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LINEAR BLOCK CODE AS ERROR CONTROL CODING

PRESENTED BY:
NAME: DEBIKA DEY
SILIGURI INSTITUTE OF TECHNOLOGY

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OVERVIEW:

SIMPLIFIED MODEL OF DIGITAL COMMUNICATION SYSTEM.
ERROR CONTROL CODING.
CLASSIFICATION OF ECC.
BLOCK CODES.
HAMMING CODE.
HAMMING DISTANCE & HAMMING WEIGHT.
PROPERTIES OF LBC.
GENERATOR MATRIX.
PARITY CHECK MATRIX.
RELATION BETWEEN G & H & C
DECODING OF A LINEAR CODE.
SYNDROME DECODING.
APPLICATION.
ADVANTAGES & DISADVANTAGES.


Simplified Model of Digital Communication System…

Error Control Coding (ECC)
Consider only binary data (0 and 1).
Method to check or detect error in transmitted bit stream.
Method to correct those detected errors of transmitted information.

Classification of Error Control Coding...


Block Codes
Data is grouped into blocks of length k bits (data word).
Some extra bits are added ® by the encoder to the block, called redundant bit or parity bit.
Total encoded ‘n’ bits block is called codeword.
This is known as a (n,k) block code, where n>k.

Hamming codes constitute a family of single-error correcting(SEC) codes defined as:
The minimum distance of the code dmin = 3
Hamming Distance (dmin)
Error control capability is determined by the Hamming distance or minimum distance (dmin).
The Hamming distance between two code words is equal to the number of differences or changes between them,
Minimum distance (dmin) is the smallest hamming distance between the valid code vector. (dmin) = n-k+1
The maximum number of detectable errors (s) is given by,
That is the maximum number of correctable errors (t) is given by,



HAMMING WEIGHT
The Hamming weight of a code word is equal to the no. of non-zero elements in the codeword. It is denoted by w©, where ‘c’ codeword.
Properties of
linear Block Code
1. Summation (mod-2/XOR) of any two codeword of a particular code vector is also a codeword of that same code vector.
2. All zero codeword(e.g.00000) is a valid codeword.
3. The minimum weight of the codeword should be equal to the minimum distance within the code vector. i.e.,



Generator Matrix
Using generator matrix all 2k codeword can be generated from a set of k bit code vector.


APPLICATIONS
of Error Control Coding


Storage:
Computer Memory (RAM)
Magnetic and Optical Data Storage (hard disks, magnetic tapes, CD-ROM’s, and other data storage systems)
Single error correcting & double error detecting code (SEC-DED) is used to improve bit oriented semi conductor memories


Communications:
Satellite and Deep Space Communications
Digital Audio and Video Transmissions


DISADVANTAGES:
In this process extra parity bit is added, so transmission bandwidth requirement is more.
These extra bits reduce the bit rate of the transmitter and also reduce its power.


ADVANTAGES:
Linear block code is the easiest & simple technique to detect and correct errors.
Extra parity bits do not convey any information by themselves but make it possible to detect and correct errors in the received message i.e. error probability is reduced.