Project ideas
 
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Project ideas for AIMS students

  1. Implement decoders for a product code, and measure their performance pb as a function of the noise level f of a binary symmetric channel.
    • Simple decoder: decode code 1 then decode code 2.
    • Iterative decoder: pass messages between the two decoders
  2. Make product codes involving a product of more than two codes.
  3. Make an error-correcting code for the binary erasure channel, and a decoder.
  4. Write a compression algorithm (and an uncompressor):
    • compress Neil's file (000000000000001000000000...);
    • or compress a text file containing ordinary language.
  5. Implement a Monte Carlo algorithm, for example
    • Gibbs sampling
    • Slice sampling
    and apply it to an inference problem or a problem from statistical physics. 
  6.  [ABC] ->  2
 [DEF] ->  3
 [GHI] ->  4
 [JKL] ->  5
 [MNO] ->  6
 [PQRS] -> 7
 [TUV] ->  8
 [WXYZ] -> 9
    The standard mobile phone encoder
    When sending text on mobile phones, some people use the iTap/T9/predictive text system, in which, for example, HELLO is written as 43556, and, since no other word in the dictionary is encoded as 43556, the phone deduces that you wanted HELLO. However, some words collide under this iTap encoding, for example KISS and LIPS are both 5477.

    Investigate how much better the iTap system would work if a different encoding of the alphabet A-Z onto the numbers 2..9 were used.