Error Correcting Codes (EE5350) : Aug-Dec 2025.

Instructor

• Myna Vajha

Timings and Venue

• Slot R: Tue: 2.30-4pm, Fri: 4-5.30pm

• CS-LH-2

• First class on Tuesday, 29th July, 2.30pm

Office Hours

• Tue: 4-5pm

Teaching Assistants (TBD)

Outline (Tentative)

• Basics of binary codes: block length, Hamming weight, minimum distance, rate

• Mathematical Preliminaries: Group, Ring, Field, Vector Spaces

• Linear block codes

  • generator and parity check matrices

  • dual code

  • puncturing and shortening techniques

• Bounds on code sizes: Hamming, Gilbert-Varshamov, Singleton bounds

• MDS codes: Reed Solomon (RS) Codes

  • Dual of RS codes,

  • Systematic Encoding of RS codes

  • Berlekamp-Welch decoding

  • Shamir's Secret Sharing

• Applications to Learning: Straggler Mitigation

  • Distributed Computation

• Applications in Post-Quantum Cryptography

  • McElice Cryptosystem

• Boolean functions, Reed Muller Codes, Polar codes

• Decoding Linear Block Codes

  • Standard Array, ML, MAP decoder

• Shannon's Channel coding theorem (time permitting)

• Generalized Distributive Law

  • LDPC codes

  • Belief Propagation/ Message Passing decoder

• Convolutional Codes, Viterbi Decoder

• Finite Fields, Cyclic Codes (BCH codes)

References

• Error Control Codes (NPTEL course) by Prof. P. Vijay Kumar.

• Cary Huffmann and Vera Pless: Fundamentals of Error-Correcting Codes, Cambridge University Press, 2003

• Tom Richardson and Ruediger Urbanke: Modern Coding Theory Cambridge University Press, 2008.

• Will add links to any additional references as course progresses