- #1
Robin04
- 260
- 16
- Homework Statement
- We try to send a message in a very noisy environment. The messages are coded with a four-letter alphabet. By convention, only the messages without lonely letters are considered to be meaningful. A letter is lonely if the next and previous letters are different (the first letter is lonely if the next is different and the last letter is lonely if the previous is different). At least how long does the message have to be if we want to have the chance of having a meaningful message to be less then ##10^{-10}## because of the noise? The noise changes the letters to other letters in the alphabet. Every letter appears independently with an equal chance.
- Relevant Equations
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The phrasing of the problem is a bit messy but here's how I understood it so far:
We make random character strings out of a four-letter alphabet. Every letter appears independently with an equal chance. The chance of having at least two identical letters next to each other in a string of length ##N## is ##p(N)##. We are looking for ##N## given that ##1-p(N) \leq 10^{-10}##
So the key is to find ##p(N)##. Can you help me a bit with that?
We make random character strings out of a four-letter alphabet. Every letter appears independently with an equal chance. The chance of having at least two identical letters next to each other in a string of length ##N## is ##p(N)##. We are looking for ##N## given that ##1-p(N) \leq 10^{-10}##
So the key is to find ##p(N)##. Can you help me a bit with that?