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Mar 14, 2006
Lecture 10
Lecturer: Madhu Sudan
Scribe: Srujan Linga
1
Last lecture
•
Universal Coding
•
LempelZiv Algorithm
2
Today
•
Channel capacity
•
Sample channels and their capacities
•
AEP for channels
3
Communication System Overview
The block diagram in Fig.1 shows an overview of the communication system.
Figure 1
: Block diagram of the communication system
The transfer of information from the transmitter to the receiver is a physical process and therefore is
subject to noise and imperfections of the signalling process itself. Hence it is a property of physics
that there are no perfect channels. A modiﬁed block diagram with an encoder and decoder introduced
into the communication system is shown in Fig.2. Source symbols
S
from some ﬁnite alphabet Ω
S
are mapped into some sequence of channel symbols
X
of alphabet Ω
X
. The output sequence
Y
of the
channel (input to the decoder) is random but has a distribution that depends on the input sequence
X
.
From the output sequence, we attempt to recover the transmitted message.
3.1
Basic features of the channel
Considering a block of
n
channel symbols, let
1.
p
X
n
(
x
n
) denote the probability distribution on an
n
element sequence from Ω
X
which is under the
designer’s control.
2.
p
Y
n

X
n
(
y
n

x
n
) denote the probability that
y
n
is received given
x
n
was transmitted.
3.
P
Y
n

X
n
(
y
n

x
n
) denote an

Ω
X

n
×
Ω
Y

n
stochastic probability transmission matrix of the channel.
101
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