# Coding_theory

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```					            Coding theory
Chapter 1 Basic concepts of linear codes
Introduction:coding theory began in the late 1948's with work of C.Shannon,
hamming, Golay and others. Historically coding theory originated as the mathematical
foundation for transmission of messages over noisy channels.
In fact amultitude of diverse applications have been discovered such as the
minimization of noise from compact disc recording, the transmition of financial
information a cross telephone lines, data transfer from one computer to another and so
on. Coding theory deals with the problr=em of detecting and correcting transmission
errors caused by noise on the channel.
The following diagram provides arough idea of a general information transmission
system.

Message                   Transmit              Commun                      Decoder           Reciver
sourse                   er                    ication
Encoder               channel

x  x1  x k
c  c1  c n                  Y=c+e             ˆ
x
codew ord                                        estimate of messge
e  e1  en
error from noise

Communication channel

```
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 views: 4 posted: 11/28/2011 language: English pages: 1