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CSCI 465 D ata Communications and Networks Lecture 9. Martin van Bommel. Errors. An error occurs when a bit is altered between transmission and reception binary 1 is transmitted and binary 0 is received or binary 0 is transmitted and binary 1 is received Single bit error

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csci 465 d ata communications and networks lecture 9

CSCI 465Data Communications and NetworksLecture 9

Martin van Bommel

CSCI 465Data Communications & Networks

errors
Errors
  • An error occurs when a bit is altered between transmission and reception
    • binary 1 is transmitted and binary 0 is received or binary 0 is transmitted and binary 1 is received
  • Single bit error
    • isolated error that alters one bit but not nearby bits
    • caused by white noise
  • Burst error
    • contiguous sequence of B bits where first and last bits and any number of intermediate bits are received in error
    • caused by impulse noise or by fading in wireless
    • effects greater at higher data rates

CSCI 465Data Communications & Networks

error detection
Error Detection
  • regardless of design you will have errors
  • can detect errors by using an error-detecting code added by the transmitter
      • code is also referred to as “check bits”
  • recalculated and checked by receiver
  • still chance of undetected error

CSCI 465Data Communications & Networks

parity check
Parity Check
  • parity
    • parity bit set so character has even or odd # of ones
      • even parity – used in synchronous transmission
      • odd parity – used in asynchronous transmission
    • even number of bit errors goes undetected
  • problem
    • noise impulses often long enough to destroy more than one bit, especially at high data rates

CSCI 465Data Communications & Networks

cyclic redundancy check crc
Cyclic Redundancy Check (CRC)
  • one of most common and powerful checks
  • for a block of k bits, transmitter generates an n-bit frame by adding an (n-k)-bit frame check sequence (FCS)
  • Transmits n bits which is exactly divisible by some predetermined number
  • receiver divides frame by that number
    • if no remainder, assume no error

CSCI 465Data Communications & Networks

side modulo 2 arithmetic
Side: Modulo-2 Arithmetic
  • Modulo-2 addition uses no carries
    • Addition and subtraction via exclusive-OR (XOR)

1100 0110 11011+ 1010 – 1100 X 101 –––––– –––––– –––––– 0110 1010 11011 11011 –––––––– 1110111

CSCI 465Data Communications & Networks

crc using mod 2 arithmetic
CRC Using Mod-2 Arithmetic
  • Define
    • T = n-bit frame to be transmitted
    • D = k-bit block of data (message), first k bits of T
    • F = (n – k)-bit FCS, last (n – k) bits of T
    • P = pattern of n – k + 1 bits (predetermined divisor)
  • Want T / P to have no remainder
    • T = 2n-kD + F (Note: 2n-kD shifts D (n-k) bits left)
  • F = remainder after dividing 2n-kD by P
  • Receiver will check that T / P has no remainder

CSCI 465Data Communications & Networks

crc mod 2 example
CRC Mod-2 Example
  • Given n = 15, k = 10, (n – k) = 5
    • Message D = 1010001101 (10 bits)Pattern P = 110101 (6 bits)FCS F = to be calculated (5 bits)Transmission T = 2n-kD + F
    • Note: 2n-kD = 25D = 101000110100000
    • 2n-kD / P = 1101010110 Remainder 01110 = F
    • Thus T = 1010001101 01110

CSCI 465Data Communications & Networks

crc mod 2 example 2
CRC Mod-2 Example (2)
  • T / P Mod-2 should have no remainder
    • T / P = 1010001101 01110/ 110101110101 111011110101 111010110101 111110110101 101111110101 110101110101 00

CSCI 465Data Communications & Networks

crc polynomials
CRC Polynomials
  • Express all values as polynomials in dummy variable X, with binary coefficients
    • E.g. for D = 110011, D(X) = X5 + X4 + X + 1 for P = 11001, P(X) = X4 + X3 + 1
    • This gives R(X) = X3 + X2 + X and thus F = 1110

CSCI 465Data Communications & Networks

error detection probability
Error Detection Probability
  • An error E(X) will be undetectable only if it is divisible by P(X)
  • The following are detectable if suitable P(X)
    • All single-bit errors (if P has at least two terms)
    • All double-bit errors (if P “primitive”)
    • Any odd number of errors (if P has (X+1) as factor)
    • Burst error of length less than (n-k) – length of F
    • Many others

CSCI 465Data Communications & Networks