Ultimate Guide to Coding Theory: Error Correction, Cryptography & More 🔐

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Coding theory | Error Correcting Code | Hamming Weight | Hamming Distance | Block Code | Binary Code | q-array Code | Bsc | Msc | Best Explanation


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Subject : Coding Theory

Unit-I
The communication channel, The coding problem, Block codes, Hamming metric, Nearest neighbour decoding, Linear codes, Generator and Parity-check matrices, Dual code, Standard array decoding, Syndrome decoding.

Unit-II
Hamming codes, Golay codes, Reed-Muller codes, Codes derived from Hadamard matrices. Bounds on codes: Sphere packing bound, Perfect codes, Gilbert-Varshamov bound, Singleton bound, MDS codes, Plotkin bound.

Unit-III
Weight distributions of codes, Mac Williams identities. Algebra of polynomials, Residue class rings, Finite fields, Cyclic codes, Generator polynomial and check polynomial, Defining set of a cyclic code.

Unit-IV
BCH bound, Encoding and decoding of cyclic codes, Hamming and Golay codes as cyclic codes, BCH codes, Reed-Solomon codes, Quadratic residue codes, Graphical codes, Convolutional codes.

Books Recommended:
1. F.J. Mac Williams and N.J.A.Sloane: The Theory of Error Correcting Codes, North Holland, 1977.
2. S. Ling and C. Xing, Coding Theory: A First Course, Cambridge University Press, 2004.
3. R.M. Roth: Introduction to Coding Theory, Cambridge University Press, 2006.
4. V. Pless: Introduction to the Theory of Error Correcting Codes, 3rd Ed., John Wiley, 1999.
5. W.C. Huffman, and V. Pless: Fundamentals of Error Correcting Codes, Cambridge University Press, 2003.
6. J. H. Van Lint: Introduction to Coding Theory, 3rd Ed., Springer, 1998. 7. T. K. Moon: Error Correction Coding, John Wiley and Sons, 2005.