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Course Outline:
Lectures 1-15
Basics of Block Codes
(2)
Linear C
(3)
Mathematical Preliminaries:groups, rings and fields
(3)
Mathematical Preliminaries:vector spaces
(3)
Bounds on
Size
(2)
Standard Decod
(2)
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Convolutional
Codes
(5)
Finite F
(4)
Course Outline:
Lectures 16-42
Generalized
Distributive Law
(8)
Low-Density Parity-Check Codes
(7)
Cyclic Cod
The EThe EThe EThe E
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REFERENCES ERROR-CORRECTING CODES
P. VIJAY KUMAR
1. Shu Lin, Daniel J.Costello, Error Control Coding - Second Edition,(often used as a coursetextbook) Pearson Education Inc. Pearson Prentice Hall, 2004.
2. W. Cary Huffman, and Vera Pless, Fundamentals of Error-Correcting Codes,(block codingemphasis) Cambridge University Press, 2010.
3. Ron M.Roth, Introduction to Coding Theory,(block coding emphasis) Cambridge UniversityPress, 2006.
4. Tom Richardson and Ruediger Urbanke, Modern Coding Theory,(emphasis on LDPC andrelated codes) Cambridge University Press, 2008.
5. F.J.Macwilliams and N.J.A.Sloane, The Theory of Error - Correcting Codes,(older but clas-sical book on block coding) North-Holland Mathematical Library, 1977.
6. Stephen B. Wicker, Error Control Systems for Digital Communication and Storage,(blockcoding emphasis) Prentice Hall Englewood Cliffs, NJ 07632, 1995.
7. Keith Chugg, Achilleas Anastasopoulos and Xiaopeng Chen, Iterative Detection:Adaptivity,Complexity Reduction, and Applications,(iterative decoding emphasis) Kluwer Academic Pub-lishers, 2001.
8. Rolf Johannesson and Kamil Sh. Zigangirov, Fundamentals of Convolutional Coding, (con-
volutional coding only)IEEE Press, 1999.9. Andrew J. Viterbi and Jim K. Omura, Principles of Digital Communication and Coding,(nice
discussion on on convolutional coding) McGraw-Hill Book Company, 2009.
10. William E. Ryan and Shu Lin, Channel Codes: Classical and Modern,(recent book treatingboth block and LDPC codes) Cambridge University Press, 2009.
11. Chris Heegard and Stephen B. Wicker, Turbo Coding,(early book on turbo codes) KluwerAcademic Publishers, 2010.
12. T. R. N. Rao and Eiji Fujiwara, Error-Control Coding for Computer Systems, Prentice Hallseries in computer engineering, Jan 1989.
13. Hideki Imai,Essentials of Error-Control Coding Techniques , Academic Press, 1990.
14. Ezio Biglieri , Dariush Divsalar , Peter J. McLane and Marvin K. Simon, Introduction toTrellis-Coded Modulation With Applications,(trellis-coded modulation) Macmillan Publishs-ing Company, 1991.
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15. V.S.Pless and W.C.Huffman, Handbook of Coding Theory : Volumes I & II,(two volumehandbook on coding theory: block and convolutional codes, allied topics) North Holland,1998.
16. Richard E. Blahut, Algebraic Codes for Data Transmission,Cambridge University Press, 2011.
17. Richard E. Blahut, Theory and Practice of Error Control Codes,Addison-Wesley PublishingCompany, 1983.
18. George C. Clark Jr. and J. Bibb Cain, Error-Correction Coding for Digital Communica-tions,(an older book, but makes for easy reading) Plenum Press, New York, June 1981.
19. Irving S. Reed and Xuemin Chen, Error-Control Coding for Data Networks , Kluwer AcademicPublishers, 1999.
20. R. J. McEliece, The Theory of Information and Coding,Cambridge University Press, 2004.
21. Elwyn R. Berlekamp, Algebraic Coding Theory Revised 1984 Edition,Aegean Park Press, 1984.
22. Stephen B. Wicker and Vijay K. Bhargava, Reed-Solomon Codes and Their Applications,IEEEPress, 1999.
23. Scott A. Vanstone and Paul C. van Oorschot, An Introduction to Error Correcting Codes withApplications,Kluwer Academic Publishers, 1989.
24. J. van Lint and G. van der Geer, Introduction to Coding Theory and Algebraic Geome-try,Birkhauser Verlag, 1989.
25. V.D.Goppa, Mathematics and Its Applications V.D.Goppa Geometry and Codes,Kluwer Aca-demic Publishers, 1988.
26. Richard B. Wells, Applied Coding and Information Theory for Engineers,Prentice Hall Infor-mation and System Sciences Series, 1998.
27. Peter Sweeney, Error Control Coding: From Theory to Practice , John Wiley and Sons, Ltd,2002.
28. Shu Lin,Tadao Kasami,Toru Fujiwara and Marc Fossorier, Trellises and Trellis-Based Decod-ing Algorithms for Linear Block Codes,Kluwer Academic Publishers, 1998.
29. H. Stichtenoth , Algebraic Function Fields and Codes,Springer-Verlag Berlin Heidelberg, 2010.
Book Chapter
30. P. V. Kumar, M. Win, H-F. Lu, C. Georghiades, Error-Control Coding Techniques and
Applications, invited chapter in the handbook, Optical Fiber Telecommunications IV, editedby Ivan P. Kaminow and Tingye Li, Spring 2002.
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Journal Articles
31. Srinivas M. Aji and Robert J. McEliece, Generalized Distributive Law IEEE Trans. Inform.Theory, March 2000.
32. T. J. Richardson, A. Shokrollahi, and R. Urbanke, Design of capacity-approaching low-densityparity-check codes, IEEE Trans. Inform. Theory, vol. 47, Feb. 2001.
33. A. J. Viterbi,Convolutional codes and their performance in communication systems, IEEETransactions on Communications Technology, , October 1971.
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Sum
maryofLecture5
:
Equivalenceclas
sesdefinedviacosets:
Proofthatitisanequivalencerelation
Thenatureo
ftheequivalenceclassE_b=Hb
Examples:
integers
modulo6andeve
nsubset
Evenpa
ritycheckcode
Elementsin
differentcosetsca
nbeplacedin1-1
correspon
dence
Ringsand
Fields
Axiomsofa
ring
Ringwithide
ntity
Commutativering
Integraldom
ain
Divisionring
Examples:w
heredoweplacethem?
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Lecture6:
VectorSpaces,
LinearIndependenceandBasis
R
ingsandFields
Examples:wheredoweplacethem?
V
ectorSpaces
Axioms
Examples
Derivedproperties
Subspaces
Definition
Example1:pla
neinR^3
Testforasubspace
Furtherexamp
les:repetitioncodeandspccode
Definitionofalinea
rcode
Showhow
the
testappliestothe
Hammingcode(nullspace
ofamatrix)
Pointoutthatasfarassubsetso
fF_2^nareconcerned,
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