Course Structure
- Introduction to Constrained Systems:
Preface and motivation, examples of practical constraints
(Run-Length Limited (RLL) and Charge Constraint (CC) encoding),
deterministic and lossless representation, irreducible systems,
finite-memory systems, capacity of constrained systems
- Perron-Frobenius Theory:
Irreducible and primitive matrices, Perron-Frobenius Theorem,
capacity in terms of Perron-Frobenius eigenvalues
- Encoders for Constrained Systems:
Encoder graphs, anticipation, approximate eigenvalues,
the state-splitting algorithm
- Two-Dimensional Constrained Systems:
Combinatorial capacity bounding methods and zero capacity regions,
algebraic capacity bounding methods, probabilistic methods for
capacity bounding, constructive capacity bounding methods, and
methods from statistical physics for bounding the capacity.
Course Bibliography
- D. Lind, B.H. Marcus,
"An Introduction to Symbolic Dynamics and Coding,"
Cambridge University Press, Cambridge, 1995.
- B.H. Marcus, R.M. Roth, P.H. Siegel,
"Constrained Systems and Coding for Recording Channels,"
Handbook of Coding Theory,
V.S. Pless and W.C. Huffman (Editors),
Elsevier, Amsterdam, 1998, pp. 1635-1764.
Grading Policy
Homework exercises 60% and student lecture 40%.
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