Page 360 - Satellite Communications, Fourth Edition

340 Chapter Eleven

those discarded. The dummy bit level is set midway between the binary
1 and 0 levels, so they do not affect the decoding process.
The block schematic for the decoder is shown in Fig. 11.12 (Burr, 2001).
The demultiplexer provides outputs for the data sequence and parity-1
and parity-2 sequences. These outputs are “soft,” meaning that some
measure of the bit level is used rather than a hard decision output of
binary 1 or 0. For example, assuming a threshold decision level of 0.5V,
the demultiplexer output might be 0.9V, 0.7V 0.1V, 0.2V, 0.9V, 0.65V, 0.3V,
suggesting a hard decision binary sequence of 1 1 0 0 1 1 0. However the
hard decision output does not make use of the likelihood of the hard deci-
sion being correct. The 0.9V level is obviously more likely to be a binary1
than the 0.65V level. Astatistical measure termed the log-likelihood ratio
(LLR) is most commonly used. For a given received value r,let p(1/r) rep-
resent the probability that a 1 was transmitted, and p(0/r) the probabil-
ity that a 0 was transmitted. The log likelihood ratio is defined as

p(1>r)
a b (11.23)
LLR log e
p(0>r)
Where the transmission of 1s and 0s are equiprobable, (the probabil-
ity of either a 1 or 0 occurring being 1/2 , rather like the probability of
heads or tails of a the toss of a fair coin) the LLR becomes:

p(r>1)
a b
LLR log e
p(r>0) (11.24)
log p(r/1) log e p(r/0)
e

2
decoder decoder
1 2 p −1 1 p
0
p −1 p

data 1 2
demultiplexer parity 2 2 buffer
input buffer

1

parity 1 1 2
received information extrinsic information
Figure 11.12 The turbo decoder for the encoder of Figure 11.11. The symbol 1 repre-
sents a deinterleaver. (Courtesy of A Burr and the IEEE.)