Figure 5.36 shows the BER performance
of Binary Phase Shift Keying (BPSK) using an ideal coherent detector. It also shows the BER performance
for K 4, 6, and 8. Focusing on the BER 1E-3 target, then the coding gains are 1.3 dB,
1.8 dB, and 2.4 dB, respectively. Also a table of some commonly used convolutional codes is given
below (see Table 5.3). Here code polynomials are provided for R1/2 and R1/3 code rates and for constrait
lengths of K 3 to K 9 [23].
We would like to compare the performance of the hard-decision and soft-decision decoders discussed
above. This will be accomplished by the following BER performance curves where we compare
their respective performance in an AWGN channel.
Eb
No
1
R
# Ec
No
Eb
No
2 # Ec
No
Eb
No
SNR
aEc
Nob SNR 3dB
aEb
Nobuncoded
SNR 3dB
Eb
No
S
N
# BW
Rb
Coding gaindB aEb
NobdB
aEb
Nobcoded
metric ak
xk # yk
250 CHAPTER FIVE
251
Rate 1/2 Convolutional Code Performance
(Hard-Decision Decoding)
1.E??“05
1.E??“04
1.E??“03
1.E??“02
3 4 5 6 7 8 9
Eb/No (dB)
BER
CD QPSK
R = 1/2, K = 4
R = 1/2, K = 6
R = 1/2, K = 8
FIGURE 5.36 Performance comparison of various constraint length codes.
TABLE 5.3 Commonly Used Convolutional Codes
Constraint
Code rate length Code Free distance
1/2 3 111 5
101
1/2 4 1111 6
1011
1/2 5 10111 7
11001
1/2 6 101111 8
110101
1/2 7 1001111 10
1101101
1/2 8 10011111 10
11100101
1/2 9 110101111 12
100011101
1/3 3 111 8
111
101
1/3 4 1111 10
1011
1101
1/3 5 11111 12
11011
10101
1/3 6 101111 13
110101
111001
1/3 7 1001111 15
1010111
1101101
1/3 8 11101111 16
10011011
10101001
The ideal antipodal BPSK curve is used as a reference.
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