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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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