Modern Coding Theory
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 Lecturer: Michael Lentmaier (2. DS, BAR 213)
 Tutor:
Nicola Michailow
(2. DS, BAR 106, 2nd week)
 Exam:
oral, date will be determined later
Related literature:
 Lin, Costello, „Error Control Coding“, 2. Edition, Prentice Hall, 2004
 Ryan, Lin, „Channel Codes: Classical and Modern“, Cambridge, 2009
 Richardson, Urbanke, „Modern Coding Theory“, Cambridge, 2008
 Bossert, „Kanalcodierung“, 2. Auflage, Teubner, 1998
Modern Coding Theory Lecture
Slide 1
Channel Capacity and Coding
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M-ASK modulation
(amplitude shift keying)
AWGN channel
without coding
Source:
Bernd Friedrichs,
„Kanalcodierung“, Springer 1995.
Modern Coding Theory Lecture
Slide 2
Development of Coding Systems
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Cutoff Rate
Source: Costello
Modern Coding Theory Lecture
Slide 3
Development of Coding Systems
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Source: Costello
Modern Coding Theory Lecture
Slide 4
Development of Coding Systems
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Source: Costello
Modern Coding Theory Lecture
Slide 5
The Practical Challenge of Coding
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Typical behavior:
waterfall region
error floor region
Modern Coding Theory Lecture
Slide 6
Contents of the course
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 Iterative decoding of concatenated codes
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Concatenation of block codes, product codes
Concatenation of convolutuional codes, turbo codes
Distance properties, error bounds, choice of permutations
 Low-density parity-check (LDPC) codes
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Regular and irregular codes, protographs
Distance properties, pseudo codewords, construction methods
LDPC convolution codes, termination, tailbiting
 Representation of codes by graphs
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Tanner graphs, factor graphs
Message passing, min-sum/sum-product decoding
 Analysis of iterative decoding
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Density evolution, EXIT charts
Optimization criteria (threshold, rate of convergence)
Modern Coding Theory Lecture
Slide 7
Capacity and Potential Coding Gain
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Uncoded transmission
compared to the
Shannon Limit
„Soft is better than hard!“
Source: Johannesson/Zigangirov
Modern Coding Theory Lecture
Slide 8