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Unformatted text preview: tion channel trades-off between the
raw transmission rate (“samples per bit” in this course) and the BER. As you increase the
bit rate at which data is sent (say, by reducing the number of samples per bit), the BER will
also increase, and then you need mechanisms to bring the BER down to acceptable values
once more—and those mechanisms will reduce the achievable bit rate. 6.2 The Simplest Code: Replication In a replication code, each bit b is encoded as c copies of b, and the result is delivered. If
we consider bit b to be the message word, then the corresponding code word is bc (i.e., bb...b,
c times). Clearly, there are only two possible message words (0 and 1) and corresponding
code words. The beauty of the replication code is how absurdly simple it is.
But how well might it correct errors? To answer this question, we will write out the
probability of decoding error for the BSC error model with the replication code. That is, if
the channel corrupts each bit with probability p, what is the pr...
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This document was uploaded on 02/26/2014 for the course CS 6.02 at MIT.
- Fall '13