Coding Theory





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Course Contents

  • Introduction: Types of codes, channel models, maximum likelihood decoding, Shannon's noisy channel coding theorem, FEC, ARQ, HARQ.

  • Linear Block Codes : Generator matrix, parity check matrix, syndrome, error detection, error correction, minimum distance of the code, dual code, weight enumeration and Mac Williams theorem. Examples of simple linear block codes. 3. Some linear block codes : Construction, properties and decoding of some popular block codes; Hamming codes, Reed Muller codes.

  • Bonds on codes : Hamming bound, Plotkin bound, Singleton Bound, Elias Bound, Gilbert Varshmov Bound, Linear programming bounds.

  • New codes from old codes : Extending a code, puncturing a code, expunging a code, augmenting a code, shortening a code, direct sum construction.



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