Algorithmic Aspects of Communication (Winter 2012)

Instructor: François Le Gall
Place: Thursday, 10:30 - 12:00, Room 102 of Science Building Number 7

Course outline

This course will address several algorithmic and complexity-theoretic aspects of communication systems. It will cover the basics of communication complexity theory and error-correcting codes, protocols for secure multiparty computation and related cryptographic tasks, and also recent topics such as network coding theory. This course will be taught in English.

Topics

1. Communication complexity: deterministic and randomized protocols, lower bounds techniques, applications
2. Secure computation: secret sharing schemes, secure function evaluation
3. Error-correcting codes: foundations and examples of efficient codes
4. Network coding: formulation and examples, the max-flow bounds

Lectures

Lecture 1 [October 4]
Guidance and introduction: quick overview of communication complexity (the equality function), secure computation (the millionaire's problem and secret sharing), error correction, and network coding.

Lecture 2 [October 11]
Communication complexity I: formal model of communication protocols and rectangles.

Lecture 3 [October 18]
Communication complexity II: lower bound techniques (the fooling set method, the rank method), applications to space-time tradeoffs for Turing machines.

Lecture 4 [November 1]
Communication complexity III: randomized communication complexity, applications to space lower bounds for data stream algorithms ( "The space complexity of approximating the frequency moments" by Alon, Matias and Szegedy).

Lecture 5 [November 8]
Secure Computation I: secret sharing schemes, Shamir's construction ( "How to share a secret" by Shamir), verifiable secret sharing schemes.

Lecture 6 [November 15]
Secure Computation II: private information retrieval.

Lecture 7 [November 29]
Secure Computation III: error-correcting codes, the Hadamard code, locally decodable codes.

Lecture 8 [December 6]
Guest lecture by Prof. Pandu Rangan.

Lecture 9 [December 13]
Secure Computation IV: locally decodable codes and applications to private information retrieval.

Lecture 10 [December 20]
Secure Computation V: general two party protocols (feasibility of secure computation, oblivious transfer, Yao's protocol).

Lecture 11 [January 10]
Network Coding I: definitions and examples, the main theorem of multicast network coding (additional material).

Lecture 12 [January 17]
Network Coding II: proof of the main theorem of multicast network coding, coding rate vs. routing rate.

Lecture 13 [January 24]
Network Coding III: average coding rate for multicast problems.

Lecture 13 [January 31, final lecture]
Network Coding IV: the k-pair problem.

Textbook and suggested reading

There is no required textbook for this course, but students who want to study in more depth communication complexity may refer to Communication Complexity by Kushilevitz and Nisan (Cambridge University Press, 1997). A very complete reference for secure computation is Chapter 7 of the two-volume book Foundations of Cryptography by Goldreich (Cambridge University Press, 2001 and 2004). A good reference for network coding is the book Network Coding Fundamentals by Fragouli and Soljanin (Now publishers, 2007), available online here.

Evaluation

Evaluation on submitted final reports.