A simple error control code is the repetition code. Assume that we have four messages 00, 01, 10, 11 that we encode in
the code words 00000, 01010, 10101, 11111 respectively. There are 25 = 32 possible words that can be received
at the end of a noisy channel. Give a list of all of these 32 words, and the maximum likelihood decoding of these words.
Show that the code cannot correct all single errors, but can detect single errors. The list should look like this:
Closest Code Word(s)
Distance to Closest Code Word
Use the Hamming code with parity matrix from Figure 3 of the Lecture Notes. Give a table that encodes all
possible 16 messages. Give two examples where you encode a message, simulate a single error during transmission,
and then correct the error. Give two examples where you encode a message, simulate a double error during transmission,
and decode to the wrong message.
Create a systematic Hamming code parity matrix of four columns. Encode a message (with about equal number of zeroes and ones),
simulate a single error during transmission, and show how it is corrected.