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Unformatted text preview: obability that the receiver
decodes the received code word correctly to produce the message word that was sent?
The answer depends on the decoding method used. A reasonable decoding method is
maximum likelihood decoding: given a received code word, r, which is some c-bit combination of 0’s and 1’s, the decoder should produce the most likely message that could have
caused r to be received. If the BSC error probability is smaller than 1/2, which will always
be true for the realm in which coding should be used, then the most likely option is the
message word that has the most number of bits in common with r.
Hence, the decoding process is as follows. First, count the number of 1’s in r. If there
are more than 2 1’s, then decode the message as 1. If there are more than 2 0’s, then decode
the message as 0. When c is odd, each code word will be decoded unambiguously. When
c is even, and has an equal number of 0’s and 1’s, the decoder can’t really tell whether the
message was a 0 or 1, and the best it can do is to make an...
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- Fall '13