1 S Digital Communication Systems Cyclic Codes

Timo O. Korhonen, HUT Communication Laboratory 2 S Digital Communication Systems u Lectures: Prof. Timo O. Korhonen, tel , Research Scientist Michael Hall, tel u Course assistants: Research Scientist Seppo Saastamoinen tel , Research Scientist Yangpo Gao ), tel , Research Scientist Naser Tarhuni ), tel (Lecture Diaries) u Compulsory study modules: Examination /Tutorials (grading:pass/rejected), Project work u Voluntary study modules: Lecture diary - Maximum increase of grade: 1.0 u Follow homepage for further info!

Timo O. Korhonen, HUT Communication Laboratory 3 Practicalities u References: –A. B. Carlson: Communication Systems (4th ed.) –J. G. Proakis, Digital Communications (4th ed.) –L. Ahlin, J. Zander: Principles of Wireless Communications u Prerequisites: S Transmission Methods in Telecommunication Systems u Homepage: u Timetables: –Lectures: Fridays 12-14, hall S2 –Tutorials: Tuesdays10-12, hall S5, start

Timo O. Korhonen, HUT Communication Laboratory 4 S Digital Communication Systems ‘04 u Encoding and decoding of cyclic codes u Convolutional codes u Decoding of convolutional codes u Trellis coded modulation (TCM) and ARQ 1 -techniques u Coding for security and secrecy u Overview to fading multipath radio channels u Bandpass digital transmission in multipath channels u Channel equalization u Diversity techniques u Spread spectrum technology and OFDM 2 u Multiuser reception u Fiber-optic communication 1 Automatic Repeat reQuest 2 Ortogonal Frequency Division Multiplexing

Timo O. Korhonen, HUT Communication Laboratory 5 Topics in channel coding u Cyclic codes –presenting codes: code polynomials –systematic and non-systematic codes –generating codes: generator polynomials, usage of shift registers –decoding: syndrome decoding u Convolutional codes –convolutional encoder –code trees and state diagram –generator sequences t structural properties –code weight, path gain, and generating function –code gain u Syndrome and maximum likelihood detection u Mod-2 arithmetic`s

Timo O. Korhonen, HUT Communication Laboratory 6 Background u Coding is used for –error detection and/or error correction (channel coding) –ciphering (security) and compression (source coding) u In coding extra bits are added or removed in data transmission u Channel coding can be realized by two approaches –FEC (forward error coding) t block coding, often realized by cyclic coding t convolutional coding –ARQ (automatic repeat request) t stop-and-wait t go-back-N t selective repeat … etc. u Note: ARQ applies FEC for error detection

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Timo O. Korhonen, HUT Communication Laboratory 17 Using shift registers for multiplication u Figure shows a shift register to realize multiplication by 1+p 2 +p 3 u In practice, multiplication can be realized by two equivalent topologies: unit delay element alternate notation of XOR-circuit

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