Single Bit Error Correction - Data Communication - Lecture Slides, Slides of Data Communication Systems and Computer Networks

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DATA

COMMUNICATION

Lecture-

Recap of Lecture 34

 Types of Redundancy Checks

 Longitudinal Redundancy Check

(LRC)

 Cyclic Redundancy Check (CRC)

Modulo-2 Division in a

CRC Generator

Modulo-2 Division in a CRC

Checker

Checksum

 Error detection method used by the higher layers

 The unit is divided into k sections, each of n bits

 All sections are added and complemented to get the checksum, using one’s complement arithmetic

Performance of Checksum

 Detects all errors involving an odd

number of bits

 Detects most errors involving an even

number of bits

 One pattern remains elusive

Example 9.

 Suppose a block of 16 bits need to be sent: 10101001 00111001 10101001 00111001

---

11100010 Sum 00011101 Checksum

 Sent pattern:

10101001 00111001 00011101 checksum Docsity.com

Performance of Checksum

 Error is invisible if a bit inversion is balanced by an opposite bit inversion in the corresponding digit of another segment

Segment1 10111101 Segment2 00101001 Checksum 00011001

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Sum 11111111

→ The error is undetected

Single-Bit Error Correction

 Error correction requires more

redundancy bits than error detection

 One additional bit can detect single-bit

errors

• Parity bit in VRC
• One bit for two states: error or no error

Redundancy Bits (r)

 r must be able to indicate at least m+r+ states

 m+r+1 states must be discoverable by r bits

 Therefore, 2r^ ≥ m+r+

 If m=7, r=4 as 2 4 ≥ 7+4+

Redundancy Bits