Two values of constraint lengths were simulated,
K 5 and K 7. The additional gain in using soft-decision decoding is approximately 2 dB
over hard-decision decoding. For example, consider K 7 and a BER 1E-3 as the point of interest,
the coding gain is approximately 4 dB for soft-decision decoding (see Fig. 5.37).
252 CHAPTER FIVE
Rate 1/2 Convolutional Code Performance
(Hard- & Soft-Decision Decoding)
1.E??“07
1.E??“06
1.E??“05
1.E??“04
1.E??“03
1.E??“02
3 4 5 6 7 8 9
Eb/No (dB)
BER
Soft
Hard
Uncoded
CD QPSK
R = 1/2, K = 5, Hard
R = 1/2, K = 5, Soft
R = 1/2, K = 7, Hard
R = 1/2, K = 7, Soft
FIGURE 5.37 Performance comparison of hard- and soft-decision decoding.
Next we plot the coding gain of rate 1/2 and 1/3 convolutional codes as a function of BER, with constraint
length, K 7 using soft-decision decoding operating in an AWGN channel [23]. Coding gain
plots can be seen in (see Fig. 5.38) [7].
Coding Gain (dB) for R = 1/3 & R = 1/2, K = 7 Code
3
4
5
6
7
8
1.E??“09 1.E??“08 1.E??“07 1.E??“06 1.E??“05 1.E??“04 1.E??“03 1.E??“02
BER
Coding Gain (dB)
FIGURE 5.38 Coding gains of convolutional codes.
The plot shows us as the BER of interest decreases, the coding gain increases nonlinearly.
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