Error correction is implemented by using more digits ( bits in case of a binary channel ) than the number strictly necessary for the samples, and having the receiver compute the most likely valid message that could have resulted in the received one.
2.
If all 4 letters are equally likely ( 25 % ), we can do no better ( over a binary channel ) than to have 2 bits encode ( in binary ) each letter : A might code as'00', B as'01', C as'10', and D as'11 '.
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