GF(q) LDPC encoder and decoder FPGA implementation using group shuffled belief propagation algorithm

International Journal of Electrical and Computer Engineering (IJECE)
Vol. 12, No. 3, June 2022, pp. 2184~2193
ISSN: 2088-8708, DOI: 10.11591/ijece.v12i3.pp2184-2193  2184
Journal homepage: http://ijece.iaescore.com
GF(q) LDPC encoder and decoder FPGA implementation using
group shuffled belief propagation algorithm
Fatima Zahrae Zenkouar1
, Mustapha El Alaou2
, Said Najah1
1
SIA Laboratory, Faculty of Sciences and Technologies, Sidi Mohammed Ben Abdellah University, Fez, Morocco
2
Laboratory of Computer Science, Signals, Automation and Cognitivism, Department of Physics, Faculty of Sciences Dhar El Mahraz,
Sidi Mohamed Ben Abdellah University, Fez, Morocco
Article Info ABSTRACT
Article history:
Received Mar 23, 2021
Revised Nov 6, 2021
Accepted Dec 4, 2021
This paper presents field programmable gate array (FPGA) exercises of the
GF(q) low-density parity-check (LDPC) encoder and interpreter utilizing the
group shuffled belief propagation (GSBP) algorithm are presented in this
study. For small blocks, non-dual LDPC codes have been shown to have a
greater error correction rate than dual codes. The reduction behavior of
non-binary LDPC codes over GF (16) (also known as GF(q)-LDPC codes)
over the additive white Gaussian noise (AWGN) channel has been
demonstrated to be close to the Shannon limit and employs a short block
length (N=600 bits). At the same time, it also provides a non-binary LDPC
(NB-LDPC) code set program. Furthermore, the simplified bubble check
treasure event count is implemented through the use of first in first out
(FIFO), which is based on an elegant design. The structure of the interpreter
and the creation of the residential area he built were planned in very high
speed integrated circuit (VHSIC) hardware description language (VHDL)
and simulated in MODELSIM 6.5. The combined output of the Cyclone II
FPGA is combined with the simulation output.
Keywords:
AWGN channel
FPGA
GSBP algorithm
NB LDPC code
This is an open access article under the CC BY-SA license.
Corresponding Author:
Fatima Zahrae Zenkouar
SIA Laboratory, Faculty of Sciences and Technologies, Sidi Mohammed Ben Abdellah University
B.P. 2202-Route Imouzzer, Fez, Morocco
Email: fatimazahrae.zenkouar@usmba.ac.ma
1. INTRODUCTION
The power of low-density parity-check (LDPC) codes based on the finite high-order field GF(q) has
long been recognized. For short and medium codeword lengths, these codes increase binary LDPC
performance. Non-binary LDPC (NB-LDPC) codes have been demonstrated to outperform turbo
convolutional codes (TCC) and binary LDPC codes, retaining the advantages of steep drop zone and low
error of short codewords (typical TCC) (typical binary LDPC) [1]–[3]. This gain, however, comes at the
expense of greater decoding difficulty. Indeed, as q rises, the complexity of the decoder rises, limiting design
options and encouraging the search for simpler decoding algorithms.
In recent years, several efforts have been made to reducing the convolution of NB-LDPC decoders,
and divers associated architecture algorithms have been proposed. [1], [4]–[6] have proposed an LDPC code
decoding algorithm with reduced complexity. This algorithm is known as the group shuffled belief
propagation (GSBP) extended minimum sum algorithm, and it is based on the minimum sum (MS)
algorithm's generalization. To decrease the computational complexity of updating the control node, the
approach involves using a restricted number of nm-reliabilities in the message at the control node's input
[7]–[9].

Int J Elec & Comp Eng ISSN: 2088-8708 
GF(q) LDPC encoder and decoder FPGA implementation using … (Fatima Zahrae Zenkouar)
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A new GSBP decoder implementation has been suggested. This technique is unique in that it solves
the memory problem of non-binary LDPC decoders while drastically decreasing the complexity per iteration.
The new GSBP decoder's major feature is that it extends the truncation concept of vector messages to control
and data node inputs. To decrease the impact of messages on code speed, the authors effectively shortened
messages from 𝑞 to 𝑛𝑚. They also have a good offset adjustment to make up for the performance loss.The
GSBP decoder's complexity is now theoretically dominated by 𝑂 (𝑛𝑚. 𝑙𝑜𝑔 𝑛𝑚), with 𝑛𝑚 << 𝑞, which is a
significant decrease in complexity over all previous techniques [10]–[15].
Our research is based on the GSBP algorithm [10], [16]–[20] This decreases the number of GF
elements that must be processed in each decoding phase from 𝑞 to 𝑛𝑚, nm and 𝑙𝑡; 𝑞, while providing
excellent functional performance. We convert the GSBP algorithm into a low latency, prefetching elementary
NC enquiry control number (ECN) that relaxes redundancy control at low error rates while sacrificing only a
tiny amount of functional performance. A new method is presented to bring variable node (VN) latency
closer to that of check node (CN), in fact this design is based on the significant reduction of combinatorial
optimization search and counting time. To achieve the highest possible pipeline efficiency, we suggest a
conflict-free memory to handle the data dependencies caused by unstructured codes. A full (2, 4) regular,
(960, 80) GF (6) LDPC decoder is prototyped on a Cyclone IV EP CE115F29C8 field programmable gate
array (FPGA) embedded on the Altera DE2115 board. The decoder achieves good error correction
performance.
We presented this article at the following section 2 presents the symbol model, LDPC codes over
GF(q). Section 3 presents the implementation LDPC: design architecture of GSBP. Section 4 presents the
FPGA results and prototype, and we conclude in section 5.
2. SYMBOL MODEL, LDPC CODES OVER GF(q)
Linear block codes, often known as LDPC codes, are a kind of linear block coding. Non-binary
LDPC codes over 𝐺𝐹(𝑞) are considered binary LDPC codes over 𝐺𝐹(𝑞) 𝑖𝑓 𝑞 = 2 (2). A vector space
projected on 𝐺𝐹(𝑞) is used to define the elements in 𝐺𝐹(𝑞). Choose 𝑞 as:
𝑞 = 2 ͫ (1)
The code is given and its value r is supplied as fallows using the ultra-sparse parity check matrix H, where 𝑚
is a positive integer and 𝑚 > 1.
𝑅 = (𝑁 − 𝑀) / 𝑁 (2)
𝑀 = 𝑁 − 𝐾, where N denotes codeword length and K denotes message length. A column weight of at least
two and a row weight that is as uniform as feasible are used to construct the sparse parity check matrix H of
size (M × N). This building method ensures:
 Every column has a certain number 𝛾 of items
 Every line has a number of elements ρ
 Non-zero elements occur in either row or column at more than one position in any two rows or columns.
According to the first two, H has a constant row and column weight and forms typical LDPC code.
The third asserts that the entire graph of code is devoid of a four-cycle cycle. First permutation matrices are
produced utilizing non binary components in 𝐺𝐹(𝑞) and dispersed in the base matrix to build parity check
matrix H in the creation of LDPC codes. In the sparse parity check matrix H, an LDPC is a linear block code
with a low density of none zero entries. Tanner graphs, also known as bipartite graphs, are used to depict
these codes, as shown in Figure 1.
2.1. System model
Figure 2 shows an NB-LDPC coded modulation system. The LDPC encoder is used to encode the k
information bits in the input message vector 𝑢 𝐺𝐹(𝑞) into a codeword, resulting in an encoded message
vector 𝑣 of length N coded bits. The equation gives the rate of the LDPC encoder (2). These bits are
modulated into QPSK symbols (represented by the letter X) and then delivered across the additive white
Gaussian noise (AWGN) channel. The received signal r is written as:
𝑟 = 𝑋 + 𝑛 (3)
where 𝑛 denotes AWGN noise and is modulated by a zero mean Gaussian. The following is a random
sequence with variance:

 ISSN: 2088-8708
Int J Elec & Comp Eng, Vol. 12, No. 3, June 2022: 2184-2193
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𝜎² = (2𝑅 𝐸ь/𝑁0) ˉ¹ (4)
where Eь/N0 is SNR.
Figure 1. The tanner graph over GF and the parity check matrix H (8)
Figure 2. Encoder global block
3. IMPLEMENTATION LDPC: DESIGN ARCHITECTURE OF GSBP
3.1. Encoding
An M × N parity check matrix H defines non-binary LDPC codes, components that are defined over
a finite field GF(q). The parity check matrix can take on q − 1 values for each non-zero member, resulting in
a parity check matrix. Because the H is not in a logical order at first, we write it as:
𝐻 = [𝑃|𝐼𝑚] (5)
where Im denotes the M×M identity matrix and P denotes the M×K dimension matrix, with 𝐾 = 𝑁 − 𝑀.
The GF is used to do all arithmetic operations (q). With dimensions K x N, a generator matrix can be created:
𝐺 = [𝐼𝑘|𝑃’] (6)
The encoder turns a message frame U from GF(q) containing K information bits into a codeword V of length
N (N symbols).

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𝑉 = 𝐺. 𝑈 (7)
The matrix multiplication is done over the finite field GF in this case (q). Finally, the encoder block sends us
the codeword V, which has a length of 𝑁 = 𝑛𝑃 𝑏𝑖𝑡𝑠. For the multiplication we use the efficient digit serial
Karatsuba multiplication method and it uses (3dm/2) AND gate,6 m+n+ (3dm/2)+m2 +d-7 XORs and 3 m-3
registers as illustrated in Figure 3.
Figure 3. Efficient digit-serial Karatsuba multiplication
3.2. Top level architecture of decoder
When it comes to decoding non-binary codes, there are two issues to consider: The first issue is the
iterative processing of control and variable nodes, and the second issue is identifying the most likely
codeword 𝑣 that meets the criteria 𝑣 𝐻 = 0, with a probability of v determined using the channel model. The
Figure 4 shows the top-level architecture design.
The GSBP algorithm is an extension of the MinSum algorithm from binary codes to NBLDPC
codes. Vectors of likelihood ratio values are transferred between the VN and CN processors in the messages
log-likelihood ratios (LLRs). The extended min sum GSBP algorithm has recently been proposed for non-
binary LDPC decoding. This novel technique can reduce the number of comparison operations by a factor of
3, resulting in a lower hardware complexity, without introducing any significant performance degradation. A
message in the GSBP algorithm is a vector of 𝑞 sub-messages. Let 𝑥𝑗 be the code symbol for the code word's
j-th character.
Let 𝜆𝑗 = [𝜆𝑗(0), 𝜆𝑗(1), . . . , 𝜆𝑗 (𝑞 − 1)] be the a priori channel information for xj. The
sub-message λj is a log-likelihood ratio (LLR) defined as 𝜆𝑗 (𝑑) = 𝑙𝑜𝑔 (𝑃𝑟𝑜𝑏 (𝑥𝑗 = 𝑧𝑗)/𝑃𝑟𝑜𝑏 (𝑥𝑗 = 𝑑)),
where zj is the most likely (ML) symbol for xj. We denote αi,j and βi,j as the V2C and C2V soft messages
passed between the i-th CN and j-th VN respectively.
Let 𝑥𝑖, 𝑗 = ℎ𝑖, 𝑗 ⊗ 𝑥𝑖.
For the i-th CN, let the configuration Li (𝑥𝑖, 𝑗 = 𝑑) be the sequence such that xi, j=d and the i-th
check-sum is satisfied. Define an s-truncated configuration such for each 𝑗 ∈ 𝑁𝑖𝑗, 𝛼𝑖, 𝑗 (𝑥𝑖, 𝑗) is of the s
smallest sub-messages of 𝛼𝑖, 𝑗(𝑑) over all ∈ 𝐺𝐹(𝑞). Let 𝐿𝑖(𝑥𝑖, 𝑗 = 𝑑|𝑠) be the set of the s-truncated
configurations. Taking 𝑠 < 𝑞 necessitates extra procedures known as message truncation, which involves
sorting the sub-messages and ignoring the 𝑞 − 𝑠 biggest ones. Let κ and κmax denote the iteration counter
and the maximum number of iterations respectively.

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Figure 4. Top-level architecture design
3.3. Definition of NB LLR values
The first step in the Min-Sum technique is to calculate the LLR value for each symbol in the
codeword. With the premise that the GF(q) symbols are equiprobable [21] yields the LLR value Lk (x) of the
𝑘-th symbol:
𝐿𝑘(𝑥) = 𝑙𝑛 [𝑃 (𝑦𝑘|˜𝑥𝑘)/ 𝑃 (𝑦𝑘|𝑥)] (8)
where ˜𝑥𝑘 is the symbol of GF(q) that maximizes 𝑃 (𝑦𝑘 |𝑥), 𝑖. 𝑒. ˜𝑥𝑘 = 𝑎𝑟𝑔 𝑚𝑎𝑥𝑥 ∈ 𝐺𝐹(𝑞) , {𝑃 (𝑦𝑘 |𝑥)} and
𝑦𝑘 is the received symbol. Note that 𝐿𝑘 (˜𝑥𝑘) = 0 and, for all x ∈ 𝐺𝐹 (𝑞), 𝐿𝑘 (𝑥) ≥ 0. When a result, as a
symbol's LLR grows, its dependability diminishes. When addressing the finite precision representation of the
LLR values, this LLR formulation eliminates the requirement to re-normalize the messages after each node
update calculation and reduces the effect of quantization. The Figure 5 shows a block diagram of the LLR
computation and the Figure 6 shows a timing diagram of the LLR computation over 𝐺𝐹 (16). 𝑁𝑚 = 10.
Figure 5. Block diagram of the LLR computation

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Figure 6. Timing diagram of the LLR computation over 𝐺𝐹(16) 𝑁𝑚 = 10
3.4. Check node architecture
The check node processor (CNP) may be constructed using either the FB architecture or a tree-based
structure [22]. The tree structure has the advantage of reducing the number of ECN in the critical route to a
bare minimum and ensuring consistency across all outputs. We considered the Tree structure in our study for
these reasons.
The symbols of the messages entering the CNP must be multiplied by the non-zero members of the
parity check matrix as illustrated in Figure 7. In addition to the CNP's output messages that are split by these
non-zero elements (the row corresponding to the CNP in the Tanner graph). As a result, the implemented
CNP architecture performs multiplications on GF(q) using the hardwired multipliers described in [23]–[25].
Figure 7. Design of the CN block
3.5. Variable node architecture
We start the VN operations immediately after the CN operation, a transfer of messages from C to V
in the memory. The message C to V is computed from the messages C to V and the previous message V to C
taking into account the GF indices that must match. To reduce latency, we allocate only 𝐿(𝑠𝑣𝑛), the length of
the sorter used in VN, to scan the vector L. Due to a lack of space, we just name the sorter in the memory.
Due to space constraints, we will only provide the algorithm and leave the rest of the discussion for a

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subsequent publication. The Figure 8 shows architecture of the VN block and the Figure 9 shows architecture
of the sorter block in VN.
Figure 8. Architecture of the VN block
Figure 9. Architecture of the sorter block in VN
4. FPGA RESULTS AND PROTOTYPE
On a Cyclone IV FPGA, the suggested decoder architecture was prototyped for a (2, 4)-regular (960,
480) NB-LDPC code over GF (64). The FPGA decoder has 10 decoding cycles and runs at 100 MHz with a
code rate of 2.44 Mbps. Based on the suggested design of this FPGA device, we were able to map a semi
complete allied decoder. This result is a substantial improvement over the current GSBP decoder
implementation. The layer decoding improves convergence and replicate show that the average number of
iterations for FER=105 decreases from 2.39 to 1.77. The Table 1 gives an overview of how they look time
required for input and output. The Figure 10 illustrate the decoding output and the Figure 11 illustrate the
performances of NB-LDPC over GF (64) using the GSBP algorithm.
Table 1. Summary of the timing
Delay 8.487 ns
Maximum frequency 117.830 MHz
Minimum input arrival time before clock 5.093 ns
After the clock, the maximum output necessary 12.119ns

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Figure 10. Decoding output
Figure 11. Performances of NB-LDPC over GF (64) using the GSBP algorithm
5. CONCLUSION
A hardware simplified decoding algorithm using the simplified extended min sum algorithm was
favorably presented. The concept was centered on considerably decreasing the combinatorial optimization
search space as well as the computing time. To minimize latency and enable effective pipeline scheduling,
VN and CN designs based on skimming, prefetching, and easing redundancy control are proposed. To
minimize pipeline delays, a conflict-free memory was utilized to handle data risks. The results suggest that
the decoding is working well. Compared to the GSBP method for NB-LDPC codes, the design has
considerably reduced computational complexity and memory use, according to our research.

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REFERENCES
[1] R. G. Gallager, Low-density parity-check codes. The MIT Press, 1963.
[2] W. Sulek, M. Kucharczyk, and G. Dziwoki, “GF(q) LDPC decoder design for FPGA implementation,” in 2013 IEEE 10th
Consumer Communications and Networking Conference, CCNC 2013, Jan. 2013, pp. 460–465, doi:
10.1109/CCNC.2013.6488484.
[3] C. Spagnol, E. M. Popovici, and W. P. Marnane, “Hardware implementation of GF(2m) LDPC decoders,” IEEE Transactions on
Circuits and Systems I: Regular Papers, vol. 56, no. 12, pp. 2609–2620, Dec. 2009, doi: 10.1109/TCSI.2009.2016621.
[4] M. M. Mansour and N. R. Shanbhag, “Memory-efficient turbo decoder architectures for LDPC codes,” in IEEE Workshop on
Signal Processing Systems, SiPS: Design and Implementation, 2002, pp. 159–164, doi: 10.1109/SIPS.2002.1049702.
[5] M. M. Mansour and N. R. Shanbhag, “Low-power VLSI decoder architectures for LDPC codes,” in Proceedings of the
International Symposium on Low Power Electronics and Design, 2002, pp. 284–289, doi: 10.1109/LPE.2002.146756.
[6] T. Zhang and K. K. Parhi, “A 54 Mbps (3,6)-regular FPGA LDPC decoder,” in IEEE Workshop on Signal Processing Systems,
2002, pp. 127–132, doi: 10.1109/SIPS.2002.1049697.
[7] E. Yeo, P. Pakzad, B. Nikolic, and V. Anantharam, “VLSI architectures for iterative decoders in magnetic recording channels,”
IEEE Transactions on Magnetics, vol. 37, no. 2, pp. 748–755, Mar. 2001, doi: 10.1109/20.917611.
[8] Y. Kou, S. Lin, and M. P. C. Fossorier, “Low-density parity-check codes based on finite geometries: a rediscovery and new
results,” IEEE Transactions on Information Theory, vol. 47, no. 7, pp. 2711–2736, 2001, doi: 10.1109/18.959255.
[9] S. H. Kang and I. C. Park, “Loosely coupled memory-based edcoding architecture for low density parity check codes,” IEEE
Transactions on Circuits and Systems I: Regular Papers, vol. 53, no. 5, pp. 1045–1056, May 2006, doi:
10.1109/TCSI.2005.862181.
[10] M. M. Mansour and N. R. Shanbhag, “On the architecture aware structure of LDPC codes from generalized Ramanujan graphs
and their decoder architecture,” in Proc. 37th Annu. Conf. Inf. Sci. Syst., 2003, pp. 215–220.
[11] D. E. Hocevar, “LDPC code construction with flexible hardware implementation,” in IEEE International Conference on
Communications, 2003, vol. 4, pp. 2708–2712, doi: 10.1109/icc.2003.1204466.
[12] L. R. Bahl, J. Cocke, F. Jelinek, and J. Raviv, “Optimal decoding of linear codes for minimizing symbol error rate,” IEEE
Transactions on Information Theory, vol. 20, no. 2, pp. 284–287, 1974, doi: 10.1109/TIT.1974.1055186.
[13] Y. Kou, S. Lin, and M. P. C. Fossorier, “Low density parity check codes based on finite geometries: a rediscovery,” in 2000 IEEE
International Symposium on Information Theory (Cat. No.00CH37060), p. 200, doi: 10.1109/ISIT.2000.866498.
[14] E. Yeo, P. Pakzad, B. Nikolić, and V. Anantharam, “High throughput low-density parity-check decoder architectures,” in
Conference Record/IEEE Global Telecommunications Conference, 2001, vol. 5, pp. 3019–3024, doi:
10.1109/glocom.2001.965981.
[15] S. T. Brink, G. Kramer, and A. Ashikhmin, “Design of low-density parity-check codes for modulation and detection,” IEEE
Transactions on Communications, vol. 52, no. 4, pp. 670–678, Apr. 2004, doi: 10.1109/TCOMM.2004.826370.
[16] S. Y. Chung, T. J. Richardson, and R. L. Urbanke, “Analysis of sum-product decoding of low-density parity-check codes using a
Gaussian approximation,” IEEE Transactions on Information Theory, vol. 47, no. 2, pp. 657–670, 2001, doi: 10.1109/18.910580.
[17] T. J. Richardson and R. L. Urbanke, “The capacity of low-density parity-check codes under message-passing decoding,” IEEE
Transactions on Information Theory, vol. 47, no. 2, pp. 599–618, 2001, doi: 10.1109/18.910577.
[18] M. M. Mansour and N. R. Shanbhag, “Turbo decoder architectures for low-density parity-check codes,” in Global
Telecommunications Conference, 2002, vol. 2, pp. 1383–1388, doi: 10.1109/GLOCOM.2002.1188425.
[19] E. Boutillon, L. Conde-Canencia, and A. Al Ghouwayel, “Design of a GF(64)-LDPC decoder based on the EMS algorithm,”
IEEE Transactions on Circuits and Systems I: Regular Papers, vol. 60, no. 10, pp. 2644–2656, Oct. 2013, doi:
10.1109/TCSI.2013.2279186.
[20] M. C. Davey and D. MacKay, “Low-density parity check codes over GF(q),” IEEE Communications Letters, vol. 2, no. 6,
pp. 165–167, Jun. 1998, doi: 10.1109/4234.681360.
[21] D. Sridhara, R. M. Tanner, and T. E. Fuja, “Low density parity check codes from permutation matrices,” in The 35th Annual
Conference on Information Sciences and Systems (CISS), 2001.
[22] M. G. Luby, M. Amin Shokrolloahi, M. Mizenmacher, and D. A. Spielman, “Improved low-density parity-check codes using
irregular graphs and belief propagation,” 1998, doi: 10.1109/ISIT.1998.708706.
[23] A. Bennatan and D. Burshtein, “Design and analysis of nonbinary LDPC codes for arbitrary discrete-memoryless channels,” IEEE
Transactions on Information Theory, vol. 52, no. 2, pp. 549–583, Feb. 2006, doi: 10.1109/TIT.2005.862080.
[24] H. Wymeersch, H. Steendam, and M. Moeneclaey, “Log-domain decoding of LDPC codes over GF(q),” in IEEE International
Conference on Communications, 2004, vol. 2, pp. 772–776, doi: 10.1109/icc.2004.1312606.
[25] C. Poulliat, M. Fossorier, and D. Declercq, “Design of regular (2, dc)-LDPC codes over GF(q) using their binary images,” IEEE
Transactions on Communications, vol. 56, no. 10, pp. 1626–1635, Oct. 2008, doi: 10.1109/TCOMM.2008.060527.
BIOGRAPHIES OF AUTHORS
Fatima Zahrae Zenkouar she received a state engineering degree in embedded
systems and industrial data from the National School of Applied Sciences, University of Sidi
Mohammed Ben Abdellah, Fez, Morocco in 2015. He is currently pursuing his Ph.D. degree
in Computer Science with the Laboratory of Intelligent Systems and Application at the
Faculty of Science and Technology of Fez. His research interests include signal/data
processing, code theory, parallel computing, and LDPC algorithms. She can be contacted at
email: fzenkouar@gmail.com.

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Mustapha El Alaoui is born in the Old Medina, Fes, Morocco, 1994. He
received his Master degree since 2017 in Micro-Electronics in Faculty of Sciences Dhar EL
Mahraz (FSDM), Sidi Mohammed Ben Abdellah University (USMBA), Fez, Morocco. He
received a Ph.D degree in Electrical Engineering in 2021 from Laboratory of Computer
Science, Signals, Automation and Cognitivism (LISAC), Department of Physics, FSDM,
USMBA, Fez, Morocco. His research interests include Li-Ion battery charger interface
(BCI) and BMS, RFID passive and active tags, CMOS mixed mode integrated circuit
design, integrated class-D power output stage and renewable energy. He can be contacted at
email: mustapha.elalaoui@usmba.ac.ma.
Said Najah He 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).
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.

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