Benjamin Hansen

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This talk concerns the transmission of a message over a noisy channel which may corrupt the message. Specifically, can we encode our messageinto a longer message so that the original message can be recovered fromthe received corrupted message with little chance of error? To overcomethe potential for errors, it is natural to believe the length of the encodedmessage must be much longer than the original message, making our rateof communication tend toward zero. The classical result in informationtheory, Shannon’s theorem, shows that such compromise is unnecessary:there exist constant rate codes where the probability of incorrect decodingtends to zero. We will discuss an outline of this theorem, examples of a fewcodes, and applications. Applications will include QR bar codes, CD andBlu-Ray Discs, deep space communications, and telecommunications. Thistalk is aimed towards undergraduates. Experience in linear algebra andprobability are helpful but not required