Digital Signal Processing Reference
In-Depth Information
signal reconstruction) can be approximated by the following complementary
error function (3.1):
Q
Q
,
S
N
color
F
ber
=
=
(3.1)
−
F
1
2
erfc
z
1
where
Q(
z
)
=
√
2
∞
2
√
π
e
−
λ
2
d
λ
and
erfc
(
x
)
x
According to Shannon's limit [Cou97, Ben02], the ideal coded communication
system requires at least that E
b
/N
0
1
.
59 dB for error-free communication.
For a qpsk system, this corresponds to a minimum required uncorrupted frac-
tion
F
≥−
58% of the total channel bandwidth.
1
Today's best high-performance
error correcting codes, such as
Turbo codes
[Ber93], can provide a ber as low
as 1
/
10
5
=
+
0
.
7 dB. This would correspond to an interference-
free bandwidth of at least
F
=
70%. The performance of the issr decoder was
evaluated by simulating the bit error rate as a function of the available band-
width
F
. The simulation was performed using a transmission block length
of 4
k
symbols, while the gain factors
A
and
B
from Figure 3.6 were set to
A
at an E
b
/N
0
of
1
.
00, respectively. In order to obtain maximum performance,
30 iterations of the issr loop were performed before the ber at the output of
the issr decoder was computed. Figure 3.7 shows the bit error rate charac-
teristic of the issr decoder as a function of the bandwidth fraction
F
and the
normalized signal to colored noise ratio E
b
/N
c
. The upper bound for the cod-
inggainoftheissr decoder with respect to the uncoded reference transmission
system is approximated by Equation (3.2):
=
1
.
05 and
B
=
10 log
10
1
F
log
2
1
F
G
issr
=−
−
+
(3.2)
1
−
F
On the performance plot of Figure 3.7, one can distinguish two main operating
regions. Turbo coding is clearly the most performing error correction mecha-
nism above the E
b
/N
c
0
.
3 dB limit. For the region below 0
.
3dBhowever,
the issr decoder provides better performance. The main reason for this is that
the issr algorithm is supported by additional information such as the modu-
lation type and the location of problematic frequency bands. Simulations have
demonstrated that the issr decoder can be concatenated to the Turbo coder.
=
1
Using SNR
=
η
·
E
b
/
N
0
. Bandwidth efficiency
η
is 2 bits/s/Hz for qpsk using raised cosine filtering with
a rolloff factor
r
=
0
.
0 ([Cou97] p. 351, 575).
