1 s.72-227 digital communication systems cyclic codes
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S.72-227 Digital Communication Systems
Cyclic Codes
2Timo O. Korhonen, HUT Communication Laboratory
S.72-227 Digital Communication Systems
Lectures: Prof. Timo O. Korhonen, tel. 09 451 2351, Research Scientist Michael Hall, tel. 09 451 2343
Course assistants: Research Scientist Seppo Saastamoinen (seppo.saastamoinen@hut.fi), tel. 09 451 5417, Research Scientist Yangpo Gao (gyp@cc.hut.fi ), tel. 09 451 5671, Research Scientist Naser Tarhuni (ntarhuni@pop.hut.fi ), tel. 09 451 2255 (Lecture Diaries)
Compulsory study modules: Examination/Tutorials (grading:pass/rejected), Project work
Voluntary study modules: Lecture diary - Maximum increase of grade: 1.0
Follow homepage for further info!
3Timo O. Korhonen, HUT Communication Laboratory
Practicalities
References:
– A. B. Carlson: Communication Systems (4th ed.)
– J. G. Proakis, Digital Communications (4th ed.)
– L. Ahlin, J. Zander: Principles of Wireless Communications
Prerequisites: S-72.245 Transmission Methods in Telecommunication Systems
Homepage: http://www.comlab.hut.fi/opetus/227/ Timetables:
– Lectures: Fridays 12-14, hall S2
– Tutorials: Tuesdays10-12, hall S5, start 3.2.2004
4Timo O. Korhonen, HUT Communication Laboratory
S.72-227 Digital Communication Systems ‘04
Encoding and decoding of cyclic codes Convolutional codes Decoding of convolutional codes Trellis coded modulation (TCM) and ARQ1-techniques Coding for security and secrecy Overview to fading multipath radio channels Bandpass digital transmission in multipath channels Channel equalization Diversity techniques Spread spectrum technology and OFDM2
Multiuser reception Fiber-optic communication
1Automatic Repeat reQuest2Ortogonal Frequency Division Multiplexing
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Topics in channel coding Cyclic codes
– presenting codes: code polynomials
– systematic and non-systematic codes
– generating codes: generator polynomials, usage of shift registers
– decoding: syndrome decoding Convolutional codes
– convolutional encoder
– code trees and state diagram
– generator sequences structural properties
– code weight, path gain, and generating function
– code gain Syndrome and maximum likelihood detection Mod-2 arithmetic`s
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Background Coding is used for
– error detection and/or error correction (channel coding)
– ciphering (security) and compression (source coding) In coding extra bits are added or removed in data transmission Channel coding can be realized by two approaches
– FEC (forward error coding) block coding, often realized by cyclic coding convolutional coding
– ARQ (automatic repeat request) stop-and-wait go-back-N selective repeat … etc.
Note: ARQ applies FEC for error detection
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Cryptography(Ciphering)
SourceCoding
CompressionCoding
Line CodingError Control Coding
Error CorrectionCoding
Error DetectionCoding
- Secrecy/ Security- Encryption (DES)
- Redundancy removal: - Destructive (jpeg, mpeg) - Non-destructive (zip)
- Makes bitsequal probable
- Strives toutilizechannelcapacity byadding extra bits
- for baseband communications- RX synchronization- Spectral shaping for BW requirements- error detection
- used in ARQ as in TCP/IP- feedback channel- retransmissions- quality paid by delay
= FEC- no feedback channel- quality paidby redundantbits
Tax
onom
y of
Cod
ing
FEC: Forward Error CorrectionARQ: Automatic Repeat RequestDES: Data Encryption Standard
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Using shift registers for multiplication
Figure shows a shift register to realize multiplication by 1+p2+p3
In practice, multiplication can be realized by two equivalent topologies:
unit delay element
alternatenotation ofXOR-circuit
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