Of 14 01/03/2015ISCA-2015: Reliable Meaningful Communication1 Reliable Meaningful Communication Madhu Sudan Microsoft, Cambridge, USA.

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Presentation transcript:

of 14 01/03/2015ISCA-2015: Reliable Meaningful Communication1 Reliable Meaningful Communication Madhu Sudan Microsoft, Cambridge, USA

of 14 Reliable Communication? Problem from the 1940s: Advent of digital age. Problem from the 1940s: Advent of digital age. Communication media are always noisy Communication media are always noisy But digital information less tolerant to noise! But digital information less tolerant to noise! 01/03/2015ISCA-2015: Reliable Meaningful Communication2 AliceAlice BobBob We are not ready We are now ready

of 14 Coding by Repetition 01/03/2015ISCA-2015: Reliable Meaningful Communication3

of 14 Shannon’s Theory [1948] 01/03/2015ISCA-2015: Reliable Meaningful Communication4 AliceAlice BobBob Encoder Decoder

of 14 Shannon’s Theorem 01/03/2015ISCA-2015: Reliable Meaningful Communication5

of 14 Challenges post-Shannon 01/03/2015ISCA-2015: Reliable Meaningful Communication6

of 14 Explicit Codes: Reed-Solomon Code 01/03/2015ISCA-2015: Reliable Meaningful Communication7

of 14 More Errors? List Decoding 01/03/2015ISCA-2015: Reliable Meaningful Communication8

of 14 Reed-Solomon List-Decoding Problem 01/03/2015ISCA-2015: Reliable Meaningful Communication9

of 14 Decoding by example + picture [S’96] Algorithm idea: Find algebraic explanation Find algebraic explanation of all points. of all points. Stare at the solution Stare at the solution (factor the polynomial) (factor the polynomial) Ssss Ssss 01/03/2015ISCA-2015: Reliable Meaningful Communication10

of 14 Decoding by example + picture [S’96] Algorithm idea: Find algebraic explanation Find algebraic explanation of all points. of all points. Stare at the solution Stare at the solution (factor the polynomial) (factor the polynomial) Ssss Ssss 01/03/2015ISCA-2015: Reliable Meaningful Communication11

of 14 01/03/2015ISCA-2015: Reliable Meaningful Communication12 Decoding Algorithm

of 14 Summary and conclusions (Many) errors can be dealt with: (Many) errors can be dealt with: Pre-Shannon: vanishing fraction of errors Pre-Shannon: vanishing fraction of errors Pre-list-decoding: small constant fraction Pre-list-decoding: small constant fraction Post-list-decoding: overwhelming fraction Post-list-decoding: overwhelming fraction Future challenges? Future challenges? Communication can overcome errors introduced by channels. Communication can overcome errors introduced by channels. Can communication overcome errors in misunderstanding between sender and receiver? Can communication overcome errors in misunderstanding between sender and receiver? [Goldreich,Juba,S. ‘2011]; [Juba,Kalai,Khanna,S.’2011] …. [Goldreich,Juba,S. ‘2011]; [Juba,Kalai,Khanna,S.’2011] …. 01/03/2015ISCA-2015: Reliable Meaningful Communication13

of 14 Thank You! 01/03/2015ISCA-2015: Reliable Meaningful Communication14