A Variable-Parameter Coding Scheme Based on LDPC
Ling Zhao, Zhong Li
School of Electronics and Information Engineering,
Beihang University (BUAA), Beijing, China
E-mail: zhaoling@buaa.edu.cn, lizhong@buaa.edu.cn
Man-Jie Zhu
Space Star Technology Co., Ltd., China Academy of
Space Technology, Beijing, China
E-mail: Felicia_8147@163.com
Abstract-The paper proposes a channel coding system with
both error correction performance and security performance.
The implementation of security performance is to construct a
cluster of parity check matrices with the same structure and to
replace check matrices constantly in the coding process, which
can be called variable-parameter coding scheme. (4096, 3328)
code is constructed based on the proposed scheme, the coding
gain achieves6.5dB on the condition that BER performanceis
10
-6
, and the number of variable check matrices reaches 2
47
.
Applications of this physical layer security method indicate
that illegal receivers cannot obtain the valid information.
Keywords- physical layer security; variable code; LDPC;
AES
I. INTRODUCTION
The history of cryptography can be traced back to ancient
Egypt in the twentieth Century B. C. However, cryptography
is became a real subject until [1] laid the theoretical
foundation of cryptography, which represents the beginning
of modern cryptography. Since Shannon proposed the
channel coding theory [2], there are many scholars
researching on how to construct a practical approximation of
the channel capacity of good codes and a lot of results are
achieved [3]-[7]. Before 1970s, channel coding theory and
cryptography were two different subjects and they were
almost independent of each other. Most of secure
communication systems are hierarchical [8] and the
communication scheme is first encrypting and then channel
coding. While it is true that the two-step operation, on the
one hand increases the complexity of the system, on the
other hand, creates a certain time delay. In 1978, McEliece
proposed the first public key cryptosystem based on
algebraic coding theory, which combines channel coding and
encryption [9]. Then, a cryptosystem which combines
McEliece scheme and LDPC is proposed in [10]. However,
there is the tradeoff between error correction capability and
security performance in this McEliece scheme, and if not
designed well, both of them will decrease. In addition, it has
been proved that the secure communication can be realized
without the key encryption if the error probability of the
eavesdropping channel is higher than that of the main
channel [11]. Reference [12] suggests to use physical layer
security ideas in traditional designs to ensure security in
wireless communication systems.
To achieve physical layer security while channel coding,
a variable-parameter coding scheme based on LDPC is
proposed. The scheme provides a method to construct a
cluster of parity check matrices with same structure, so that
check matrix can be replaced constantly by changing certain
parameters when transmitting information. Besides, the set
of matrices contains hundreds of trillions of elements. Since
it has been proved by physical layer security theory that the
channel error can improve the security of the system [13] and
channel noise exists, illegal receiver can only obtain the
encoded information instead of effective information without
obtaining the correct matrix. Approaching from the angle of
physical layer, this scheme takes advantages of propagation
characteristics of the wireless channel and noise to solve the
information security problem. In addition, with the goal of
realizing high bit error rate performance as well as
encryption performance, bidiagonal matrix structure is used
in the proposed variable-parameter coding scheme.
The rest of this paper is organized as follows. Section II
introduces bidiagonal matrices and corresponding encoding
algorithms. Section III illustrates the proposed variable-
parameter coding scheme and (4096, 3328) code is
demonstrated as well. Both encryption performance and
error-correcting performance are verified to be good. Section
IV shows an application using the proposed scheme and
gives the simulation results and analysis. Finally, a
conclusion is drawn in Section V.
II. LDPC ENCODING ALGORITHM BASED ON
BIDIAGONAL MATRIX
To simplify the encoding algorithm by taking advantage
of the check matrix, the lower triangular bidiagonal matrix is
utilized to construct the LDPC codes. The bidiagonal matrix
is described by
1 0 0 0 0
1 1 0 0 0
0 1 1 0 0
0 0 1 1 0
0 0 0 1 1
p
H
(1)
The check matrix based on the bidiagonal matrix is
formulated by
[]
pd
H H H
(2)
where H
p
is the bidiagonal matrix with the size of (N-M)(N-
M), and H
d
is composed of the circulant sub-matrices with
the size of (N-M)M. It has the same property with the QC-
LDPC matrix. Note that N is the code length of the LDPC
codes and M is the length of the information bit. In Figure 1,
3rd International Conference on Wireless Communication and Sensor Network (WCSN 2016)
Copyright © 2017, the Authors. Published by Atlantis Press.
This is an open access article under the CC BY-NC license (http://creativecommons.org/licenses/by-nc/4.0/).
Advances in Computer Science Research, volume 44
127
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