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UID:www.tcs.tifr.res.in/event/323
DTSTAMP:20230914T125919Z
SUMMARY:The Shannon Capacity of the 5-Cycle
DESCRIPTION:Speaker: Rakesh Venkat\n\nAbstract: \nImagine a secret agent in
  a terrorist camp who needs to get messages to the outside world. He has s
 carves of 5 colours $(A\,B\,C\,D\,E)$\, and depending on the colour of the
  scarf he wears each day\, an intelligence team who have satellite photogr
 aphy of the area decipher the message.\nUnfortunately\, the satellite syst
 em is not perfect and tends to mix up certain colours in it's images: $A$ 
 may be confused with $E$ or $B$\, $B$ with $A$ or $C$\, and so on. The con
 fusion graph forms a 5-cycle $A-B-C-D-E-A$. What protocol can the agent us
 e to transmit his messages with the highest efficiency? (in terms of #mess
 ages per symbol).\nFor instance\, if he uses just colours $A\,C\,$ then he
  transmits 1 bit every day and these are not confused. So he sends one of 
 $2^k$ messages in $k$ days. But there is a better protocol that allows him
  to transfer one of $5^(k/2)$ messages in $k$ days.\nIn a gem of a proof\,
  Lovasz showed that this is indeed tight\, and the agent can do no better.
  We shall see the proof of this result in the talk.\n
URL:https://www.tcs.tifr.res.in/web/events/323
DTSTART;TZID=Asia/Kolkata:20121130T150000
DTEND;TZID=Asia/Kolkata:20121130T163000
LOCATION:A-212 (STCS Seminar Room)
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