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Coded distributed computing studies how tools from coding theory can be used to make large-scale distributed computation faster, more reliable, private, and secure. The course introduces the mathematical foundations of coded computation and then develops modern coding-based methods for distributed matrix multiplication, polynomial computation, and distributed learning. The main emphasis is on straggler mitigation, recovery thresholds, storage-computation-communication tradeoffs, and robustness against erroneous or adversarial workers.

Course Content / Chapter Outline
• Chapter 1: Motivation and distributed-computing model: Master-worker architectures, stragglers, worker failures, communication bottlenecks, adversarial workers, and the recovery-threshold viewpoint.
• Chapter 2: Review of Coding-theory fundamentals: Finite fields, polynomial evaluation/interpolation, linear codes, MDS/Reed-Solomon codes, erasure correction, error correction, and basic secret-sharing ideas.
• Chapter 3: Coded matrix multiplication: Polynomial codes, MatDot/PolyDot-type schemes, entangled polynomial codes, decoding by interpolation, and storage-computation-communication tradeoffs.
• Chapter 4: Lagrange coded computing: Lagrange interpolation for general polynomial computations, resilience to stragglers, Byzantine security, and information-theoretic privacy.
• Chapter 5: Gradient coding for distributed learning: Distributed gradient descent, data replication, exact and approximate gradient recovery, stochastic gradient coding, and convergence/redundancy tradeoffs.
• Chapter 6: Privacy and security in coded computing: Private Lagrange coded computing, secure/private distributed matrix multiplication, colluding workers, GASP-type constructions, and privacy guarantees.
• Chapter 7: Robust and error-tolerant coded computation: Detection and correction of erroneous worker outputs, Byzantine-tolerant decoding, robustness-performance tradeoffs, and limitations of coded schemes.
• Chapter 8: Advanced topics and research outlook: Applications in distributed learning and large-scale linear algebra, recent research directions, open problems, and optional paper discussion.

• Linear algebra, including vector spaces, rank, matrix multiplication, and basic polynomial algebra.
• Basic probability, algorithms, and mathematical maturity at the advanced B.Sc. or M.Sc. level.
• Introductory knowledge of error-correcting codes (e.g., channel coding) is helpful but not required; the required coding-theory tools are reviewed in the course.

Teaching and Learning Methods
• Lectures introduce the theoretical concepts, code constructions, mathematical foundations and derivations.
The lecturer uses slides and the blackboard (or an iPad) to explain the fundamental theoretical concepts.
Lectures are designed to be interactive and to encourage the students to ask questions and initiate discussions with
the lecturer and each other.

• Tutorial/problem-solving sessions: reinforce the material through concrete examples and guided discussion.
The lecturer, or teaching assistants, solve concrete problems to simplify the understanding of the theoretical
content and help the students better understand the material.