P, it should be 1-bit smaller (1) COE 341 – Dr. Marwan Abu-Amara

  27. CRC Generation – Modulo-2 Arithmetic Method • At TX: CRC Generation (using previous rules): • Multiply: 2(n – k) D (left shift by (n-k) bits) • Divide: 2(n – k)  D / P • Use the resulting (n – k)-bit remainder as the FCS • At RX: CRC Checking: RX divides the received T (i.e. T’) by the known divisor (P) and checks if there is any remainder COE 341 – Dr. Marwan Abu-Amara

  28. Example – Modulo-2 Arithmetic Method • Given • D = 1 0 1 0 0 0 1 1 0 1 • P = 1 1 0 1 0 1 • Find the FCS field • Solution: • First we note that: • The size of the data block D is k = 10 bits • The size of P is (n – k + 1) = 6 bits  Hence the FCS length is n – k = 5  Total size of the frame T is n = 15 bits COE 341 – Dr. Marwan Abu-Amara

  29. Example – Modulo-2 Arith. Method • Solution (continued): • Multiply 2(n – k) D • 2(5) 1 0 1 0 0 0 1 1 0 1 = 1 0 1 0 0 0 1 1 0 1 0 0 0 0 0 • This is a simple shift to the left by five positions • Divide 2(n – k) D / P (see next slide for details) • 1 0 1 0 0 0 1 1 0 1 0 0 0 0 0 ÷ 1 1 0 1 0 1 yields: • Quotient Q = 1 1 0 1 0 1 0 1 1 0 • Remainder R = 0 1 1 1 0 • So, FCS = R = 0 1 1 1 0: Append it to D to get the full frame T to be transmitted • T = 1 0 1 0 0 0 1 1 0 1 0 1 1 1 0 M FCS COE 341 – Dr. Marwan Abu-Amara

  30. Example – Modulo-2 Arith. Method # of bits < # of bits in P,  result of division is 0 Checks you should do (exercise): - Verify correct operation, i.e. that 2(n-k)D = P*Q + R - Verify that obtained T (101000110101110) divides P (110101) exactly (i.e. with zero remainder) = FCS = F COE 341 – Dr. Marwan Abu-Amara

  31. Problem 6-12 • For P = 110011 & D = 11100011, find the CRC COE 341 – Dr. Marwan Abu-Amara

  32. Chances of missing an error by CRC error detection • Let E be an n-bit number with a bit = 1 at the position of each error bit error occurring in T • Error occurring in T causes bit reversal • Bit reversal is obtained by XORing with 1 • So, received Tr = T  E • Error is missed (not detected) if Tr is divisible by P • Since T is made divisible by P, this requires that E is also divisible by P!. • That is a ‘bit’ unlikely! COE 341 – Dr. Marwan Abu-Amara

  33. CRC Generation – Polynomial Method • A k-bit word (D) can be expressed as a polynomial D(x) of degree (k-1) in a dummy variable x, with: • The polynomial coefficients being the bit values • The powers of X being the corresponding powers of 2 bk-1 bk-2 … b2 b1 b0 bk-1Xk-1 + bk-2Xk-2 + … + b1X1 + b0X0 where bi (k-1 ≤ i ≤ 0) is either 1 or 0 • Example1: an 8 bit word D = 11011001 is represented as D(X) = x7+x6+x4+x3+1 • Ignore polynomial terms corresponding to 0 bits in the number COE 341 – Dr. Marwan Abu-Amara

  34. CRC – Mapping Binary Bits into Polynomials • Example2: What is x4D(x) equal to? x4D(x) = x4(x7+x6+x4+x3+1) = x11+x10+x8+x7+x4, the equivalent bit pattern is 110110010000 (i.e. four zeros appended to the right of the original D pattern) • Example3: What is x4D(x) + (x3+x+1)? x4D(x) + (x3+x+1) = x11+x10+x8+x7+x4+ x3+x+1, the equivalent bit pattern is 110110011011 (i.e. pattern 1011 = x3+x+1 appended to the right of the original D pattern) COE 341 – Dr. Marwan Abu-Amara

  35. CRC Generation: The Polynomial Way Polynomial Binary Arithmetic • T = 2(n – k) D + F • T(X) = X(n – k) D(X) + F(X) COE 341 – Dr. Marwan Abu-Amara

  36. CRC Calculation - Procedure • Shift pattern D(X), (n-k) bits to the left, i.e. perform the multiplication X(n-k)D(X) • Divide the new pattern by the divisor P(X) • The remainder of the division, R(X) (i.e. n-k bits), is taken as FCS • The frame to be transmitted T(X) is X(n-k)D(X) + FCS COE 341 – Dr. Marwan Abu-Amara

  37. Example of Polynomial Method • D = 1 0 1 0 0 0 1 1 0 1 (k = 10) • P = 1 1 0 1 0 1 (n – k + 1 = 6) n – k = 5 n = 15 • Find the FCS field • Solution: • D(X) = X9 + X7 + X3 + X2 + 1 • P(X) = X5 + X4 + X2 + 1 • X5D(X)/P(X) = (X14 + X12 + X8 + X7 + X5)/(X5 + X4 + X2 + 1) • This yields a remainder R(X) = X3 + X2 + X (details on next slide) • i.e. F = 01110 • R is n – k = 5-bit long  Remember to indicate any 0 bits! COE 341 – Dr. Marwan Abu-Amara

  38. Example of Polynomial Method F = R D 1 0 1 0 0 0 1 1 0 1 01110 T Insert 0 bits to make 5 bits 110101 P COE 341 – Dr. Marwan Abu-Amara

  39. Choice of P(X) • How should we choose the polynomial P(X) (or equivalently the divisor P)? • The answer depends on the types of errors that are likely to occur in our communication link • As seen before, an error pattern E(X) will be undetectable only if it is divisible by P(X) • It can be shown that all the following error types are detectable : • All single-bit errors, if P(X) has two terms or more • All double-bit errors, if P(X) has three terms or more • Any odd number of errors, if P(X) contains the factor (X+1) • Any burst error whose length is less than the FCS length (n – k) • A fraction (=1-2-(n-k-1) ) of error bursts of length (n-k+1) • A fraction (=1-2-(n-k) ) of error bursts of length > (n-k+1) COE 341 – Dr. Marwan Abu-Amara

  40. Choice of P(X) • In addition, if all error-patterns are equally likely, and r = n - k = length of the FCS, then: • For a burst error of length (r + 1), the probability of undetected error is 1/2(r – 1) • For a longer burst error i.e. length > (r + 1), the probability of undetected error is 1/2 r • There are four widely-used versions of P(X) • CRC-12: P(X) = X12 + X11 + X3 + X2 + X + 1 (r = 13 -1 = 12) • CRC-16: P(X) = X16 + X15 + X2 + 1 (r = 17 -1 = 16) • CRC-CCITT: P(X) = X16 + X12 + X5 + 1 • CRC-32: P(X) = X32 + X26 + X23 + X22 + X16 + X12 + X11 + X10 + X8 + X7 + X5 + X4 + X2 + X + 1 (r = 33 -1 = 32) FCS is 1-bit shorter than P: FCS Size P(X) always starts with 1 COE 341 – Dr. Marwan Abu-Amara

  41. Some CRC Applications • CRC-8 and CRC-10 (not shown) are used in ATM • CRC-12 is used for transmission of 6-bit characters. Its FCS length is 12-bits • CRC-16 & CRC-CCITT are used for 8-bit characters in the US and Europe respectively • Used in HDLC • CRC-32 is used for IEEE 802.3 LAN standard COE 341 – Dr. Marwan Abu-Amara

  42. Data Block, D 1010001101 CRC Generation – Digital Logic • k = 10 (size of D) (known data to be TXed) • n – k + 1 = 6 size of P (known divisor) P (X) = X5+X4+X2+1 (110101) • n – k = 5 size of FCS (to be determined at TX) • n = 15 • 5-element left-shift register • Initially loaded with 0’s • After n left shifts, register will contain the required FCS Always An XOR at C0 P = X5+X4+X2+X0 • Divisor is “hardwired” as feedback connections • via XOR gates into the shift register cells • Starting at LSB, for the first (n-k) bits of P, add an XOR only for 1 bits COE 341 – Dr. Marwan Abu-Amara

  43. CRC Generation at TX P = X5+X4+X2+X0 Start with Shift Register Cleared to 0’s C0 in C2 in C4 in MSB D Inputs formed with Combination Logic MSB FCS generated in the shift register after n (=15) shift steps COE 341 – Dr. Marwan Abu-Amara

  44. CRC Checking at RX P = X5+X4+X2+X0 Start with Shift Register Cleared to 0’s C0 in C2 in C4 in MSB 15 bits D D Received Frame, T MSB FCS Inputs formed with Combination Logic 0’s in the shift register after n (=15) shift steps (if no errors) COE 341 – Dr. Marwan Abu-Amara

  45. Problem 6-13 • A CRC is constructed to generate a 4-bit FCS for an 11-bit message. The generator polynomial is X4+X3+1 • Draw the shift register circuit that would perform this task • Encode the data bit sequence 10011011100 (leftmost bit is the LSB) using the generator polynomial and give the code word • Now assume that bit 7 (counting from the LSB) in the code word is in error and show that the detection algorithm detects the error COE 341 – Dr. Marwan Abu-Amara

  46. Problem 6-13 – Solution Input data   C1 C0 C3 C2 a) P(X) = X4+X3+1 b) Data (D) = 1 0 0 1 1 0 1 1 1 0 0 D(X) = 1 + X3 + X4 + X6 + X7 + X8 X4D(X) = X12 + X11 + X10 + X8 + X7 + X4 T(X) = X4M(X) + R(X) = X12 + X11 + X10 + X8 + X7 + X4 + X2 Code = 0 0 1 0 1 0 0 1 1 0 1 1 1 0 0 c) Code in error = 0 0 1 0 1 0 0 1 1 0 0 1 1 0 0 yields a nonzero remainder  error is detected LSB COE 341 – Dr. Marwan Abu-Amara

  47. Error Correction • Once an error is detected, what action can RX take? (i.e. I found an error, now what? ) • Two alternatives: • RX asks for a retransmission of the erroneous frame • Adopted by data-link protocols such as HDLC and transport protocol such as TCP • A Backward Error Correction (BEC) method • RX attempts to correct the errors if enough redundancy exists in the received data • TX uses Block Coding to allow RX to correct potential errors • A Forward Error Correction (FEC) method • Use in applications that leave no time for retransmission, e.g. VoIP. COE 341 – Dr. Marwan Abu-Amara

  48. Error Correction vs. Error Control • Backward error correction by retransmission is not recommended in the following cases: • Error rate is high (e.g. wireless communication) • Will cause too much retransmission traffic  network overloading • Transmission distance is long (e.g. satellite, submarine optical fiber cables) • Network becomes very inefficient (Not utilized properly) • Usually: • Error Correction methods: Those that use FEC techniques • Error Controlmethods: Those that use retransmission COE 341 – Dr. Marwan Abu-Amara

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