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발표제목
발표제목 둘째 줄
2000년 11월
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연세대학교 전기전자공학과
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Table of Contents
 Introduction to Error Correction: 3-16
– Linear Binary [n,k,d] Code
 Binary Hamming Codes: 17-37
– Hamming Codes, Parity Check Matrix and Syndrome Decoding
– Standard Array Decoding, Shortening and Extending
 Coding Gain of some BCH code and MPSK modem: 38-55
– Uncoded MPSK vs Coded MPSK
– Coding Gain
– etc
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TYPES OF CODES
 Source Coding (Data Compression + Formatting) : remove as
much redundancy as possible, subject to unique recovery at the
receiver. Huffman code, LPC, CELP, JPEG, MPEG,...
 Channel Coding (Error Control Coding) : add some redundancy
so as to detect and/or correct possible errors at the receiver.
Hamming code, RS code, Convolution code, Turbo code
 Secrecy Coding (Encryption + Authentication) : convert the
message in one format into another so that no unintended user
may detect/understand/modify the content. DES, RSA,...
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Digital Communication Systems
Source
Source
Encoder
Secrecy
Encoder
CRC
Encoder
Block/Conv
Encoder
Inter-lea
ver
Modulator
(Writing)
Channel Encoder
Impairments
Noise,Fading
Channel
(Storage
Media)
Channel Decoder
Sink
(User)
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Source
Decoder
Secrecy
Decoder
CRC
Decoder
Block/Conv
Decoder
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Deinterleaver
Demodulator
(Reading)
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Example of Channel Coding :
Repetition code
0
0
1-p
 Binary Symmetric Channel 
p
p
1
•
1-p
1
Message = (101)
• Message Error Probability Without
Coding :
Puncoded ( E)  1  (1  p)3
• With Coding : 0  000, 1  111
Decoding rule : majority vote for every 3 bits
• Message error probability :Pcoded ( E)  1  (1  q)3
• where
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q  p  3 p (1  p)
3
2
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Example of Channel Coding : Repetition
code (Performance)
Comparison of MEP between Uncoded and Coded Systems
0.00
1.00
Message Error Probability
-LOG10 (P(error))
2.00
3.00
4.00
5.00
P(uncoded)
P(coded)
6.00
7.00
8.00
9.00
1.00E+00
1.00E-01
1.00E-02
1.00E-03
1.00E-04
1.00E-05
Bit Error Probability p
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Advantages of ECC
 Principle (Shannon, 1948)

If you transmit information at a rate less than the
channel capacity, then error-free transmission is
possible by using some ECC.
 Practice

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At a given Bit Error Rate, you can reduce the
amount of power to be transmitted.
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