Content uploaded by Abdelilah Kadi
Author content
All content in this area was uploaded by Abdelilah Kadi on May 30, 2022
Content may be subject to copyright.
Indonesian Journal of Electrical Engineering and Computer Science
Vol. 26, No. 3, June 2022, pp. 1692∼1700
ISSN: 2502-4752, DOI: 10.11591/ijeecs.v26.i3.pp1692-1700 r1692
Girth aware normalized min sum decoding algorithm for
shorter length low density parity check codes
Abdelilah Kadi1, Hajar El Ouakili2, Rachid El Alami2, Said Najah1
1Laboratory of Intelligent Systems and Application, Sidi Mohamed Ben Abdellah University, Fez, Morocco
2Laboratory of Computer Science, Signals, Automation and Cognitivism, Sidi Mohamed Ben Abdellah University, Fez, Morocco
Article Info
Article history:
Received Aug 30, 2021
Revised Mar 14, 2022
Accepted Mar 29, 2022
Keywords:
5G
Low density parity check
Normalized min sum
Short block code
Wireless regional area
network
ABSTRACT
Recently, short block codes are in great demand due to the emergent applications re-
quiring the transmission of a short data unit and can guarantee speedy communication,
with a minimum of latency and complexity which are among the technical challenges
in today’s wireless services and systems. In the context of channel coding using low
density parity check (LDPC) codes, the shorter length LDPC block codes are more
likely to have short cycles with lengths of 4 and 6. The effect of the cycle with the
minimum size is that this one prevents the propagation of the information in the Tan-
ner graph during the iterative process. Therefore, the message decoded by short block
code is assumed to be of poor quality due to short cycles. In this work, we present a
study of the evolution of the messages on check nodes during the iterative decoding
process when using the LDPC decoding algorithm normalized min sum (NMS), to see
the destructive effect of short cycles and justify the effectiveness of the girth aware
normalized min sum (GA-NMS) decoding LDPC codes algorithm in terms of correc-
tion of the errors, particularly for the codes with short cycles 4 and 6. In addition to
this, the GA-NMS algorithm is evaluated in terms of bit error rate performance and
convergence behavior, using wireless regional area networks (WRAN) LDPC code,
which is considered as a short block code.
This is an open access article under the CC BY-SA license.
Corresponding Author:
Abdelilah Kadi
Laboratory of Intelligent Systems and Application, Sidi Mohamed Ben Abdellah University
Fez, Morocco
Email: abdelilah.kadi@usmba.ac.ma
1. INTRODUCTION
We are living in an era of advanced technology, the need for wireless access for voice and multimedia
has increased enormously. This need has created a wide range of technical challenges like cost, high speed,
throughput, low complexity, low power and low latency as in [1]-[4]. Low density parity check (LDPC) codes
[5] of shorter length (i.e., codes with dimension k in the range of 50 to 1000 bits) are considered as they offer
advantages in terms of latency and complexity, at the cost of performance degradation due to the increased
number of short cycles in the tanner graph (TG) [6], contrary to the LDPC code with the large block length as
we can see in the study presented in [7] or [8]. The advantages of short codes nominate them to be used in new
application classes such as enhanced mobile broadband (eMBB) communication, ultra-reliable and low latency
communications (uRLLC), massive machine type communications (mMTC), and the internet of things (IoT),
which have gained significant interest recently for 5G wireless networks as mentioned in [9]-[13].
During the decoding iterative process using LDPC code, the circulation of messages between different
nodes is beneficial to error correction. The major problem when using a short block LDPC code is the existence
Journal homepage: http://ijeecs.iaescore.com
Indonesian J Elec Eng & Comp Sci ISSN: 2502-4752 r1693
of short cycles with lengths (4, 6, or 8) as shown in Figure 1. So when a node is connected to a cycle with a
short length (4, 6, or 8), the message coming out of this node may enter into a short loop and cannot interact
with the other nodes during the iterative process. This prevents the evolution of the message and the correction
of errors. In order to get rid of this drawback, there are several research attempts that can be divided into two
axes, the first one focusing on creating codes without cycles 4 and cycles 6, or at least without cycle 4. In this
context, we can see the work presented in the papers [14]-[17].
Figure 1. Graphic and matrix representation of cycles with size (4, 6 and 8)
The second approach that is used to reduce the destructive effect of a girth in the LDPC code consists
of multiplying a node in Tanner graph by a factor depending on the number of short cycles passing through
the nodes, in this context we find exponential factor appearance probability belief probability (EFAP-BP) [18],
variable factor appearance probability belief propagation (VFAP-BP) [19] which are the improved version of
belief propagation (BP) algorithm for decoding LDPC code. The decoding process using EFAP-BP and VFAP-
BP is similar to the BP decoding algorithm except that the decoding process of these two algorithms consists in
putting a weighting on the messages transiting between the nodes in TG to free themselves from the short cycle
and to evolve through the iterations, the weighting parameter added is dependent on the cyclic structure of the
code. In the context of the min sum algorithm for decoding LDPC code which is designed in order to reduce
the complexity of the previous BP, we find in the literature the girth aware normalize min sum algorithm (GA-
NMS) [20] which is inspired from the two algorithms discussed previously and which make the normalization
factor dependent on the cyclic structure of the code, unlike the standard normalized min sum (NMS) algorithm
which uses a constant normalization factor [21].
The GA-NMS is already evaluated using WIMAX IEEE P802.16e codes [22] and showed good per-
formance in front of the NMS algorithm, in this paper we provide a statistical study that proves the destructive
effect of cycles 4 and 6. From this study we could deduce that the nodes need to be multiplied by a factor depen-
dent on the information of short cycles passing through it, in addition to this, the GA-NMS algorithm has been
applied on WRAN IEEE 802.22 codes [23] which is considered short block code with the length (384, 192).
The organization of this paper is as shown in section 2 introduces a state of the art which includes a detailed
description of the GA-NMS algorithm. In section 3, a Statistic study of soft likelihood ratio (LLR) messages
is presented. Section 4 shows the simulation results along with discussions. Finally, section 5 concludes the
paper.
2. RESEARCH METHOD
2.1. Girth aware normalized min sum algorithm
LDPC is one of the most efficient error correcting codes, discovered for the first time by Robert
Gallager in the year 1962 in the context of his thesis [5], among the most popular LDPC decoding algorithm we
can find the normalized min sum. The NMS is an algorithm that can be placed between the belief propagation
which provides very good performance in error correction at the price of computational complexity and min
sum decoding algorithm which is a simplified version of the BP algorithm in terms of complexity with mediocre
performance quality. However, the NMS algorithm presents a good compromise between performance and
computational complexity, this makes it suitable for hardware implementation. The NMS decoding algorithm
Girth aware normalized min sum decoding algorithm for shorter length low density parity ... (Abdelilah Kadi)
1694 rISSN: 2502-4752
was developed in the year 2002 and from this year, there are many versions developed of this algorithm we can
see in the literature [20], [24].
The GA-NMS is one of the improved versions of the NMS algorithm that consists in multiplying the
messages transiting from check node to variable node in TG by a normalization factor α(G(k)) that depend
on the shortest cycle G(k)passing through the check node kinstead of multiplying all messages going from
check nodes to variable nodes by a constant empirical factor 0< α < 1. The determination of the values of
α(G(k)) of the GA-NMS algorithm is done using an off-line process. The knowledge of a cyclic structure of
LDPC code is required when using the GA-NMS algorithm, More precisely, we need to know for each check
node kin the TG the shortest cycle passing through it. There are many pieces of research that were done in
this context and many efficient algorithms were proposed in the literature that can be used to determine the
cyclic structure of LDPC code [25], [26]. We consider that the binary message that we have to transmit over
an additive white Gaussian noise (AWGN) channel using a binary phase-shift keying (BPSK) modulation is
u= (u1, ..., uK)and the received symbol is v= (v1, ..., vK). We note:
− H, correspond to the tanner graph of an LDPC code.
−γkis defined as the information derived from the log-likelihood ratio of the received symbol vk.
−bl,k, is defined as the information coming from CNlto VNkas depicted in Figure 2.
−al,k, is defined as the information coming from VNkto CNlas depicted in Figure 2.
− HV(l)is the set of variable nodes that are connected to the CNl.
− HC(k)is the set of check nodes that are connected to the VNk.
−k0∈ HV(l)\krepresent HV(l)except the variable node k.
−l0∈ HC(k)\lrepresent HV(l), except the check node l.
−G(l)is the size of the shortest cycle in the tanner graph passing through node l.
−gis the shortest cycle in the tanner graph and can be written as g= minl=1···LG(l).
Figure 2. Tanner graph corresponds to the H matrix
The decoding using GA-NMS algorithm is done during an iterative process i= 1,2,3, ..., Imax, for
each iteration i, we have to do the following four steps:
Firstly the priori information γkis calculated using (1) for each VNk, and messages that should be transmitted
from a variable node to check node al,kare initialized ∀k= 1, ..., K;∀l∈ HC(k).
γk=log p(uk= 1|vk)
p(uk= 0|vk)(1)
al,k=γk(2)
Indonesian J Elec Eng & Comp Sci, Vol. 26, No. 3, June 2022: 1692–1700
Indonesian J Elec Eng & Comp Sci ISSN: 2502-4752 r1695
In the second step the messages that should be transmitted from check-to-variable messages bl,kare updated
according to the al,kmessages computed previously, with k0∈ HV(l)\ {k};∀l= 1, ..., L;∀k∈ HV(l)
and α(G(l)) normalization factor depending on the short cycles passed through the node l, this parameter is
determined empirically for each check node l:
bl,k=α(G(l)) ×Y
k0∈HV(l)\k
sgn (al,k0)×min
l0∈HV(l)\k|al,k0|(3)
thirdly the messages αm,n are updated again according to the input γkvalue and the messages bl,kcomputed
in the last step, with m0∈ HC(n)\ {m} ∀n= 1, ..., N ;∀m∈ HC(n);
al,k=γk+X
l0∈HC(k)\l
βl0,k (4)
finally the outgoing messages from variable node also called a posteriori LLRs (AP-LLR) are calculated by the
following equation. These values are used to take a hard decision on each coded-bit ∀k= 1, ..., K:
˜γi
k=γk+X
l∈HC(k)
bl,k(5)
then the estimated CodeWod vector ˆu= [ˆu1,ˆu2,...,ˆun]is calculated by:
ˆun=(0if and only if ˜γk≤0,
1if and only if ˜γk>0.(6)
when the estimated CodeWord satisfy z=H׈ut= 0, or if the maximum number of iterations has been
reached, the iterative process stops.
3. STATISTIC STUDY OF SOFT LLR MESSAGES
As already shown in [20]. The WIMAX IEEE P802.16e code with size N= 576 and rate r= 1/2
has three types of variable nodes, 168 VNs crossed by girth 4, 144 VNs crossed by girth 6, and 264 crossed by
girth 8 as mentioned in (Table I). The specific cyclic structure of this code is an advantage that will allow us to
see the negative effect of short cycles and the evolution of the messages during the iterative process.
Table 1. Distribution of short cycles with sizes (4, 6 and 8) in the code chosen from IEEE P802.16e
Length of short cycle HCN impacted VN impacted
Cycle 4 96 144 168
Cycle 6 528 120 144
Cycle 8 7344 24 264
In this research, we propose to make a statistical analysis of the outgoing messages from variables
nodes. In this a statistical analysis we consider just the received vectors ynthat fail to be decoded by Normalized
MS after 50 iterations at SN R = 3dB, for each vector we calculate the SLLR messages by:
∀k= 1, ..., K SLLRn= ˜γk×sign(vk)(7)
then we calculate the mean of SLLR value for each class of variable nodes and we accumulate it, the obtained
curve shows that there are appearances of an offset between the average of SLLR outgoing from variable
nodes connected to girth 4, variable nodes connected to girth 6 and variable nodes connected to girth 8 and the
majority of messages are between [-1.5 -2.5] after 50 iterations, as indicated in the following figure Figure 3.
This result is considered due to the cyclic structure of the code which prevents the evolution of the messages
during the iterative process.
Based on this result, we suppose that the check nodes connected to girth 4 need an optimization
factor α1less than the nodes connected to girth 6, and girth 8. The check nodes passed by girth 6 should be
Girth aware normalized min sum decoding algorithm for shorter length low density parity ... (Abdelilah Kadi)
1696 rISSN: 2502-4752
multiplied by an optimization factor α2> α1. Finally the check nodes with girth 8 should be re-weighted by
an optimization factorα3between α2and 1.
-14 -12 -10 -8 -6 -4 -2 0
Soft LLR (SLLR)
0
100
200
300
400
500
600
700
800
900
1000
Avarage of the outgoing messages Soft LLR
VN with girth 4
VN with girth 6
VN with girth 8
Figure 3. Average of the outgoing message soft LLR from variable nodes with girth [4, 6, 8]
4. METHOD FOR DETERMINATION OF VARIABLE OPTIMIZATION FACTOR FOR WRAN
CODE
4.1. Wireless regional area network (WRAN)
In this study we have chosen to apply the GA-NMS method on short block code that consumes low
power can be implemented in a small area and have good performance in terms of BER and throughput. For
this reason, we chose WRAN code which is from IEEE 802.22 standard for wireless broadband access for
the same reason why the authors in [27] chose it for hardware implementation. WRAN uses cognitive radio
techniques for dynamically configuring to use the best wireless channels that are available in the area. This
standard is highly suitable for providing broadband access to low population density areas worldwide. WRAN
standard uses LDPC codes for error correction with 1/2,2/3,3/4and 5/6as code rates as depicted in the
paper [28].
4.2. Optimization factor
In this section, the behavior and decoding performances of the GA-NMS algorithm obtained from
computer simulations when decoding shorter length LDPC code are presented and compared with the standard
MS and NMS. To illustrate the potential application of the GA-NMS algorithm, we have tested WRAN code
from IEEE 802.22 standard with the rate r= 1/2and size N= 384 from the database [23]. We performed
simulations assuming binary phase-shift keying (BPSK) modulation and transmission over the additive white
Gaussian noise (AWGN) channel. For each simulation, the decoder stops when a valid codeword is found or
the decoder achieves the maximum number of iterations, which is limited to 50 iterations. The study of the
cyclic structure of the WRAN codes has shown that this code has, on the one hand, 32 short cycles with size
g=4 and 384 short cycles with size g=6, on the other hand, there are 64 check nodes connected to girth 4 and
128 check nodes connected to girth 6 as shown in (Table 2). Before proceeding to the decoding step, we need
to determine the optimization factor γfor the NMS algorithm, and the variable optimization factors γ1, γ2for
the proposed GA-NMS algorithm as we did previously for the WIMAX code in [20]. The simulations show
that γfor NMS takes the value 0.8 and γ1, γ2takes the values 0.8 and 0.9 as depicted in figure Figure 4.
Indonesian J Elec Eng & Comp Sci, Vol. 26, No. 3, June 2022: 1692–1700
Indonesian J Elec Eng & Comp Sci ISSN: 2502-4752 r1697
Table 2. Distribution of short cycles with sizes 4 and 6 in the code chosen from IEEE 802.22 standard
Length of girth HCN impacted
Cycle 4 32 64
Cycle 6 352 128
0 0.5 1
10−4
10−3
10−2
10−1
100
α
FER
α
1
α
2
0 0.5 1
10−4
10−3
10−2
10−1
100
α
FER
α
α=0.8
α
1=0.8 α
2=0.9
Figure 4. Determination of a normalization factor αfor NMS, and α1, α2parameters for GA-NMS at
non-noisy region SN R = 3dB and a maximum number of iterations Imax = 50 for WRAN code
5. SIMULATION AND RESULTS
5.1. BER and FER performances
The BER and FER performance of the algorithm GA-NMS are evaluated in comparison with NMS
and standard MS algorithms using WRAN code. The result shows that the GA-NMS has almost similar perfor-
mance as NMS algorithm in the noisy region. But we can see a small difference between GA-NMS and both
algorithms (MS and NMS) particularly at error floor region at SNR=3dB as shown in the Figure 5.
2 2.5 3 3.5 4
10−8
10−7
10−6
10−5
10−4
10−3
10−2
10−1
100
SNR[dB]
BER & FER
MS
NMS
GA−NMS
FER
BER
Figure 5. Performance evaluation of the decoding algorithms (GA-NMS, NMS and MS) in terms of (BER,
FER)/SNR using a short block code chosen from IEEE 802.22 standard when the maximum number of
iterations is 50
Girth aware normalized min sum decoding algorithm for shorter length low density parity ... (Abdelilah Kadi)
1698 rISSN: 2502-4752
5.2. Convergence behaviors
In Figure 6, the decoding algorithms of LDPC codes GA-NMS, NMS, and the standard MS are
studied and evaluated in terms of convergence behaviors throughout the iterations when decoding messages
coded by WRAN code at non-noisy region SNR=[3, 4, 5, 6] dB. The GA-NMS converges faster than the NMS
at higher SNR values SNR=[4, 5, 6] dB, by comparing the efficiency of the GA-NMS algorithm for the both
WRAN and WIMAX codes already evaluated in [20]. It is seen that the results obtained by WIMAX code are
better than those obtained by WRAN code, resulting from the difference of size a difference of cyclic structure
for both codes and others parameters. However, generally the simulation results showed that GA-NMS is better
than NMS and standard MS.
0 5 10 15 20
10−6
10−5
10−4
10−3
10−2
10−1
100
Iterations
FER
MS
NMS
GA−NMS
SNR=3dB
SNR=4dB
SNR=5dBSNR=6dB
Figure 6. Convergence behaviors of the (GA-NMS, NMS and MS) decoding algorithms at non-noisy region
SNR equal to 3 dB, 4 dB, 5 dB and 6 dB when decoding WRAN code with length (384, 192)
6. CONCLUSION
In this paper, an analysis of the behavior of the outgoing messages when decoding using normalized
MS is presented, this analysis shows the destructive effect of short cycles and proves that we can classify
the nodes according to the length of the short cycle connected to it and that each class of nodes needs to be
multiplied by a factor different to the others classes, which explain the effectiveness of the GA-NMS when
already tested on WIMAX code. On the other hand, in this paper, the GA-NMS decoding algorithm is tested
on WRAN code with the length (384, 192) which is considered among the short LDPC codes, the result shows
that the GA-NMS algorithm is better than NMS and MS algorithms in performances and can be efficient for
short block LDPC codes. Summarizing this, the GA-NMS algorithm can be considered as a solution to the
short block codes, which have the problem of short cycles of sizes 4 and 6.
REFERENCES
[1] M. Almahamdy and N. Al-Falahy, “Combining serial and parallel decoding for turbo codes,” Indonesian Journal of Electrical
Engineering and Computer Science (IJEECS), vol. 24, no. 2, pp. 896-903, 2021, doi: 10.11591/ijeecs.v24.i2.pp896-903.
[2] K. Zhu and Z. Wu, “Comprehensive study on cc-ldpc, bc-ldpc and polar code,” in 2020 IEEE Wireless Communications and
Networking Conference Workshops (WCNCW), 2020, pp. 1-6, doi: 10.1109/WCNCW48565.2020.9124897.
[3] A. Larbi, A. Bassou, and M. Lahcene, “Higher performance and lower complexity turbo decoding scheme for 4G-LTE using un-
punctured turbo trellis-coded modulation,” Indonesian Journal of Electrical Engineering and Computer Science (IJEECS), vol. 18,
no. 1, pp. 351–360, 2020, doi: 10.11591/ijeecs.v18.i1.pp351-360.
[4] I. Maaz and S. Alabed, “Efficient time reversal strategy for MISO-OFDM systems,” Indonesian Journal of Electrical Engineering
and Computer Science (IJEECS), vol. 20, no. 1, pp. 239-247, 2020, doi: 10.11591/ijeecs.v20.i1.pp239-247.
[5] R. Gallager, “Low-density parity-check codes,” IRE Transactions on Information Theory, vol. 8, no. 1, 1962, doi:
10.1109/TIT.1962.1057683.
Indonesian J Elec Eng & Comp Sci, Vol. 26, No. 3, June 2022: 1692–1700
Indonesian J Elec Eng & Comp Sci ISSN: 2502-4752 r1699
[6] R. M. Tanner, “A recursive approach to low complexity codes,” IEEE Transactions Information Theory, vol. 27, no. 5, pp. 533–547,
Sep. 1981, doi: 10.1109/TIT.1981.1056404.
[7] A. Al-Askery and A. Hammadi, “On the performance of coded copper wire systems for G-fast communications,” In-
donesian Journal of Electrical Engineering and Computer Science (IJEECS), vol. 14, no. 3, pp. 1272–1280, 2019, doi:
10.11591/ijeecs.v14.i3.pp1272-1280.
[8] Z. Majeed, A. Jaffaar, and S. Hadi, “PAPR reduction in OFDM system for DVB-S2,” Indonesian Journal of Electrical Engineering
and Computer Science (IJEECS), vol. 17, no. 1, pp. 317-323, 2020, doi: 10.11591/ijeecs.v17.i1.pp317-323.
[9] B. Salima, A. Lakhdar, and B. Ridha Ilyas, “Performance comparison of channel coding schemes for 5G massive machine type
communications,” Indonesian Journal of Electrical Engineering and Computer Science (IJEECS), vol. 22, no. 2, pp. 294–300,
2021, doi: 10.11591/ijeecs.v22.i2.pp902-908.
[10] M. Shirvanimoghaddam et al., “Short block-length codes for ultra-reliable low latency communications,” IEEE Communications
Magazine, vol. 57, no. 2, pp. 130–137, Feb. 2019, doi: 10.1109/MCOM.2018.1800181.
[11] “R1-1804849 Remaining Issues on URLLC Data Channel Coding,” 3rd Generation Partnership Project, 3GPP TSG RAN WG1
Meeting Discussion and Decision Std., Apr. 2018. [Online] Available: https://www.3gpp.org/DynaReport/TDocExMtg–R1-92b–
18780.html.
[12] I. Li, T. Li, J. Ren, and H. Chao, “Enjoy the benefit of network coding: Combat pollution attacks in 5G multihop networks,” Wireless
Communications and Mobile Computing, vol. 2018, pp. 1–13, Sep. 2018, doi: 10.1155/2018/3473910.
[13] N. el Maammar, S. Bri, and F. Jaouad, “A comparative simulation study of different decoding schemes in LDPC coded OFDM
systems for NB-PLC channel,” Indonesian Journal of Electrical Engineering and Computer Science (IJEECS), vol. 15, no. 1, pp.
306-313, 2019, doi: 10.11591/ijeecs.v15.i1.pp306-313.
[14] M. Asif, W. Zhou, Q. Yu, X. Li, and N. A. Khan, “A deterministic construction for jointly designed quasicyclic LDPC coded-relay
cooperation,” Wireless Communications and Mobile Computing, vol. 2019, pp. 1–12, Sep. 2019, doi: 10.1155/2019/5249373.
[15] H. Zhu, L. Pu, H.Xu, and B.Zhang, “Construction of quasi-cyclic LDPC codes based on fundamental theorem of arithmetic,”
Wireless Communications and Mobile Computing, vol. 2018, pp. 1–9, Apr. 2018, doi: 10.1155/2018/5264724.
[16] J. Fan, Y. Xiao, and K. Kim, “Design LDPC codes without cycles of length 4 and 6,” Research Letters in Communications, vol.
2008, no. 5, Feb. 2008, doi: 10.1155/2008/354137.
[17] C. Gao, S. Liu, D. Jiang, and L. Chen, “Constructing LDPC codes with any desired girth,” Sensors, vol. 21, no. 6, 2021, doi:
10.3390/s21062012.
[18] A. Kadi, S. Najah, and M. Mrabti, “An exponential factor appearance probability belief propagation algorithm for regular and
irregular LDPC codes,” AEUE International Journal of Electronics and Communications Elsevier, vol. 69, no. 6, pp. 933–936,
2015, doi: 10.1016/j.aeue.2015.02.009.
[19] J. Liu and R. C. de Lamare, “Low-latency reweighted belief propagation decoding for LDPC codes,” IEEE Communications Letters,
vol. 16, no. 10, pp. 1660–1663, Oct. 2012, doi: 10.1109/LCOMM.2012.080312.121307.
[20] A. Kadi, M. Mrabti, S. Najah, and E. Boutillon, “Novel method for improving performances of normalized MS decoder using
WIMAX code,” in 2016 International Conference on Advanced Communication Systems and Information Security (ACOSIS), Oct.
2016, pp. 1–5, doi: 10.1109/ACOSIS.2016.7843926.
[21] J. Chen and M. P. Fossorier, “Near optimum universal belief propagation based decoding of low-density parity check codes,” IEEE
Transaction Communications, vol. 50, no. 3, pp. 406–414, 2002, doi: 10.1109/26.990903.
[22] A. Agrawal, “Air interface for fixed and mobile broadband wireless access systems,” IEEE802, Oct. 2005.
[23] M. Helmling and S. Scholl. “Database of channel codes and ML simulation results.” www.uni-kl.de. www.uni-kl.de/channel-codes
(accessed Mar. 13, 2022).
[24] I. Yun, H. Lee, and J. Kim, “An alternative approach obtaining a normalization factor in normalized min-sum algorithm
for low-density parity-check code,” Wireless Communications and Mobile Computing, vol. 2018, pp. 1–7, Oct. 2018, doi:
10.1155/2018/1398191.
[25] T. R. Halford and K. M. Chugg, “An algorithm for counting short cycles in bipartite graph,” IEEE Transaction on Information
Theory, vol. 51, no. 1, pp. 287–292, Jan. 2006, doi: 10.1109/TIT.2005.860472.
[26] M. Karimi and A. H. Banihashemi, “A message-passing algorithm for counting short cycles in a graph,” in 2010 IEEE Information
Theory Workshop on Information Theory (ITW 2010, Cairo), Jan. 2010, pp. 1–5, doi: 10.1109/ITWKSPS.2010.5503171.
[27] N. A. F. Neto, J. R. S. de Oliveira, W. L. A. de Oliveira, and J. C. N. Bittencourt, “VLSI architecture design and implementation
of a LDPC encoder for the IEEE 802.22 wran standard,” in 2015 25th International Workshop on Power and Timing Modeling,
Optimization and Simulation (PATMOS), 2015, pp. 71–76, doi: 10.1109/PATMOS.2015.7347589.
[28] V. Savin, “Chapter 4 - LPDC decoders,” Academic Press Library in Mobile and Wireless Communications, pp. 211–259, 2014, doi:
10.1016/B978-0-12-396499-1.00004-2.
BIOGRAPHIES OF AUTHORS
Abdelilah Kadi received a Ph.D. degree in Engineer sciences, Physics, Mathematics
and Computer Sciences from the Faculty of Science and Technology, Sidi Mohamed Ben Abdellah
University, Fez, Morocco in 2017. He is currently an Embedded Software Architect in the ALTEN
company. He is a member of the Laboratory of Intelligent Systems and Application (LSIA Labora-
tory). His current research interests include channel coding/decoding (LDPC codes), Model Based
Design development approach. He can be contacted at email: abdelilah.kadi@usmba.ac.ma.
Girth aware normalized min sum decoding algorithm for shorter length low density parity ... (Abdelilah Kadi)
1700 rISSN: 2502-4752
Hajar El Ouakili received Master degree in Micro-Electronics from the Faculty of Sci-
ences, Sidi Mohammed Ben Abdellah University (USMBA), Fez, Morocco in 2018. She is currently
pursuing her Ph.D. degree in computer science with the Laboratory of Computer Science, Signals,
Automation and Cognitivism (LISAC), FSDM, USMBA, Fez, Morocco. Her research interests in-
clude the channel coding/decoding, LDPC codes, code theory and FPGA implementation. She can
be contacted at email: hajar.elouakili@usmba.ac.ma.
Rachid El Alami is a Professor in Department of Physics, FSDM, USMBA, Fez, Mo-
rocco. He received his BS. degree in Electronics from Polydisciplinary Faculty of Taza, the MS and
PhD degrees in Signals, Systems and Informatics in FSDM, USMBA, Fez, Morocco, in 2008 and
2013 respectively. His research interests include the channel coding/decoding (LDPC codes), FPGA
implementation and image processing. He can be contacted at email: rachid.elalami@usmba.ac.ma.
Said Najah received a Ph.D. degree in Computer Science from the Faculty of Science,
University Sidi Mohamed Ben Abdellah, Fez, Morocco in 2006. He is currently a professor of the
Department of Computer Science, Faculty of Science and Technology Fez Morocco. He is a member
in the Laboratory of Intelligent Systems and Application (LSIA Laboratory). His current research
interests include parallel computing, code theory, signal processing and artificial intelligence. He can
be contacted at email: said.najah@usmba.ac.ma.
Indonesian J Elec Eng & Comp Sci, Vol. 26, No. 3, June 2022: 1692–1700
