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Unformatted text preview: graphical codes.1 6.1 Bit error models In the previous lectures, we developed a model for how channels behave using the idea of
linear time-invariance and saw how noise corrupted the information being received at the
other end of a channel. We characterized the output of the channel, Y , as the sum of two
y [n] = ynf [n] + noise,
where y [n] is the sum of two terms. The ﬁrst term is the noise-free prediction of the channel
output, which can be computed as the convolution of the channel’s unit sample response
with the input X , and the second is a random additive noise term. A good noise model for
many real-world channels is Gaussian; such a model is has a special name: additive white
Gaussian noise, or AWGN.2 AWGN has mean 0 and is fully characterized by the variance,
σ 2 . The larger the variance, the more intense the noise.
One of the properties of AWGN is that there is always a non-zero probability that a
voltage transmitted to represent a 0 will arrive at the receiver with enough noise that it
will be interpreted...
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This document was uploaded on 02/26/2014 for the course CS 6.02 at MIT.
- Fall '13