464 IEEE COMMUNICATIONS LETTERS, VOL. 21, NO. 3, MARCH 2017
EXIT Chart Aided LDPC Code Design for Symmetric
Alpha-Stable Impulsive Noise
Bin Dai, Rongke Liu, Member, IEEE, Yi Hou, Ling Zhao, and Zhen Mei
Abstract—In this letter, an iterative analysis method based
on an extrinsic information transfer (EXIT) chart and quan-
tized density evolution is developed for low-density parity-
check (LDPC) codes over channels with symmetric alpha-stable
(SαS) impulsive noise. Based on the proposed scheme,
a method to optimize ensembles of LDPC codes under different
levels of impulsiveness is presented and it is shown that the infor-
mation rates of our optimized code ensembles can achieve 95.4%
and 94.7% of the channel capacity for α = 1.8andα = 1, respec-
tively. Furthermore, experimental results, including EXIT curves,
thresholds, and bit-error rate performance of optimized code
ensembles, are obtained to verify the effectiveness of our analysis.
Index Terms—LDPC codes, EXIT chart, impulsive noise,
symmetric alpha-stable distribution.
I. INTRODUCTION
L
OW-DENSITY parity-check (LDPC) codes are a class
of linear block codes which received a lot of attention
due to their near-capacity performance. In addition, they are
widely applied to different recent standards such as WiMAX
and DVB-S2, owing to their high error-correction capability
and low decoding complexity.
Conventionally, Gaussian distributions are used to describe
noises in communication systems. However, some commu-
nication systems exhibit non-Gaussian noise which appears
impulsive in nature, namely, wireless networks [1], shallow
water communications [2] and powerline communica-
tions (PLC) [3]. These impulsive noises last for a very short
duration and have much greater amplitudes than Gaussian
noises. In particular, under very general assumptions, the
first-order distribution of impulsive interference follows a
symmetric alpha-stable (SαS) law [4]. Hence, the non-
Gaussian impulsive noise channel can be modeled by additive
white SαS noise (AWSαSN).
However, as a class of powerful error-correction codes, the
performance of LDPC codes is not well studied over impulsive
noise channels, especially for the code design. There are
several approaches, such as density evolution (DE) [5], quan-
tized DE (QDE) [6] and extrinsic information transfer (EXIT)
charts [7], that have been employed to analyze the asymptotic
Manuscript received July 18, 2016; revised September 19, 2016 and
November 20, 2016; accepted November 27, 2016. Date of publication
December 6, 2016; date of current version March 8, 2017. The work was
supported by the National Natural Science Foundation of China (91438116,
61401010) and the Program for New Century Excellent Talents in University
of China (NCET-12-0030). The associate editor coordinating the review of
this letter and approving it for publication was M. Baldi.
B. Dai, R. Liu, Y. Hou, and L. Zhao are with the School of Electronic
and Information Engineering, Beihang University, Beijing 100191, China
(e-mail: daibinok@buaa.edu.cn; rongkeliu@buaa.edu.cn; mokyy@buaa.
edu.cn; zhaoling@ buaa.edu.cn).
Z. Mei is with the School of Electrical and Electronic Engineering,
Newcastle University, Newcastle upon Tyne NE1 7RU, U.K. (e-mail:
z.mei@ncl.ac.uk).
Digital Object Identifier 10.1109/LCOMM.2016.2636178
behavior of LDPC codes. Compared with DE, EXIT charts not
only provide a visible tool to predict LDPC code performance,
but can also be used to design LDPC codes by matching
the transfer curves of variable-node (VN) decoder and check-
node (CN) decoder. To our best knowledge, there is no liter-
ature on EXIT chart analysis for LDPC codes over AWSαSN
channels. Since the probability density function (PDF) of SαS
distribution is not given in closed-form, the analytic expression
of EXIT functions is difficult to obtain.
In this letter, an EXIT chart analysis for LDPC code design
over AWSαSN channels is proposed. Our contributions are
divided into two aspects: 1. An EXIT chart analysis based
on QDE for LDPC codes is proposed. 2. We propose a code
optimization method which based on EXIT chart analysis to
design capacity-approaching irregular LDPC codes. Moreover,
simulation results of optimized code ensembles are obtained
to verify the effectiveness of our method.
This letter is organized as follows: Section II describes the
background knowledge of the SαS distribution. Section III
presents the QDE based EXIT chart analysis and EXIT chart
based code optimization for AWSαSN channels. Results
are shown in Section IV and finally we conclude the letter
in Section V.
II. B
ACKGROUND
A. The Symmetric Alpha-Stable Distribution
The SαS distribution is a generalization of the Gaussian
distribution that accommodates impulsive characteristics.
A difficulty in dealing with the SαS distribution is the
lack of closed-form expression of PDF except the Gaussian
(α = 2) and Cauchy (α = 1) distribution. Generally, the
SαS distribution is defined by its characteristic function
φ(ω) = e
−
|
γω
|
α
, (1)
where γ>0 is the dispersion which measures the spread of
the SαSPDF.α is the characteristic exponent (0 <α≤ 2),
which represents the tail heaviness of the SαSPDF.Since
the second-order moment of SαS distribution does not exist,
the geometric signal-to-noise ratio (GSNR) proposed in [8] is
used for AWSαSN channels. Using GSNR instead of SNR,
the corresponding E
b
/N
0
for AWSαSN channels is defined
as
E
b
N
0
=
GSNR
2R
,whereR is the code rate.
III. PROPOSED CODE OPTIMIZATION FOR LDPC CODES
BASED ON EXIT CHART ANALYSIS OVER
AWSαSN CHANNELS
EXIT chart analysis is based on tracking the mutual infor-
mation (MI) between the transmitted bits and the soft messages
which exchanged between VN and CN. The soft message is
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