https://doi.org/10.31449/inf.v47i10.5219                                                                                                 Informatica 47 (2023) 93–102   93 
Development of Dynamic Channel Coding Strategy for Multi-User 
MIMO -NOMA 5G Downlink Communication by Concatenation of 
Coding Method 
 
Pavithra B, Parnasree Chakraborty
*
 
Department of ECE, B.S. Abdur Rahman Crescent Institute of Science and Technology, Chennai-48 
E-mail: pavithrab_ece@crescent.education, prernasree@crescent.education 
*Corresponding author 
 
Keywords: mimo, noma, polar codes, channel coding, 5g, bler 
 
Received: September 22, 2023 
 
The aim of this work is to develop a dynamic coding strategy for a Multi user MIMO NOMA 5G downlink 
communication by means of concatenation of coding methods. The ultimate motive behind 5G technology 
is to deliver data at an ultra-high speed of multi - Gbps rate with extremely low latency, being highly 
reliable, offering huge network capacity, readily available channels and a much stable user experience 
accommodating multiple simultaneous users. This in turn demands a highly flexible and an effective 
channel coding method as it helps out the communication to be almost error free by reducing the bit 
errors of the transmitted data by saving it from the channel noise and the available interference in the 
channel. This paper provides an efficient approach based on the concatenation of Polar codes that is 
suited for a multi user mimo NOMA system that meets the criteria of the 5G standard. To compare the 
performance of mimo NOMA systems with that of concatenated PDCCH (Physical Downlink Control 
CHannel) polar codes 
𝐸 𝑠 𝑁 0
⁄ (Symbol Energy to Noise Ratio) versus BLER (BLock Error Rate) 
simulations have been performed. The results show that the suggested approach performs better in terms 
of Sum Rate Capacity versus SNR in multiuser mimo NOMA system. 
Povzetek: Cilj pristopa je razviti dinamično kodirno strategijo za Multi-user MIMO NOMA 5G, s 
konkatenacijo Polar kod za visoko učinkovitost.
1 Introduction 
The maximum possible rate achievable by a communication 
link at which a reliable transfer of information takes place 
is termed as Channel Capacity. Shannon’s coding theorem 
for a noisy channel is given by, say if C is the Channel 
Capacity. C is the rate at which information could be 
transmitted over a noisy channel such that it is not possible 
to achieve even more with no errors as well. In practice, 
there is a concept called Error correcting codes, that exists 
in any communication link aiding in the successful 
transmission of data at the rate little lesser than the C but 
with preferably at a small BER value. Channel coding 
technique is the methodology of including intentional 
redundancy to the source coded data bits to reduce the error 
rate aiming at a lower BER transmission. The formation of 
the channel codes should be dynamic such that the coding 
method should adopt itself to the dynamic nature of the 
channel to enhance the Forward Error Correction (FEC) 
enabling the reduction in the error rate with better data 
transfer. The dynamic nature of channel could be modeled 
using Gilbert Model based on a Two-State Markov process 
scheme [1].  
 
2   Related works 
The key requirements of a 5G network in short includes 
extremely high rates of data transmissions almost 1000 
times greater than a 4G network, extremely low latency (< 
1ms), a completely efficient spectrum resulting in a high 
spectrum efficiency coefficient and a highly energy 
efficient network almost 100 times better than a 4G network 
to be more precise. Channel polarisation is a method for 
creating code sequences that may operate at the symmetric 
capacity I(W) of any particular discrete memoryless 
channel with binary input (BDMC) W. The speed of 
channel polarisation has a limit stated. As a result, a prior 
constraint on the likelihood of mistake for polar coding is 
enhanced [2, 3]. In 3GPP, the NR, multiplexing and channel 
coding has specified [4]. The primary concepts of the polar 
codes and the decoded algorithms are explained and the 
concatenation of polar codes are simulated in [5]. The 
algorithm includes searching through many potential 
design-SNRs. comparing the effectiveness of various 
building algorithms using several simulations. If the design-
SNR is improved, the authors discover that all polar code  
 
 

94   Informatica 47 (2023) 93–102                                                                                                                                     Pavithra B. et al. 
 
generation methods produce equally excellent polar codes 
in an AWGN channel [6]. The authors provide two 
approximation techniques that "sandwich" a deteriorated 
and an enhanced version of the original bit-channel. Both 
estimates are easily computed and, in reality, prove to be 
very close [7]. The performance of polar codes and 
concatenated codes built on them may be precisely 
predicted using the Gaussian approximation for density 
evolution [8]. As a theoretical framework for investigating 
the rapid creation of polar codes based on a recursive 
structure of universal partial order (UPO) and polarisation 
weight (PW) algorithms, the authors of [9] devised the -
expansion, a number theory concept. In each recursive 
phase, a large number of polynomial equations can be 
constantly solved in order to create the polar codes from 
UPO. Both encoders and decoders must be aware of relative 
reliabilities: in multi-mode systems with numerous code 
lengths and code rates supported, storing relative 
reliabilities can lead to considerable implementation 
complexity. The authors discovered patterns in code 
reliabilities and suggest an approximation computing 
approach for representing the reliabilities of numerous 
codes using a small number of variables and update rules 
[10]. The article introduces a novel SC decoder variant 
known as the SC flip decoder [11]. The authors describe the 
successive-cancellation list decoder for polar codes, which 
is an extension of Arikan's classic successive-cancellation 
decoder. Up to L decoding paths are taken into account 
concurrently at each decoding stage of the proposed list 
decoder [12]. The authors show how to improve the 
efficiency of the full concatenated polar code's belief 
propagation (BP) decoding. The performance of multiple 
polar code architectures is examined in an additive white 
Gaussian noise (AWGN) channel. This research suggests a 
novel form of punctured polar coding. The codes are formed 
by setting constraints on both puncturing patterns and 
frozen sets, so that the decoder knows what the punctured 
bits are worth. They proposed polar codes using a CRC 
adaptable SC (Successive Cancellation)-List decoder. 
Before this adaptive SC-List decoder increases the list size, 
at least one survival path must pass CRC [13, 14, 15, 16]. 
Having said so, the channel coding method used should be 
of extremely efficient resulting in no latency, reduced 
complexity, enabling higher data rates with less or no re-
transmission of data at the cost of less energy consumption 
as well. The channel coding methods namely convolution 
codes or block codes method, turbo codes method, LDPC 
based coding method and polar codes have been evaluated 
by the 3GPP standard and it has been found that polar codes 
have been found capable of meeting up higher rates of data 
and the requirements of satisfying a diverse scenario of 
typical 5GNR (5G New Radio) namely eMBB (enhanced 
Mobile Broadband), mMTC (massive Machine Type 
Communication) and uRLLC (ultra Reliable Low Latency  
 
 
Communication) [17, 18, 19]. Polar codes have been chosen 
up by the 3GPP standard for the control channels of eMBB  
 
 
 
 
 
 
 
 
 
 
 
Figure 1: A polar coder 
as in 5G/NR technology. This polar code technology could 
be further improvised by means of Concatenated coding 
method and by employing a decoding scheme based on 
combined methods as proposed. 
The paper is organized further like the next section 2 briefs 
about proposed model of Polar codes - introduction, need 
for it and construction, followed by section 3 explaining the 
simulation results and discussions followed by section 4 
concluding the work and the paper closes with the valuable 
references made to come up with this work successfully. 
2 Proposed modelling  
Channel codes play a very vital role in information theory, 
wherein Polar codes have started gaining a very great power 
of attraction as it is the only provable channel code that 
achieves the Shannon capacity. It was introduced by Erdal 
Arikan lately in 2009 and belong to the linear block code 
type of error correction codes [1]. A simple polar coder 
block diagram is shown below figure (1). 
A polar code is constructed by recursive process of 
concatenation over a short code typically called a kernel 
code, which actually tries to modify the real channel into 
multiple possible virtual channels. With the increase in the 
recursive additions, the virtual channel either tries to 
polarize or get sparse. In other terms, the channel either 
becomes highly reliable (Good State) or unreliable (Bad 
State) virtually. This reliability factor helps to transfer data 
via the highly reliable channels for that matter making the 
transmission towards error free communication. It has been 
proven by Erdal Arikan in his work that the polar codes help 
achieving a reliable capacity for various channels with a 
Polar 
Encoder 
BPSK Modulator 
Polar 
Decoder 
AWGN Channel 
(𝜎 2
 = 
𝑁 0
2
) 
      a ∈
 {±1}
K
,  
K 
N - 
Bits 
x 
∈ {±1}
N
 
y ∈
 R
N
 
𝑢 ො 

 Development of Dynamic Channel Coding Strategy for Multi-User…                                                  Informatica 47 (2023) 93–102   95 
complexity for a given code length say N is of the order of 
0(N log N). The lesser complexity and the nature of being 
of good spectral efficiency has pushed polar codes into 
limelight in the field of digital communication. Basically 
polar codes were constructed to work with code lengths of 
the order of 2
𝑛 , where n is an integer and it is usually termed 
as the Mother kernel code. The mother code of dimension 
say K is given by (𝑁 𝑚 , 𝐾 𝑚 ) for a given code length of 
𝑁 𝑚 =2
𝑛 . The matrix form of representing Polar codes based 
on the transformation matrix by means of the application of 
the product called Kronecker product onto the kernel is 
given by, 𝜏 𝑁 𝑚 
= 𝜏 2
⊗𝑛 . The kernel matrix is represented as 
𝜏 2
and its value is generally given by, 𝜏 2
 = [
1 0
1 1
]. The 
frozen bit set is given by F ⊆ { 1, . . . , N
m
}, whose 
dimension is said to be 𝑁 𝑚 − 𝐾 𝑚 . The frozen set of bits are 
framed in such a way that it helps in minimizing the 
probability of errors aiding the process of successive 
cancellation method of decoding done at the receiving end 
in general. The frozen bits are usually positioned at the 
given 𝑁 𝑚 − 𝐾 𝑚 bit locations preferably having the possible 
least re-liabilities as computed. The computation of the 
possible reliability associated with the bits is generally done 
by means of methods like variance calculation, mutual 
information, tracking of the mean value, Gaussian 
approximation and by means of analysing the 
Bhattacharyya parameter of the Gaussian L – densities. 
 Encoding is the process of coding the information 
bits with code words. If the information bits are assumed to 
be a  ∈ 𝔽 2
K
m
 say, then the codewords they are encoded into 
is given by x  ∈ 𝔽 2
K
m
. If the encoding process is represented 
as a vector form for the frozen and actual bits, then it takes 
up the form of v  ∈ 𝔽 2
K
m
. To be in detail v has two sub 
vectors namely, 𝑣 𝕀 =   = a and v_F  = 0. The computed 
codeword is given as, x = v. τ
N
m
 . The encoding process 
here is performed in terms of permutation of Bit - reversal 
done over a length say N_m and given as 𝐵 𝑁 𝑀 .𝜏 𝑁 𝑀 . The 
permutation of bit reversal is actually a procedure in which 
at first, indexing is done to the number sequence starting 
from 0 until 𝑁 𝑚 − 1. Then the sequence having indexed is 
reversed in terms of its binary equivalent of each number as 
in the sequence. At times, the Cyclic Redundancy Check 
(CRC) is also added. If the number of channels is assumed 
to be N, the matrix used in generation of polar codes is given 
by 𝑀 𝑁 . The generation of polar codes is given by, 
𝑀 𝑁 = 𝐵 𝑁 𝜏 ⊗𝑛 = 𝑃 𝑁 (𝐼 2
⊗ 𝐵 𝑁 /2
)𝜏 ⊗𝑛                             (1) 
Where, the B represents the bit reversal function, P 
represents the permutation function, ⊗ stands for the 
Kronecker product of the I matrix.  
The encoded bit generation in total is given by, 
𝑔 1
𝑁 = 𝑎 1
𝑁 𝑀 𝑁                                                                             (2) 
Where, the term 𝑎 1
𝑁 is the information bit. 
 The initial conventional method of decoding the polar 
codes was based on the Successive Cancellation (SC) 
method. The method of Successive Cancellation is actually 
a very simple yet an efficient method as well. But probably 
it suffers from decoding errors as well. This was improvised 
by the new method called Successive Cancellation List 
(SCL) method of decoding aiming at the betterment of 
Block errors. The encoder at the transmitter, generates a 
coded data bits from the original information data bits and 
then pass it via the polarized channel distinguishing them 
like active bits through reliable channels and frozen bits 
through noisy channels. At the decoder in the receiving end, 
the frozen bits are actually frozen to fixed values and based 
on the knowledge of the frozen bit value say𝑎 𝐴 𝑐 aand the 
code word vector say  𝑍 1
𝑁 , an estimated value of the 
information is computed to get the value of 𝑎 ො
1
𝑁 along with 
the help of the vector A. The successive cancellation 
method of decoding is made use of to compute the estimated 
value𝑎 ො
1
𝑁 , given by 
𝑎 ො
𝑖 ≜ {
𝑎 𝑖 , 𝑖𝑓 𝑖 ∈ 𝐴 𝑐 𝐷𝑖 (𝑧 1
𝑁 , 𝑎 ො
1
𝑖 −1
), 𝑖𝑓 ∈ 𝐴                                      (3) 
The value of the function D is the decision made over the 
value of the bits to be computed. 
The conditional decision making function of D is given by, 
𝐷𝑖 (𝑧 1
𝑁 , 𝑎 ො
1
𝑖 −1
) = {
0
1
  
𝑖𝑓
𝐶 𝑖 𝑁 (𝑧 1
𝑁 ,𝑎 1
̂
𝑖 −1
| 0)
𝐶 𝑖 𝑁 (𝑧 1
𝑁 ,𝑎 1
̂
𝑖 −1
|1)
𝑒𝑙𝑠𝑒 (4) 
The level of polarization of the virtual channels formed by 
means of Polar encoding is actually denoted by the values 0 
and 1 in the equation above. From the above discussion, it 
would be inferred that the computation of the estimated 
value involves complexity along with inaccuracies as well. 
To out-beat the shortcomings, a new level of approach 
called Belief Propagation mechanism of decoding is 
suggested at the receiving end to decode the polar coded 
information bits aiming at its successive recovery. 
In the Belief Propagation based decoding process, a new 
concept called Factor Graph is introduced. A Factor Graph 
is obtained from the generated Polarization matrix say 𝐺 𝑁 . 
The factor graph takes up the form of n - stages, wherein the 
value of n is given by n = log N and the corresponding 
number of factor graph nodes is given by, (n + 1)N. The 
factor graph is constructed such that each stage of the n-
stages involved is provided with 
𝑁 2
⁄ number of elements 
for processing. Every node present in the corresponding 
stages of the factor graph, helps evaluating two types of 

96   Informatica 47 (2023) 93–102                                                                                                                                     Pavithra B. et al. 
LLRs each. Two LLRs are being evaluated in such a way 
that one LLR is looked up along the flow from left to right 
and the other LLR is looked up in the vice versa direction, 
giving up evaluated message values say 𝑅 𝑖 ,𝑗 (𝑡 )
 and 𝐿 𝑖 ,𝑗 (𝑡 )
 
respectively. If for instance, BPSK modulation is 
considered to map the input bits, x ∈ { 0,1}
N
to   ∈
 {+1, −1}
N
, then the left to right denotation of the evaluated 
message is given by, 
𝑅 1,𝑗 (0)
= {
0, 𝑖𝑓 𝑗 ∈ 𝐴 +∞, 𝑖𝑓 𝑗 ∈ 𝐴 𝑐   
 (5) 
The LLR or the Log Likelihood of the given polar code is 
computed by means of the equation given by, 
𝐿 𝑛 +1,𝑗 0
= ln
𝑃𝑟 (𝑥 𝑗 = +1/𝑟 𝑗 )
𝑃𝑟 (𝑥 𝑗 = −1/𝑟 𝑗 )
                                                 (6) 
The modulated and the received codewords are given by 𝑥 𝑗 
and 𝑟 𝑗 , respectively. The LLR value computed gets updated 
with each iterative propagation based on certain specific 
regulatory conditions. The conditional equations are 
summarized as below. 
𝐿 𝑖 ,𝑗 (𝑡 )
= 𝑔 (𝐿 𝑛 +1,𝑗 (𝑡 −1)
, 𝐿 𝑛 +1,𝑗 (𝑡 −1)
, 𝐿 𝑖 +1,𝑗 +𝑁 /2 
(𝑡 −1)
 + 𝑅 1,𝑗 +𝑁 /2
𝑖 
(𝑡 )
)
𝐿 𝑖 ,𝑗 +𝑛 /2
𝑖 (𝑡 )
= 𝑔 (𝐿 𝑛 +1,𝑗 (𝑡 −1)
, 𝑅 𝑖 ,𝑗 (𝑡 −1)
 + 𝐿 𝑖 +1,𝑗 +𝑁 /2 
(𝑡 −1)
)
𝑅 𝑖 +1,𝑗 (𝑡 )
= 𝑔 (𝑅 𝑖 ,𝑗 (𝑡 −1)
, 𝐿 𝑖 +1,𝑗 +𝑁 /2
𝑖 (𝑡 −1)
  𝐿 𝑖 +1,𝑗 +𝑁 /2
𝑖 (𝑡 )
)
𝑅 𝑖 +1,𝑗 +𝑁 /2
𝑖 (𝑡 )
= 𝑔 (𝑅 𝑖 ,𝑗 (𝑡 )
, 𝐿 𝑖 +1,𝑗 (𝑡 −1)
 + 𝑅 𝑖 ,𝑗 +𝑁 /2
𝑖 
(𝑡 )
)
 (7) 
The g(x,y) function as in the above 7 expressions stands for 
the operation called the box plus function given in detail as, 
𝑔 (𝑥 , 𝑦 ) ≜ 𝐼𝑛
1+𝑒 𝑥 +𝑦 𝑒 𝑥 +𝑒 𝑦 (8) 
The computation of the𝑎 ො
𝑗  and  𝑥 ො
𝑗 namely the value of the 
information bit and the code word bit estimated respectively 
is done from the calculated LLR value after the successive  
completion of the maximum possible iterations.If the 
calculated value of the LLRs is represented by 𝛤 𝑗 𝑎 and 
𝛤 𝑗 𝑥 respectively corresponding to the information a_jand the 
code word 𝑥 𝑗 , then the value of 𝛤 𝑗 𝑎 is given b𝛤 𝑗 𝑎 = 𝑅 1,𝑗 (𝑇 )
+
 𝐿 1,𝑗 (𝑇 )
y. And the value of 𝛤 𝑗 𝑥 is equal to 𝑅 𝑛 +1,𝑗 (𝑇 )
+ 𝐿 𝑛 +1,𝑗 (𝑇 )
. The 
simplified condition for decision making is given by, 
𝑎 ො
𝑗 = {
0, 𝑖𝑓 Γ
𝑗 𝑎 > 0
1, 𝑜𝑡 ℎ𝑒𝑟𝑤𝑖𝑠𝑒 (9) 
The factor graph of code length N=8 is given below figure 
(2). 
 
Figure 2: Factor Graph for N=8 Length 
The Factor Graph is drawn indicating the flow of Look Up 
direction in the process of the LLR value computation, 
which in turn helps in the decision making of the value in 
the process of data bits estimation. 
3 Simulation results and discussion 
The above discussed system model based on the processing 
of polar coded control signals, whose role is highly 
commendable in the effective functioning of a MIMO - 
NOMA based 5G NR system was simulated taking up some 
essential parameters of assumptions and approximations as 
well. ased on the above simulation parameters listed, the 
suggested system model is simulates and the resulting plots 
have been discussed below in terms of the system 
performance namely its SNR (in dB) Vs BER, Capacity (in 
Mbps) Vs SNR (in dB), BLER Vs Es/No (in dB). The 
tabulation below lists the parameters considered for the 
simulation done. 
 
 
 
 
 
 
 
 

 Development of Dynamic Channel Coding Strategy for Multi-User…                                                  Informatica 47 (2023) 93–102   97 
 
Fig 3 (a and b). Capacity vs SNR performance of an uplink 
and downlink MIMO-NOMA system. 
 
The above Figure 3 (a and b) depicts the capacity in Mbps 
vs. the SNR in dB of a MIMO - NOMA system in the Uplink 
and Downlink. The control information used in the 
functioning of a typical 5G NR system is generally said to 
be UCI abbreviated from Uplink Control Information and 
DCI abbreviated from Downlink Control Information. The 
UCI is taken care of by the physical channel termed as 
PDCCH, expanded to be Physical Downlink Control 
CHannel and at times the duty of communicating the control 
information is done by PDSCH also. Where, PDSCH is the 
Physical Uplink Shared CHannel, which carries both data 
and control information. The DCI on the other hand is taken 
care only by means of PDCCH called as the Physical 
Downlink Control CHannel, solely dedicated for downlink 
control information alone. The PDSCH (Physical Downlink 
Shared CHannel) does not support the communication of 
control signals through it and supports only the transfer of 
data.
 
Figure 4: BLER versus (
𝐸 𝑠 𝑁 0
) (in dB) for A = 16 Bits 
 
 
Figure 5: BLER versus (
𝐸 𝑠 𝑁 0
)  (in dB) for A = 32 Bits 
Parameter Values Assumed 
Number of users  2 per cluster 
Number of clusters 3 
Order of the MIMO system 2X2 
Modulation Method QPSK 
Number of Errors 10,100 
Size of the Successive 
Cancellation List 
1 
Input data bit length (A) 16,32,64,128,256,512 
and 1024 
Bit selection length (E) 54,108,216,432,864, 
1728,3456,6912 and 
13824 
Table 1: Simulation parameters used 

98   Informatica 47 (2023) 93–102                                                                                                                                     Pavithra B. et al. 
 
Figure 6: BLER versus (
𝐸 𝑠 𝑁 0
)  (in dB) for A = 64 Bits 
 
Figure 7: BLER versus (
𝐸 𝑠 𝑁 0
)  (in dB) for A = 128 Bits 
 
Figure 8: BLER versus (
𝐸 𝑠 𝑁 0
)  (in dB) for A = 256 Bits 
 
Figure 9: BLER versus (
𝐸 𝑠 𝑁 0
)  (in dB) for A = 512 Bits 

 Development of Dynamic Channel Coding Strategy for Multi-User…                                                  Informatica 47 (2023) 93–102   99 
 
Figure 10: BLER versus (
𝐸 𝑠 𝑁 0
)  (in dB) for A = 1024 Bits 
BLER stands for Block Error Rate. The actual target of 
BLER at the 5G NR is 10%. It means, 90% of the data 
grouped in blocks are error free and a 10% being erroneous 
is acceptable. The BLER is a crucial parameter of 
discussion at the receiving end of a 5G NR system. The 
BLER is computed as the ratio of the number of blocks 
received with errors to the total number of blocks received. 
The PDCCH polar codes of input data bit length A (16, 32, 
64, 128, 256, 512, and 1024) with the bit selection length E 
(54, 108, 216, 432, 864, 1728, 3456, 6912, and 13824) 
shown in figures (4-10) indicate that the BLER is lowered 
as the input bit length increases with regard to 
𝐸 𝑠 𝑁 0
⁄ .This 
computation is done after de - interleaving the received data 
at the physical layer and performing the decoding operation 
by means of CRC verification done on every block of data 
being received. The throughput of a given system keeps 
increasing with the decreasing value of the BLER value. 
 
 
 
 
 
 
 
 
Table 2: Simulation Parameters considered for channel 
encoded MIMO NOMA system 
CHANNEL 
CODING 
LTE 
TURBO 
CODE 
5G LDPC 
CODE 
5G 
POLAR 
CODE 
Input data bit 
length 
1024 1024 1024 
Information 
bit length 
512 512 512 
Code Rate 1/2 1/2 1/2 
Performance 
evaluation 
parameters 
BLER, 
SNR, Sum 
Rate 
Capacity 
BLER, 
SNR, Sum 
Rate 
Capacity 
BLER, 
SNR, Sum 
Rate 
Capacity 
Speed 
achieved 
(x 10^6 
Mbps) 
1.3 (at 
max 20 dB 
SNR) 
1.0 (at 
max 20 dB 
SNR) 
1.9 (at 
max 20 dB 
SNR) 
 
 
 
 
 
 
 
 
 
 
 
 
 
Figure 11: Comparison of SNR Vs BLER for 4 x 4 MIMO 
NOMA 

100   Informatica 47 (2023) 93–102                                                                                                                                     Pavithra B. et al. 
Figure 12: SNR versus Sum Rate Comparison for 4 x 4 
MIMO NOMA 
Figures 11 and 12 demonstrate a comparison of polar code, 
turbo code, and LDPC codes, as well as the no coding 
condition, when applied to a 4 x 4 MIMO NOMA system. 
Figure 11 depicts a gain of around 0.5 dB over LDPC and 
Turbo codes, with a corresponding block error rate (BLER) 
of 10^-2 for polar codes with input data bit lengths A of 
A16, A32, A64, and A128. The polar codes in figure 12 
outperform the system when compared to the Turbo and 
LDPC codes (red line). Sum rate capacity ranging from 0 to 
2 x 10^6 Mbps and SNR ranges of 0 to 20 dB illustrate the 
higher performance of polar codes has gain the speed of 
approximately 0.6x10^6 Mbps at the maximum of 20 dB 
SNR. 
4   Conclusion 
In a 5G NR system, a channel code's goal is to be extremely 
dynamic and assist the system in achieving almost error-free 
communication in a dynamic fashion without driving up the 
system's cost or increasing the complexity of the structure. 
In that case, the suggested polar codes outperform the 
existing channel coding methods and helps the system to be 
very effective in terms of error combating and the ease of 
its implementation complexity as well. The comparative 
analysis of SNR Vs BLER and SNR Vs Sum rate analysis 
of various typical coding schemes including no coding 
condition, LDPC code, Turbo code and the suggested Polar 
code of different block lengths (A = 16,32,64 and 128), 
shows the highlighted performance of the polar coding 
method in precise. In figure 11, the detailed analysis of 
Polar codes shows that they perform better than LDPC and 
turbo codes, and their performance increases as the length 
of the Polar code utilized increases. The figure 12, shows 
the comparative performance of various channel codes in 
terms of SNR Vs Sum rate wherein the suggested polar code 
method gives a better performance when being applied to a 
typical 4 x 4 MIMO NOMA system. 
Acknowledgement 
We thank B.S. Abdur Rahman Crescent Institute of Science 
and Technology to provide us the facilities and licensed 
software to carry out our research work. 
Conflict of Interest 
The authors declare that there are no conflicts of interest. 
References 
[1] Gilbert EN, 1960. “Capacity of a burst noise 
channel”, in Bell Syst. Tech.J., vol. 398, pg.no.1253-
1266. https://ieeexplore.ieee.org/document/6768434 
[2] Arikan E, 2009. “Channel polarization: A method 
for constructing capacity achieving codes for 
symmetric binary-input memoryless channels”, 
Information Theory, in IEEE Transactions, vol. 55, 
pg.no. 3051-3073. 
https://ieeexplore.ieee.org/document/4595172 
[3] Arikan E Telatar E, 2009. “On the rate of channel 
polarization”, in, IEEE International Symposium on 
Information Theory, pg.no.1493–1495. 
https://doi.org/10.1109/ISIT.2009.5205856 
[4] 3GPP TS 38.212 Technical Specification Group 
Radio Access Network, 2014. “NR, Multiplexing 
and Channel Coding”, https://www.etsi.org  
2017;RTS/TSGR-0138212vg20. 
[5] Niu K, Chen K, Lin J, Zhang QT, 2014. “Polar 
codes: Primary concepts and practical decoding 
algorithms”, in IEEE Communications magazine, 
  vol.52, pg.no.192–203. 
doi:https://ieeexplore.ieee.org/document/6852102 
[6] Vangala H, Viterbo E, Hong Y, 2015. “A 
comparative study of polar code constructions for 
the AWGN channel”, 2015; 
https://arxiv.org/pdf/1501.02473.pdf 
[7] Tal I, Vardy A, 2013. “How to construct polar 
codes,” in IEEE Transactions on Information 
Theory, vol. 59, pg.no.6562–6582. doi: 
https://ieeexplore.ieee.org/document/6557004 
[8] Peter Trifonov, “Effificient Design and decoding of 
polar codes”, in IEEE Transactions on 
Communications, vol. 60, no. 11, 2012;3221–3227. 
doi: https://ieeexplore.ieee.org/document/6279525 
[9] He G, Belfifiore JC, Land I, Yang G, Liu X, Chen Y, 
Li R, Wang J, Ge Y, Zhang R, Tong W, 2017. “Beta-
expansion: a theoretical framework for fast and 
recursive construction of polar codes,” in IEEE 
Global Communications Conference 
(GLOBECOM), Singapore.                                      doi: 
https://ieeexplore.ieee.org/document/8254146 
[10] Condo C, Hashemi SA, Gross WJ, 2017. “Effificient 
bit-channel reliability computation for multi-mode 
polar code encoders and decoders”, in IEEE 
International Workshop on Signal Processing 
Systems (SiPS), pg.no.2374-7390. doi: 
https://ieeexplore.ieee.org/document/8109987 

 Development of Dynamic Channel Coding Strategy for Multi-User…                                                  Informatica 47 (2023) 93–102   
101 
[11] Afifisiadis O, Balatsoukas-Stimming A, Burg A, 
2014. “A low-complexity improved successive 
cancellation decoder for polar codes”, in IEEE 
Asilomar Conference on Signals, Systems and 
Computers, pg.no.1058-6393. doi: 
https://ieeexplore.ieee.org/document/7094848 
[12] Tal I, Vardy A, 2015. “List decoding of polar codes”, 
in IEEE Transactions on Information Theory, vol. 
61, pg.no.2213–2226. doi: 
https://ieeexplore.ieee.org/document/6033904 
[13] B. Li, H. Shen, D. Tse, 2012. “An adaptive 
successive cancellation list decoder for polar codes 
with cyclic redundancy check”, in IEEE 
Communications Letters, vol. 16, pg.no.2044–2047. 
doi: 
https://ieeexplore.ieee.org/document/6355936?deni
ed= 
[14] Richardson T, Urbanke R, 2008. “Modern Coding 
Theory”, in Cambridge University Press; doi: 
https://doi.org/10.1017/CBO9780511791338 
[15] Wang R, Liu R, 2014. “A novel puncturing scheme 
for polar codes”, in IEEE Communications Letters, 
pg.no.2081–2084. doi: 
https://ieeexplore.ieee.org/document/6936302 
[16] Guo J, Qin M, Guillén i Fàbregas A, Siegel PH, 
2014. “Enhanced Belief Propagation Decoding of 
Polar Codes through Concatenation”, in IEEE Inter. 
Symp. Inf. Theory (ISIT), 2014. Pg.no.2987–2991. 
doi: https://ieeexplore.ieee.org/document/6875382 
[17] Bhuvaneshwari Pitchaimuthu Vairaperumal, Tharini 
Chandrapragasam, 2023. “Novel algorithm to 
construct QC-LDPC codes for high data rate 
applications”, in Informatica an International Journal 
of Computing and Informatics, Vol 47, No.8. 
https://www.informatica.si/index.php/informatica/a
rticle/view/4937/2466 
[18] Shelesh Krishna Saraswat, Vinay Kumar Deolia, 
Aasheesh Shukla, 2023. “Computational Analysis of 
Uplink NOMA and OMA for 5G Applications: An 
Optimized Network”, in Informatica an International 
Journal of Computing and Informatics, Vol 47, No.3. 
https://www.informatica.si/index.php/informatica/a
rticle/view/4145/2421 
[19] John Paul Tan Yusiong, Prospero Clara Naval, 2020. 
“ A Semi-Supervised Approach to Monocular Depth 
Estimation, Depth Refinement, and Semantic 
Segmentation of Driving Scenes using a Siamese 
Triple Decoder Architecture”, in Informatica an 
International Journal of Computing and Informatics, 
Vol 44, No 4. 
https://www.informatica.si/index.php/informatica/a
rticle/view/3018/1460 
 
 
 
Authors 
 
Pavithra B (First author), received 
B.E (ECE) in Sudharsan Engineering College, Pudukkottai 
in the year 2016 secured First Class. Completed M.E 
(Communication Systems) in the year 2020 secured first 
class with distinction and currently pursuing PhD, 
Department of ECE, B S Abdur Rahman Crescent Institute 
of Science and Technology. Published 2 journal papers in 
IJRTE and IJEAT and 1 International conference in IEEE 
Xplore. Area of interest includes wireless communication, 
error control coding and information theory, 5G and beyond 
technologies, MIMO etc. mail id is: 
pavithrab_ece@crescent.education 
 
 
 Dr. Parnasree Chakraborty 
(Second / Corresponding Author*) received B.E. degree in 
Electronics and Communication Engineering from SJCIT, 
Chikballapur, Visvesvaraya Technological University, 
Belgaum in the year 2002 and secured first-class with 
distinction. She did her Masters in M.E Communication 
Systems from Crescent Engineering College, Anna 
University in the year 2007 and completed her Ph. D in the 
year 2019. She has sixteen years of teaching experience. Her 
Ph.D. Degree in signal processing in sensor networks in the 
department of Electronics and Communication Engineering 
of B.S. Abdur Rahman Institute of Science & Technology. 
Her areas of interest include signal processing, image 
processing, communication engineering etc. She has 
published eight papers in international journals and 
presented many papers in international conferences. Her e-
mail ID is: prernasree@crescent.education and her contact 
number is: +91-9884083532. 
 
 
 
 

102   Informatica 47 (2023) 93–102                                                                                                                                     Pavithra B. et al.