ERROR CONTROL CODING




Basic Concepts


Received: 011. What was transmitted?
scenario A: 111 with one error in 1st location
scenario B: 000 with two errors in 2nd & 3rd locations.


Hamming Distance

Def.: The Hamming distance between two codewords ci and cj, denoted by d(ci,cj), is the number of components at which they differ.


Maximum Likelihood Decoding reduces to Minimum Distance Decoding, if the priory probabilities are ....etc

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ERROR CONTROL CODING



W hen a digital signal is transmitted between two systems(such as computers),the signal gets distorted because of addition of noise to the transmitted signal. The noise can introduce an error in the binary train of bit travelling from one system to the other .this means that a 0 may change to 1 or a 1 may change to 0.These error can become a serious problem to the accuracy and performance of the digital system. Therefore it is essential to det ....etc

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Introduction

The packet transport service provided by representative packet-switched networks, including IP networks, is not reliable and the quality-of-service cannot be guaranteed. Packets may be lost due to buffer overflow in switching nodes, be discarded due to excessive bit errors and failure to pass the cyclic redundancy check at the page link layer, or be discarded by network control mechanisms as a response to congestion somewhere in the network. Forward Error Correction coding has often been p ....etc

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LINEAR BLOCK CODE AS ERROR CONTROL CODING

PRESENTED BY:
NAME: DEBIKA DEY
SILIGURI INSTITUTE OF TECHNOLOGY

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.


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Abstract
We present matrix network coding methods that are
naturally amenable to a distributed implementation method, i.e.,
do not require the knowledge of network topology, and that are
suitable for network error correction. First, the Singleton bound
can be K-fold increased by employing a K×K matrix coefficient.
Moreover, we prove that matrix network coding outperforms
linear network coding, since it corrects more errors than linear
network coding, while the amount of header overhead per packet
can be kept the same by reduci ....etc

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