Tratamiento No Lineal

Constellation Shaping for
Bit-Interleaved LDPC Coded APSK

arXiv:1207.2215v1 [cs.IT] 10 Jul 2012

Matthew C. Valenti, Senior Member, IEEE, Xingyu Xiang, Student Member, IEEE,

Abstract—An energy-efficient approach is presented for shaping a bit-interleaved low-density parity-check (LDPC) coded
amplitude phase-shift keying (APSK) system. A subset of the
interleaved bits output by a binaryLDPC encoder are passed
through a nonlinear shaping encoder whose output is more
likely to be a zero than a one. The “shaping” bits are used
to select from among a plurality of subconstellations, while
the unshaped bits are used to select the symbol within the
subconstellation. Because the shaping bits are biased, symbols
from lower-energy subconstellations are selected more frequently
thanthose from higher-energy subconstellations. An iterative
decoder shares information among the LDPC decoder, APSK
demapper, and shaping decoder. Information rates are computed
for a discrete set of APSK ring radii and shaping bit probabilities,
and the optimal combination of these parameters is identified
for the additive white Gaussian noise (AWGN) channel. With
the assistance ofextrinsic-information transfer (EXIT) charts,
the degree distributions of the LDPC code are optimized for use
with the shaped APSK constellation. Simulation results show that
the combination of shaping, degree-distribution optimization, and
iterative decoding can achieve a gain in excess of 1 dB in AWGN
at a rate of 3 bits/symbol compared with a system that does
not use shaping, uses an unoptimizedcode from the DVB-S2
standard, and does not iterate between decoder and demodulator.

I. I NTRODUCTION
Amplitude phase-shift keying (APSK) is a modulation consisting of several concentric rings of signals, with each ring
containing signals that are separated by a constant phase
offset. APSK has recently become widely adopted, due primarily to its inclusion in the second generation of theDigital
Video Broadcasting Satellite standard, DVB-S2 [1], where it
is combined with low-density parity-check (LDPC) coding.
APSK offers an attractive combination of spectral and energy
efficiency, and is especially well suited for the nonlinear
channels typical of satellite systems.
For a given modulation order M , an APSK constellation is
characterized by the number of rings, the number ofsignals in
each ring, the relative radii of the rings, and the phase offset of
the rings relative to each other. In [2] and [3], these parameters
are optimized with an information-theoretic technique involving the maximization of the symmetric information rate (SIR),
Paper approved by H. Leib. Manuscript received Aug. 24, 2011; revised
Feb. 13, 2012; accepted Apr. 18, 2012.
Portions of this paperwere presented at the IEEE International Conference
on Communications (ICC), Kyoto, Japan, June 2011, and the IEEE Military
Communications Conference (MILCOM), Baltimore, MD, 2011.
This work was sponsored by the National Science Foundation under Award
No. CNS-0750821 and by the United States Army Research Laboratory under
Contract W911NF-10-0109.
M. C. Valenti and X. Xiang are with WestVirginia University, Morgantown,
WV, U.S.A. (email: valenti@ieee.org, xiang.xxy2008@gmail.com)).
Digital Object Identifier 10.1109/TCOMM.2012.XX.XXXXXX

which is the mutual information between channel input and
output under the assumption of equally-likely input symbols.
The SIR is a suitable objective function when the M symbols
are selected with uniform probability, which is the case formany conventional systems, such as DVB-S2. However, the
SIR is not necessarily equal to the capacity of the channel,
which is the information rate optimized over all possible
input distributions. Achieving the capacity of APSK requires
a nonuniform distribution of symbols. In [3], a nonuniform
symbol distribution is considered and optimal symbol probabilities are determined by maximizing the...