Error Detection

¾ An error occurs when a is altered between transmission and reception ¾ Single bit errors z only one bit altered z caused by white noise ¾ Burst errors z contiguous sequence of B in which first last and any number of intermediate bits in error z caused by impulse noise or by fading in wireless z effect greater at higher data rates

Sources of Noise and Prevention

Error Detection

¾ will have errors ¾ detect using error-detecting code (principle of redundancy) ¾ added by transmitter and recalculated and checked by receiver ¾ still chance of undetected error

Error Detection Techniques • Parity checks • Longitudinal Redundancy Checking (LRC) • Polynomial checking – – (CRC)

Parity Check • Oldest and simplest • Doesn’t catch all errors – If two (or an even number of) bits have been transmitted in error at the same time, the parity check appears to be correct – Detects about 50% of errors

To be sent: Letter V in 7-bit ASCII: 0110101

Longitudinal Redundancy Checking (LRC) • Adds an additional character (instead of a bit) – Block Check Character (BCC) to each block of data – Determined like parity but, but counting longitudinally through the message (as well as vertically) • Major improvement over parity checking – 98% error detection rate for burst errors ( > 10 bits) – Less capable of detecting single bit errors

Example: Determine the VRC and LRC for the following encoded message: THE_CAT. Use odd parity for the VRC and even parity for the LRC.

Character T H E sp C A T LRC Hex 54 48 45 20 43 41 54 2F b0 0 0 1 0 1 1 0 1 b1 0 0 0 0 1 0 0 1 b2 1 0 1 0 0 0 1 1 b3 0 1 0 0 0 0 0 1 b4 1 0 0 0 0 0 1 0 b5 0 0 0 1 0 0 0 1 b6 1 1 1 0 1 1 1 0 Parity bit b7 0 1 0 0 0 1 0 0 (VRC)

The LRC is 00101111 in binary (2F) which is the character (/). Therefore, after the LRC character is appended to the message, it would read THE_CAT/. Note: With VRC, even parity is generally used, whereas with VRC, odd parity is generally used.

Cyclic Redundancy Check – Most powerful and most common – Almost detects 100% of errors

Example: Determine the BCS for the following data and CRC generating polynomial: Data G(x) = x7 + x5 + x4 + x2 + x + 1 = 10110111 CRC P(x) = x5 + x4 + x + 1 = 110011

Checksum – Form of redundancy where each character has a numerical value assigned to it. – Characters within the message are combined together to produce an error-checking character.

International Standard Book Number • A unique, numerical commercial book identifier, based upon the 9-digit Standard Book Numbering (SBN) code created in the UK. • The 10-digit ISBN format was developed by the International Organization for Standardization and published as an international standard in 1970. • Since January 1, 2007, International Standard Book Numbers have been of 13 digits.

Overview An ISBN is assigned to each edition and variation (except reprintings) of a book. An International Standard Book Number consists of 4 or 5 parts: 1. for a 13 digit ISBN, a GS1 prefix: 978 or 979 2. the group identifier, (language-sharing country group) 3. the publisher code, 4. the item number, and 5. a checksum character or check digit.

Example: • The check digit for an ISBN-10 of 0-306-40615-? is calculated as: s = 0×10 + 3×9 + 0×8 + 6×7 + 4×6 + 0×5 + 6×4 + 1×3 + 5×2 = 0 + 27 + 0 + 42 + 24 + 0 + 24 + 3 + 10 = 130 130 / 11 = 11 remainder 9 11 - 9 = 2 (check digit)

Note: If the result is 11, a '0' should be substituted; if 10, an 'X' should be used.

The ISBN-13 check digit of 978-0-306-40615-? is calculated as: s = 9×1 + 7×3 + 8×1 + 0×3 + 3×1 + 0×3 + 6×1 + 4×3 + 0×1 + 6×3 + 1×1 + 5×3 = 9 + 21 + 8 + 0 + 3 + 0 + 6 + 12 + 0 + 18 + 1 + 15 = 93 93 / 10 = 9 remainder 3 10 – 3 = 7 (check digit)