83)
The log likelihood consists of three parts: the systematic, extrinsic, and a priori information.
A block diagram of a turbo decoder is given in Fig. 5.47.
Lm S Em
Lm logaP[ y0 Zd 1]
P[y0 Zd 0]b logaP[ymZd 1]
P[ ymZd 0]b logaP[d 1]
P[d 0]b
Lm logaP[d 1Zy0,ym]
P[d 0Zy0,ym]b
260 CHAPTER FIVE
T +
Data Bits
dk
Xk
T
+
+ Y1,k
T + T
+
+ Y2,k
?
FIGURE 5.46 Block diagram of a rate 1/3 turbo encoder (K 3).
MAP
Decoder 1 MAP
Decoder 2
y0
y1
y2
y0
LE1
LE2
?
??“1
?
?
FIGURE 5.47 General block diagram of a turbo decoder.
The first MAP decoder uses the systematic and first parity bit, along with a priori estimates to
come up with soft decisions on the transmitted bit sequence in the block of N bits. This extrinsic information
is interleaved along with the systematic bits to be used by the second MAP decoder. The second
MAP decoder output extrinsic information is de-interleaved and becomes the a priori probability
for the first MAP decoder. This process or iteration begins over again.
Many publications exist that compare performance of various decoders such as MAX Log MAP,
SOVA, and so on. The reader should refer to the reference section for a list of some of these
comparisons.
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