Modulator and modulation method using non-uniform 16-symbol signal constellation for low-density parity check codeword having 3/15 code rate
A modulator and a modulation method using a non-uniform 16-symbol signal constellation are disclosed. The modulator includes a memory and a processor. The memory receives a codeword corresponding to a low-density parity check (LDPC) code having a code rate of 3/15. The processor maps the codeword to 16 symbols of the non-uniform 16-symbol signal constellation on a 4-bit basis.
1. A modulator for generating a non-uniform 16-symbol constellation signal, comprising:
a memory configured to receive a codeword corresponding to a code rate of 3/15; and
a processor configured to modulate the codeword to one of 16 symbols of the non-uniform 16-symbol constellation signal on a 4-bit basis,
wherein the 16 symbols are defined as shown in the following Table:
TABLE
w
Constellation
0
0.3620 + 0.5534i
1
0.5534 + 0.3620i
2
0.5940 + 1.1000i
3
1.1000 + 0.5940i
4
−0.3620 + 0.5534i
5
−0.5534 + 0.3620i
6
−0.5940 + 1.1000i
7
−1.1000 + 0.5940i
8
0.3620 − 0.5534i
9
0.5534 − 0.3620i
10
0.5940 − 1.1000i
11
1.1000 − 0.5940i
12
−0.3620 − 0.5534i
13
−0.5534 − 0.3620i
14
−0.5940 − 1.1000i
15
−1.1000 − 0.5940i.
2. The modulator of claim 1 , wherein the 16 symbols have non-uniform distances therebetween, and comprise a first group of four symbols of a 1st quadrant, a second group of four symbols symmetric to the four symbols of the first group with respect to an imaginary axis, a third group of four symbols symmetric to the four symbols of the first group with respect to an origin, and a fourth group of four symbols symmetric to the four symbols of the first group with respect to a real axis.
3. The modulator of claim 2 , wherein a vector corresponding to the four symbols w 0 , w 1 , w 2 , and w 3 of the first group is w, a vector corresponding to the four symbols w 4 , w 5 , w 6 and w 7 of the second group is −conj(w) (conj(w) is a function that outputs conjugate complex numbers of all elements of w), a vector corresponding to the four symbols w 12 , w 13 , w 14 and w 15 of the third group is −w, and a vector corresponding to the four symbols w 8 , w 9 , w 10 and w 11 of the fourth group is conj(w).
4. The modulator of claim 3 , wherein the four symbols of the first group are w 0 , w 1 , w 2 and w 3 , |real(w 0 )|=|imaginary(w 1 )| (real(i) is a function that outputs a real component of i, imaginary(i) is a function that outputs an imaginary component of i, and i is an arbitrary complex number), |real(w 1 )|=|imaginary(w 0 )|, |real(w 2 )|=|imaginary(w 3 )|, and |real(w 3 )|=|imaginary(w 2 )|.