1553-877X (c) 2018 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information.
This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication. Citation information: DOI 10.1109/COMST.2018.2878035, IEEE
Communications Surveys & Tutorials
11
assessed the behavior of some LDPC code design techniques
over the AWGN wiretap channel, in terms of security gap.
In [43], the authors studied the application of a special type
of LDPC codes based on serially concatenated low-density
generator matrix to the Gaussian wiretap channel. In [44],
the equivocation rate of Eve’s channel is exploited as an
optimization criteria for designing an algorithm in the finite
codeword length regime. By using this algorithm, irregular
LDPC codes with smaller codeword lengths are constructed
that can approach the ultimate performance limits.
A brief summary of some of the key contributions related
to secure LDPC codes is provided in Table II.
Recently, polar codes, which are known as capacity achiev-
ing codes, are proposed to be used as secrecy capacity
achieving codes too. In [45], authors used polar codes to
construct a coding scheme that achieves the secrecy capacity
for a wide range of wiretap channels. Their scheme works
for any instantiation of the wiretap channel model, as long as
both main and wire-tap channels are symmetric and binary-
input, and wire-tap channel is degraded with respect to the
main channel. Moreover, they clarified how to modify their
construction in order to provide strong security, in the sense
defined by Maurer. In [46], it was shown that polar codes
can achieve nonzero perfect secrecy rates for the binary-
input degraded wiretap channel with low encoding-decoding
complexity. Also, in the special case of having symmetric
channels for both Bob and Eve, this coding technique achieves
the secrecy capacity. This approach was also extended to the
multiple-access channel with a degraded eavesdropper where
a nontrivial achievable secrecy region is established. In [47], a
new multi-block polar coding scheme is introduced on top of
[45] to resolve the difficulty in providing both strong security
and reliability using polar codes, which occurs due to the
existence of a small number of bit-channels that are both
unreliable and unsecure.
In [48], authors proposed a concatenated coding scheme
based on polar codes and LDPC codes for the AWGN wiretap
channel. They also presented a transmission scheme using
rate compatible Polar-LDPC codes to adapt for different dy-
namic environments. In [49], a feedback-based secrecy coding
scheme using polar code over wiretap channels was proposed,
where authors’ results show that the proposed scheme using
polar code can transmit confidential messages reliably and
securely. In [50], authors proposed an alternative approach
to the traditional way of generating secret keys, based on
polar codes that jointly deals with reliability and secrecy. In
[51], a low-complexity and secrecy capacity achieving polar
coding scheme was developed for the discrete memoryless
wiretap channel. The scheme extends previous work by us-
ing a nearly optimal amount of uniform randomness in the
stochastic encoder, and avoiding assumptions regarding the
symmetry or degraded nature of the channels. In [52], polar
codes are developed to relax the symmetric and degraded
constraints. In addition, the coding scheme is also extended to
the interference channel with confidential message (IC-CM),
broadcast channel with confidential message (BC-CM), and
to the multiple access wiretap channel (MA-WC). Besides,
a secrecy capacity achieving coding scheme is introduced
in [53] for general wiretap channel based on polar codes
(not necessarily symmetric or degraded). In [54], the authors
proposed an interesting security technique for the wiretap
channel based on polar codes and artificial noise (AN). In
this technique, the channel quality advantage of Bob over over
that of Eve is not assumed. In the first step, upper and lower
bounds on the symmetric capacity of the polarized bit-channels
are derived that depends on the SNR of each use of physical
channel. Based on these bounds they prove that there is an
existence of bit channels that are hostile to signal reception of
the wiretap channel but beneficial to main channels. Moreover,
they also introduce a method to achieve these bit channels
based on injecting AN and also prove the security of proposed
AN method theoretically. Furthermore, they also introduce two
power allocation schemes for AN.
A short summary of some of the main contributions related
to secure polar codes is made in Table III.
Besides designing security schemes based on LDPC and
polar codes, there are other secrecy schemes based on lattice
codes such as the works reported in [55], [56] and [57]. In
addition, the application of the practical convolutional and
turbo codes to Gaussian wiretap channel using randomized
encoding approach and based on using security gap metric
has recently been studied in [58].
Lesson 1: Most of the security codes surveyed in the
aforementioned studies are usually designed based on the
criterion of weak or strong secrecy notion which generally
assumes infinite block length, making it less practical for
multimedia communication services (such as voice, video,
etc.) where the block length is finite due to having constraints
on the delay and throughput of these type of services that also
do not usually require perfectly zero block error probability.
Particularity, the research community should pay more atten-
tion to the fact that we need to design practical security codes
for the cases where the block length is finite
5
(does not go to
infinity [63]), and secrecy rate does not necessary require to be
exactly equal to the main channel capacity where there is zero
information leakage to Eve. This is due to the fact that Eve
cannot practically benefit from a service that does not meet or
comply with its minimal quality requirements. Moreover, the
design of practical security codes that not only can achieve the
secrecy capacity limit of finite block length, but also comply
with the practical constrains including delay, throughput and
complexity of some of the emerging communication services
in 5G and beyond scenarios such as URRLC and mMTC
remains a challenging task to achieve. Besides, to the best of
authors’ knowledge, designing generic secrecy codes without
considering any information knowledge on the channel of the
eavesdropper (which is a very practical scenario) is also not
yet clear or known thus far in the literature. Therefore, novel
coding techniques are indeed needed to address the above
challenges.
5
Note that there are a few primarily recent theoretical results related to the
fundamental limits of secrecy coding for finite block length as can be found
in [59]–[62].