Lastly, we present a few suggestions on how to improve decoding
performance and possibly reduce implementation complexity [38].
TFCI Encoder Details. The encoding bit stream is based on a second-order Reed-Mueller code.
This code can be represented as a combination of two vector spaces. The first vector space comprises
of a set of orthogonal vectors, while the second comprises of mask vectors (not orthogonal to the first
vector space).
There are a total of 1024 combinations of the transport format, and thus, we only require the TFC
to be 10 bits in length. This is referred to as the TFC index. This index will essentially choose a certain
combination of the above-mentioned vector spaces to create a single TFCI code word of length
32 bits. A graphical representation of this is shown in Fig. 7.99.
422 CHAPTER SEVEN
FIGURE 7.99 Graphical representation of TFCI code-word generation.
X
X
X
X
+
..
.
.
.
.
W0
W5
W6
W9
TFC Index = a(n)
TFCI Code Word = b(n)
The block diagram in Fig. 7.99 can be mathematically represented as follows:
(7.147) b(n) ca9
j0
a( j) # wj(n) dModulo 2
; (n 0,c, 31)
Alternatively, this can be written as (given and are row vectors and are column vectors)
(7.148)
Let us provide some insight into the generated TFCI code word based on the TFC index value.
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