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 ([email protected]), tel. 09 451 5417, Research Scientist Yangpo Gao ([email protected] ), tel. 09 451 5671, Research Scientist Naser Tarhuni ([email protected] ), 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!


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


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


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


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


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

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Cod

ing

FEC: Forward Error CorrectionARQ: Automatic Repeat RequestDES: Data Encryption Standard


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

1 s.72-227 digital communication systems cyclic codes

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