# US 9,520,898 B2 · Modulator and modulation method using non-uniform 16-symbol signal constellation for low-density parity check codeword having 3/15 code rate

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- Number: US 9,520,898 B2
- Document ID: US9520898B2
- Status: Granted
- Kind: B2
- Application number: 14/618,972
- Filed: 2015-02-10
- Published: 2015-08-13
- Granted: 2016-12-13
- Earliest claimed: 2014-02-13
- Assignees: Electronics and Telecommunications Research Institute
- Applicants: Electronics and Telecommunications Research Institute
- Inventors: Sung-Ik Park; Sun-Hyoung Kwon; Jae-Young Lee; Heung-Mook Kim; Nam-Ho Hur
- Web page: https://patentgrep.com/patent/US9520898B2

## CPC

- H03M 13/1165: {QC-LDPC codes as defined for the digital video broadcasting [DVB] specifications, e.g. DVB-Satellite [DVB-S2]}
- H03M 13/255: {with Low Density Parity Check [LDPC] codes}
- H03M 13/2792: {Interleaver wherein interleaving is performed jointly with another technique such as puncturing, multiplexing or routing}
- H03M 13/616: {Matrix operations, especially for generator matrices or check matrices, e.g. column or row permutations}
- H03M 13/6552: {DVB-T2}
- H04L 1/0041: {Arrangements at the transmitter end}
- H04L 1/0042: {Encoding specially adapted to other signal generation operation, e.g. in order to reduce transmit distortions, jitter, or to improve signal shape (H04L1/0067 takes precedence)}
- H04L 1/0058: {Block-coded modulation}
- H04L 1/0071: {Use of interleaving (interleaving per se H03M13/27)}
- H04L 27/3422: {in which the constellation is not the n - fold Cartesian product of a single underlying two-dimensional constellation}
- H04L 1/0057: {Block codes (H04L1/0061, H04L1/0064 take precedence)}
- H03M: CODING; DECODING; CODE CONVERSION IN GENERAL (using fluidic means F15C4/00; optical analogue/digital converters G02F7/00; coding, decoding or code conversion, specially adapted for particular applications, see the relevant subclasses, e.g. G01D, G01R, G06F, G06T, G09G, G10L, G11B, G11C, H04B, H04L, H04M, H04N; ciphering or deciphering for cryptography or other purposes involving the need for secrecy G09C)
- H04L: TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION (arrangements common to telegraphic and telephonic communication H04M)

## Abstract

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.

## Claims

### Claim 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.

### Claim 2 (depends on 1)

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.

### Claim 3 (depends on 2)

The modulator of claim 2, wherein a vector corresponding to the four symbols w0, w1, w2, and w3 of the first group is w, a vector corresponding to the four symbols w4, w5, w6 and w7 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 w12, w13, w14 and w15 of the third group is −w, and a vector corresponding to the four symbols w8, w9, w10 and w11 of the fourth group is conj(w).

### Claim 4 (depends on 3)

The modulator of claim 3, wherein the four symbols of the first group are w0, w1, w2 and w3, |real(w0)|=|imaginary(w1)| (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(w1)|=|imaginary(w0)|, |real(w2)|=|imaginary(w3)|, and |real(w3)|=|imaginary(w2)|.