Page 774 - 5G Basics - Core Network Aspects

2 Transport aspects

The constellation mapping ensures that the two LSBs of a constellation point comprise the index i of the
i
2-dimensional coset C in which the constellation point lies. The bits (v1, v0) and (w1, w0) are in fact the
2
binary representations of this index.
The three bits (u2, u1, u0) are used to select one of the eight possible 4-dimensional cosets. The eight cosets
are labelled C where i is the integer with binary representation (u2, u1, u0). The additional bit u3 (see
i
4
Figure 10-6) determines which one of the two Cartesian products of 2-dimensional cosets is chosen from
the 4-dimensional coset. The relationship is shown in Table 10-3. The bits (v1, v0) and (w1, w0) are computed
from (u3, u2, u1, u0) using the linear equations given in Figure 10-6.

1 3 1 3 1 3 1 3
0 2 0 2 0 2 0 2
1 3 1 3 1 3 1 3
0 2 0 2 0 2 0 2
1 3 1 3 1 3 1 3

0 2 0 2 0 2 0 2
1 3 1 3 1 3 1 3
0 2 0 2 0 2 0 2

Figure 10-8 – Mapping of 2-dimensional cosets

Table 10-3 – Relation between 4-dimensional and 2-dimensional cosets

4-D coset u3 u2 u1 u0 v1 v0 w1 w0 2-D cosets
0
0
0 0 0 0 0 0 0 0 C  C 2
2
0
C 4 3 3
1 0 0 0 1 1 1 1 C 2  C 2
0
3
0 1 0 0 0 0 1 1 C  C 2
2
4
C 4
3
1 1 0 0 1 1 0 0 C  C 0
2
2
0 0 1 0 1 0 1 0 C 2  C 2
2
C 2 2
4
1
1 0 1 0 0 1 0 1 C  C 1
2
2
2
0 1 1 0 1 0 0 1 C  C 1 2
2
6
C 4
2
1
1 1 1 0 0 1 1 0 C  C 2
2
2
0
0 0 0 1 0 0 1 0 C  C 2
2
C 1 4 3 1
1 0 0 1 1 1 0 1 C 2  C 2
0
0 1 0 1 0 0 0 1 C 2  C 1
2
5
C 4
3
2
1 1 0 1 1 1 1 0 C  C 2
2
0
2
0 0 1 1 1 0 0 0 C  C 2
2
3
C 4
3
1
1 0 1 1 0 1 1 1 C  C 2
2
3
2
0 1 1 1 1 0 1 1 C  C 2
2
7
C 4
1
0
1 1 1 1 0 1 0 0 C  C 2
2
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