chapter5 data link layer in data communications and networking.ppt

Chapter 5 Dr. Ali Al-Hamdi 1
Chapter 5
Error Detection and
Correction
Part III: Data-Link Layer

 Net. criterion related to error occurrence, data form types
applications and error manipulation?
 Error manipulation in data-link layer and in other layers
when frames corrupted between 2 nodes?
 Chapter topics include:
 Errors types, redundancy concept, error detection & correction,
 Block coding discussion and introduction to Hamming distance,
 Cyclic coding discussion, from different perspectives,
 Checksum discussion,
 Forward error discussion.
Lead-in

 5.1.1 Types of Errors
 Errors causes
 Which type is dominant? Why? Examples?
5.1 Introduction

 5.1.2 Redundancy
 Definition and goal
 Task of sender and receiver related to redundant bits
 5.1.3 Detection vs. Correction
 Which is more difficult? Why? Examples
 5.1.4 Coding
 At the sender, and at the receiver
 Categories of coding schemes
 Schemes complexity
5.1 Introduction

5.2 Block Coding
 5.2.1 Concept
 Message division into blocks, each of (k) bits, called
datawords.
 Redundant bits (r) addition to each block to result
codewords, each of (n) bits, n= k + r.
 Since n > k, the number of possible codewords > the
number of possible datawords.
 Since the block coding process is one-to-one, 2k
codewords are used and 2n
− 2k
codewords are not.

5.2 Block Coding
 5.2.1 Concept
 While used codewords are called valid codewords,
unused codewords are called invalid or illegal
codewords.
 Invalid codewords represent a trick in error detection at
the receiver if a codeworde was corrupted during
transmission.
 How this problem can be solved?

5.2 Block Coding
 5.2.2 Error Detection
 2 Conditions permitting the receiver to detect errors
 Receiver has a list of valid codewords
 Original codeword has changed to an invalid or valid ones
 Problem with 2nd
condition?
 ED process

 Example (1): consider table 10.1 and assume the sender codes
dataword 01 as 011, specify the transmission situation and the
receiver decision if it receives the following cases: 011, 111,
000?
5.2 Block Coding

 Hamming Distance
 Definition
 Condition
 Why important?
 For example: if the codeword 00000 is sent and 01101 is
received, HD ?
 Logic operator used?
 Example (2)
5.2 Block Coding

 Minimum Hamming Distance for Error Detection
 Definition
 Concept
5.2 Block Coding

 Minimum Hamming Distance for Error Detection
 Example (3): in table 10.1, what type of error can be detected
if a codeword is corrupted, and what is the value of dmin?
 Example (4)
if dmin=4, s?
5.2 Block Coding

 Types: linear and nonlinear, dominant one, why?
 Linear Block Codes
 Required knowledge?
 Definition (based on table 10.1)?
 Example (5): table 10.1 is LBC?
5.2 Block Coding

 Minimum Hamming Distance for LBC?
 Example (6): in table 10.1.
 dmin in general and in table (10.1)=? And type of error?
5.2 Block Coding

5.2 Block Coding

 Parity-check: encoder & Decoder
 Structure
 Operation
5.2 Block Coding

 Linear Block Codes: Partity-check encoder & Decoder
 Example (7): assume the sender sends codeword 10111 ,
specify the transmission situation and the receiver decision if
it receives the following cases: 10111, 10011, 10110, 00110,
01011?
5.2 Block Coding

 5.3.1 Concept
 Definition
 Properties
 4.3.2 Cyclic Redundancy Check (CRC)
 Applications
 (Network-based)
5.3 Cyclic Codes

5.3 Cyclic Codes
 Structure
 Operation

5.3 Cyclic Codes
 Division in encoder

5.3 Cyclic Codes
 Division in decoder
 Divisor selection?

 5.3.3 Polynomials
 Concept
 Benefit?
5.3 Cyclic Codes

 5.3.3 Polynomials
 Degree of polynomial
 Adding and Subtraction Polynomials
 Multiplying or Division Terms or
 Multiplying Two Polynomials
 Dividing One Polynomial By Another
 Shifting
5.3 Cyclic Codes

 5.3.4 Cyclic Code Encoder Using Polynomials

4.1.4 Coding
5.3 Cyclic Codes

 5.3.5 Cyclic Code Analysis
5.3 Cyclic Codes

 Single-Bit Error
5.3 Cyclic Codes

 Two Isolated Single-Bit Errors
5.3 Cyclic Codes

 Odd Numbers of Errors
 Burst Errors
5.3 Cyclic Codes

 Burst Errors
 Summary
5.3 Cyclic Codes

 Standard Polynomials
5.3 Cyclic Codes

 5.3.6 Advantages of Cyclic Codes
 Can detect all types of errors with high performance
 Simple to implement is S/W and H/W
 So, they are used in many networks
 5.6.7 Other Cyclic Codes
 Reed Solomon code for error detection and correction
5.3 Cyclic Codes

 5.4.1 Generalities
 Definition
 Used in layers
 Operation
5.4 Checksum

 5.4.2 Concept
 Example (10.11):
 At the sender: message to be sent is of 4-bit numbers=(7, 11, 12, 0, 6).
With sum message=(7, 11, 12, 0, 6, 36)
 At receiver: numbers are added and compare with the sum. If the two are
the same, the numbers are accepted, and discards the sum. Otherwise,
there is an error somewhere and the message is not accepted.
 Drawback?
 Solution: One’s Complement Addition
 Reducing number of bits of sum using
 Example (10.12) =(7, 11, 12, 0, 6, 6)
5.4 Checksum

 5.4.2 Concept
Solution: One’s Complement Addition
 At sender: add the number in one’s complement to get the sum then
complement to get the checksum. Example (10.13) =(7, 11, 12, 0, 6, 9)
 At receiver: if there is no error (7, 11, 12, 0, 6, 9) is received and add
them in one’s complement to get 15 which is complemented to get 0 .
5.4 Checksum

 5.4.2 Concept
 Internet Checksum
5.4 Checksum

 5.4.2 Concept
 Algorithm
 Performance
 Small (16-bit) to large size error
 Not strong as CRC
 Not weighted
5.4 Checksum

 5.4.3 Other Approaches to Checksum
 Fetcher checksum
 Devised to weight each data item according to its position.
 Two algorithms are proposed: 8-bit and 16-bit.
 The 1st
calculates on 8-bit data items and creates a 16-bit checksum.
 The 2nd
calculates on 16-bit data items and creates a 32-bit checksum.
 The algorithm uses two accumulators: L and R.
 The first adds data items together; the second adds a weight to the
calculation.
 16-bit Fletcher checksum is similar to the 8-bit Fletcher checksum, but it
is calculated over 16-bit data items and creates a 32-bit checksum.
5.4 Checksum

 Fetcher checksum
 Algorithm example
5.4 Checksum

 Adler checksum
 32-bit checksum
 It is similar to the 16-bit Fletcher with three differences:
 Calculation is done on single bytes instead of 2 bytes at a time.
 The modulus is a prime number (65,521) instead of 65,536.
 L is initialized to 1 instead of 0.
5.4 Checksum

 Adler checksum
 Algorithm
5.4 Checksum

 Usefulness of packet retransmission in RT multimedia?
 5.5.1 Using Hamming Distance
 More distance is needed, dmin= 2t + 1 to correct t errors
 This means a lot of redundant bits need to be sent with the data.
 Example: famous BCH code
5.5 Forward Error Correction

5.5.2 Using XOR
Recreating any of data items using exclusive-ORing all of the
items, replacing the one to be created by the result of the previous
operation (R).
This means dividing a packet into N chunks, create the exclusive
OR of all the chunks and send N + 1 chunks.
If any chunk is lost or corrupted, it can be created at the receiver.
 Value of N depends on the # of lost chunks during transmission.
Example: if N = 4, 25 % extra data to correct the data if only one
chunk is lost.

 5.5.3 Chunk Interleaving
 Concept: missing one packet

 5.5.4 Combining Hamming Distance &
Interleaving
 First n-bit packets are created that can correct t-bit errors.
 Then m rows interleaved and send the bits column by column.
 In this way, burst errors up to m × t-bit errors can be corrected
automatically.

 5.5.5 Compounding High-and low-resolution
packets

chapter5 data link layer in data communications and networking.ppt

More Related Content

Similar to chapter5 data link layer in data communications and networking.ppt (20)

Recently uploaded (20)

chapter5 data link layer in data communications and networking.ppt