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Summary of schemes with and without retransmission
No retransmission
Given a code with correction capability
⎥
⎦
⎥
⎢
⎣
⎢
−
=
2
1
min
d
t
we have correct reception when
there are
up to t errors, and incorrect reception when there are more than t errors.
P(C)=P(correct block)=P(up to t errors)=
t
n
t
n
n
j
n
j
p
p
t
n
p
p
n
p
p
n
p
p
C
P
−
−
−
−
=
−
⎟
⎟
⎠
⎞
⎜
⎜
⎝
⎛
+
+
−
⎟
⎟
⎠
⎞
⎜
⎜
⎝
⎛
+
−
⎟
⎟
⎠
⎞
⎜
⎜
⎝
⎛
=
−
⎟
⎟
⎠
⎞
⎜
⎜
⎝
⎛
=
∑
)
1
(
...
)
1
(
1
)
1
(
0
)
1
(
j
n
)
(
1
1
0
0
t
0
j
If p<<1 we can approximate with the first term:
n
n
p
p
p
n
C
P
)
1
(
)
1
(
0
)
(
0
0
−
=
−
⎟
⎟
⎠
⎞
⎜
⎜
⎝
⎛
≈
−
j
n
j
p
p
P
P
E
P
−
+
=
−
⎟
⎟
⎠
⎞
⎜
⎜
⎝
⎛
=
=
=
∑
)
1
(
j
n
errors)
t
than
more
(
error)
block
(
)
(
n
1
t
j
If p<<1 we can approximate with the first term:
1
1
1
1
)
1
(
1
)
1
(
1
)
(
−
−
+
−
−
+
−
⎟
⎟
⎠
⎞
⎜
⎜
⎝
⎛
+
≈
−
⎟
⎟
⎠
⎞
⎜
⎜
⎝
⎛
+
≈
t
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This note was uploaded on 04/24/2011 for the course EE 4421 taught by Professor Mondin during the Spring '11 term at California State University Los Angeles .
 Spring '11
 Mondin

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