STUDY OF DIFFERENT CODING METHODS OF

POLAR CODE IN 5G COMMUNICATION

SYSTEM

Atish A. Peshattiwar

Reaserch Scholar Department of Electronics Engineering, Yeshwantrao Chavan College of

Engineering, Nagpur, Maharashtra, (India).

E-mail: atishp32@gmail.com

Atish S. Khobragade

Professor, Department of Electronics Engineering, Yeshwantrao Chavan College of Engineering,

Nagpur, Maharashtra, (India).

E-mail: atish_khobragade@rediffmail.com

Reception: 01/12/2022 Acceptance: 16/12/2022 Publication: 29/12/2022

Suggested citation:

Peshattiwar, A. A., y Khobragade, A. S. (2022). Study of different coding methods of polar code in 5G

communication system. 3C Tecnología. Glosas de innovación aplicadas a la pyme, 11(2), 90-99. https://doi.org/

10.17993/3ctecno.2022.v11n2e42.90-99

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ABSTRACT

Sure, most of you are aware that right now everyone is thinking or at least the industry and

researchers are thinking about the next generation, the first generation of what will 5G be, and that a

significant part of the 5G telecommunication standard has been finalised, in particular the error

control codes that will be used in 5G telecommunication. One of the codes that will be used is called a

Low-Density Parity Check code (or LDPC code for short), and the other is called Polar Code. These

two famous and celebrated codes have distinct and fascinating histories. Both technologies are now

capable of providing near-capacity results, making them formidable competitors in the race to become

the 5G communication system's ultimate provider. In this paper, we zeroed in on the 5G Polar codes

and their encoding methods.

KEYWORDS

5G Communication System, Channel Coding, LDPC Codes, Polar Codes, Coding Methods.

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1. INTRODUCTION

The POLAR codes are a new type of capacity-achieving codes developed by Arkan [1]. Since 2008,

polar codes have been the subject of increasing study and interest in both the academic and

professional worlds. As part of the ongoing standardisation process for 5th generation wireless

systems, the 3rd Generation Partnership Project (3GPP) has certified polar codes as the channel coding

for uplink and downlink control information for the enhanced mobile broadband (eMBB)

communication service (5G). Polar coding is one of the proposed encoding methods for the two new

frameworks that 5G expects, namely extremely reliable low-latency communications (URLLC) and

massive machine-type communications (mMTC).

Creating a polar code involves determining the values of channel dependability associated with each

bit of information to be encoded. This id can be accomplished with a specific signal-to-noise ratio and

code length. Due to the expected wide range of code lengths, transmission rates, and channel

conditions in the 5G architecture, it is impractical to calculate separate reliability vectors for each

possible parameter combination. A lot of work has gone into creating polar codes that are

straightforward to implement, require little in the way of descriptive complexity, and provide adequate

error-correction across a wide range of code and channel parameters.

In light of their impending widespread deployment, researchers would do well to take into account the

one-of-a-kind codes created for 5G and their encoding procedure when evaluating error-correction

performance and constructing encoders and decoders. Almost all works of contemporary literature fall

short of this goal. Polar code properties have an immediate effect on decoder performance, and there

may be substantial time and effort costs associated with encoding and decoding. Publications that

focus on hardware and software implementations of the 5G standard may be able to increase their

readership if they emphasise compliance with the standard.

An "industry standard" is a set of guidelines for providing a service that has been accepted by a

number of different companies. In most cases, an agreement between multiple manufacturers to create

products that are compatible with one another leads to a standardisation of details, which is the result

of a commercial trade-off. A standard is a compromise between competing goals that ultimately results

in a hodgepodge of techniques that, when combined, achieve satisfactory performance.

Here, we zeroed in on one particular 5G coding method—Polar Codes—to see what all the fuss is

about. 2014 saw the introduction of new encoding schemes for the polar code [2] developed by kia

niu.

The remainder of the paper is organised as follows. Polar code: the basics Section II focuses on

encoding, while Section III discusses the more advanced design elements and ideas used in 5G

decoding, such as SC, SCF, and SCL. In Section IV, we compare the results of our Latency and

Throughput measurements, and in Section V, we draw some conclusions based on our findings.

2. 5G POLAR CODE ENCODING

The method employed by the 5G standard to encode polar codes is discussed at length here. In what

follows, I'll be making use of the notation defined by the 3GPP technical specification [2]. Polar codes

are used to transmit uplink control data over the physical uplink shared channel and uplink control

channel. Both the payload on the physical broadcast channel and the downlink control information

(DCI) on the physical down-link control channel (PDCCH) are encrypted using polar codes during the

downlink transmission (PBCH). For the upper communication layers in 5G applications, the required

rate R = A/E is specified, where A is the amount of information bits.

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A mother polar code of length N = 2n is required for this purpose. When the code is too long (or too

short) for the specified code length E, it is punctured, shortened, or repeated until it is. Depending on

the channel, the minimum and maximum code lengths N for the uplink and downlink are 32 and 512,

1024, respectively. An additional cap is imposed by the minimum allowable coding rate of 1/8. Figure

6 depicts the various encoding methods planned for use in the 5G polar codes design. The bits of

information contained in vector a, denoted by the G code, will be conveyed using the payload of G

code bits. Depending on the parameters of the encoding scheme, the message could be split into two

parts, each of which would be encoded separately before being sent. For every AJ-bit segmented

vector, a polar code-word of length E will be generated. There is an associated L-bit CRC for each AJ-

bit vector. The resulting vector c is fed into an interleave, which requires K = AJ + L bits. To generate

a mother polar code of length N, we need to know the expected coding rate R, the expected codeword

length E, the relative bit channel reliability sequence, and the frozen set. While the remaining bits of

the N-bit u vector are held steady, the interleaved vector cJ and any parity-check bits are added to the

information set.

Using the generator matrix of the selected mother code, GN = G2n, we encode the vector u as d = u

GN. Sub-block interleaving is then used to divide the encoded d into 32 blocks of the same length.

Then, the circular buffer receives these blocks after they have been scrambled to produce y. For rate

matching, the N-bit vector y is modified in some way (puncturing, shortening, or repeating) to yield

the E-bit vector e. In the event that concatenation is necessary, the computed vector f is then ready to

be modulated and transmitted as g.

Having the parameters A and E in play makes it clear that there is a cap on the effectiveness of the

channel being used. While A 11 uses many different block codes, the uplink uses 12 A 1706. The

agreed upon codeword length range is 18 E 8192, even though G 16384 may cause the payload length

G to be longer. Segmentation could be used to do this, dividing the data bits into two polar codewords.

. For PDCCH in the downlink, the maximum value of A is 140, but in this case, if A is 11, the message

will be zero-padded until A = 12. Although E 8192 is employed for uplink, the presence of the CRC

lower limits E to 25. There is only one valid PBCH passcode that utilises the combination of A = 32

and E = 864. These flags are the Input Bits Interleaver Activation (IBIL) signal and the Channel

Interleaver Activation (CIA) (IIL). There are two kinds of PC helper bits, and NPC and nwm both

provide the total number of them.

Fig. 1. Yellow, red, and orange blocks are used in downlink, uplink, and both, respectively, in the 5G polar codes encoding chain.

3. DECODING CONSIDERATION

Even though the 3GPP does not provide any decoding instructions, the final code structure provides

some pointers on how to decode polar codes, which are commonly used in 5G. Figure 1 shows an

encoding sequence; flipping the sequence facilitates decoding. The received encoded symbols are then

padded and deinterleaved to the length of the mother polar code following a second block

segmentation and deinterleaving operation for the uplink. A rate-matching algorithm will be used to

determine the type of padding to be used, with punctuation requiring the addition of zeros, shortening

requiring the use of saturated symbols, and repetition calling for the merging of symbols. The

importance of properly handling the code's helper bits at this stage will be emphasised. After padding,

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the number of encoded symbols is a power of two, which is readable by common polar code decoders

[1]. Next, we consider SCL in light of these repercussions and current needs.

When the check for all active pathways fails, the list decoder triggers its early decoding termination

feature; decoding continues when at least one active pathway succeeds. The decoder's BLER

performance may, however, depend on how it deals with routes that have become unavailable.

Keeping the unsuccessful paths in the list is the simple solution to keeping the number of active paths

constant and simplifying the decoder design. After each bit estimate, one strategy is to immediately

turn off failed paths. As a result, the BLER performs better, and the computational complexity and

energy consumption of the decoder are reduced. However, this causes a variation in the total number

of possible courses of action. Last but not least, distributed assistance bits could be thought of as

dynamically frozen bits that supply the bit's value for the check. The BLER's efficiency is the same

using this method as it was using the ineffective path deactivation. Since all surviving paths are

guaranteed to get the work done, assistance bits do not have the same impact on the decoder's

computational complexity or power consumption as dynamically frozen bits do. As an added bonus,

they do not lead to dismissal in the midst of the work week.

However, the number of viable paths varies based on the computational complexity and power

requirements of the decoder. Finally, distributed assistance bits can be viewed as dynamically frozen

bits that supply the bit with the value the check requires. The BLER's efficiency is the same using this

method as it was using the ineffective path deactivation. However, unlike dynamically frozen bits,

which reduce computational complexity and power consumption of the decoder and lead to early

termination, assistance bits do not guarantee that all remaining pathways will pass the check.

Native successive cancellation (SC) decoding of polar codes is also recommended in [1]. Like a left-

biased depth-first binary tree search, its decoding time is linear in N log N. N bits are approximable at

the leaf nodes, while the root node has soft information on the received code bits. Figure 4 depicts the

decoding tree for a (8, 4) polar code, where black leaf nodes represent the information bits and white

nodes represent the frozen bits. Figure 3 shows how the message flow can be defined recursively with

a node at the tth stage as the starting point. The node receives 2t soft inputs from its parent node and

uses them to generate 2t1 soft outputs _, which are then sent to the node's left child via the formula I =

f I i+2t1); later, the node combines the 2t1 hard decisions it receives from the node's left child with to

generate 2t1 soft outputs r for the Finally, it combines the 2t1 hard decisions r it received from its right

child with to determine the 2t hard decisions it will send to its parent node, with I = I ri if I 2t1 and I =

r i2t1 otherwise. When a leaf node is accessed, the soft information is used to make a hard decision

regarding the value of the information bits; frozen bits are always decoded as zeros.

In particular, the channel model affects update rules f and g for left and right child nodes. In BEC,

hard decisions can take on any value from 0 to 1, while soft values are limited to 0 and 1.

Fig. 2. White and black dots in the SC decoding of a (8, 4) polar code over a BEC stand for frozen and information bits.

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Fig. 3. SC decoding node.

3.1. DECODING FOR SUCCESSIVE-CANCELLATION (SC)

The SC decoding method, as first described [1], operates by sequentially traversing the graph

representation of Fig. 2 while iteratively computing u from the noisy channel data. Do this from top to

bottom and from right to left. It was first advised to calculate two bits at once in order to decrease time

and boost throughput [3]. By utilising specialised, quicker decoding algorithms on selected network

nodes [6] or even pruning the graph using a priori knowledge of the locations of the frozen bits [5], the

SC technique was further improved. One candidate codeword is always considered, regardless of the

SC algorithm version that is being used.

Fig. 4. Graph representation of a (8, 4) polar code.

3.2. PERFORMANCE OF SC DECODING

Fig. 5 compares the (2048, 1723) 10GBASE-T LDPC code's error-correction performance to polar

codes running at the same rate. These results were obtained by modulating the binary-input additive

white Gaussian noise (AWGN) channel with random codewords and binary phase-shift keying

(BPSK). First, it must be stated that the (2048, 1723) polar code performs substantially poorer than the

LDPC code. Up until Eb/N0 = 4.25 dB, the LDPC code works better than the PC(32768, 27568) polar

code, which was intended to perform best for Eb/N0 = 4.5 dB. There is a growing performance

difference over the LDPC code after that. The final polar error-rate curve, abbreviated PC*, is

produced by combining the output of two polar codes (32768, 27568). (32768, 27568). The first,

which has been in use up until this point, was constructed for 4.25 dB, whereas the second was

designed for 4.5 dB. Polar codes can be easily decoded because of their predictable structure, which

makes it easy to create a decoder that can decipher any polar code of a specific length. Therefore,

polar code changes inside a system are easier than LDPC code modifications.

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These findings demonstrate that a (32768, 27568) polar code built with an Eb/N0 of 4.5 dB or higher

is required to surpass the (2048, 1723) LDPC one in the low error-rate zone and that this may be done

even in high error-rate regions by combining numerous polar codes. Even though the polar code is

longer than the LDPC code, its decoder is nevertheless built in a simpler manner. The performance

difference between the (2048, 1723) code and the LDPC code with a list size of 32 and a 32-bit CRC

is reduced by using the list-CRC technique [4], as illustrated in Fig. 2.

The use of some of these strategies to list decoding will need more study. Due to its serial nature, SC

decoding has a limited throughput. ASIC decoders for (1024, 512) polar codes currently offer the

fastest implementation, processing data at a rate of 48.75 Mbps while operating at 150 MHz [11]. The

fastest decoder, on the other hand, can handle data at a rate of 26 Mbps for the (32768, 27568) code

and is FPGA-based. Although it may be significantly increased by employing the SSC or ML-SSC

decoding algorithms, this poor throughput renders SC decoders unusable for the bulk of systems.

Fig. 5. Polar codes' error-correction performance is contrasted with an LDPC code of the same rate. In addition to a rate 0.9 polar code's

functionality.

3.3. DECODING USING SUCCESSIVE-CANCELLATION FLIP (SCF)

Similarities exist between the SC algorithm and the SCF decoding technique [8]. At first, its operation

is similar to that of SC decoding; however, in addition to decoding, it also keeps track of the bits that

are the least reliable. A cyclic redundancy check must also be used to string together the polar code

(CRC). The SCF decoder generates a full codeword candidate and checks if the computed CRC is the

same as the expected one. When the CRC verification fails, the SC decoding process continues until

the least reliable bit-decision is found. The SCF makes a contrasting conclusion and continues

decoding SC. After two tries, if the CRC does not match the expected CRC, the bit-decision with the

second-lowest confidence is swapped and the process is repeated. Until the CRC comparison is

conclusive or until the maximum number of trials have been conducted, this technique is repeated.

3.4. DECODING OF THE SUCCESSIVE-CANCELLATION LIST (SCL)

As their names imply, the SCL algorithm [7] and the SC algorithm have some similarities. In contrast to SC

decoding, the output of the SCL decoding method is a smaller set of up to L possible codewords. It considers

both ui options for the locations I where data bits can be found. A path dependability metric computed

during the method is used to filter out all but the L best pathways from the final list of survivors. At the end

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of the decoding process, the estimated codeword is selected from among the L candidates based on which

one has the highest route dependability score.

If a polar code and a CRC are paired, the projected CRC and computed CRC for each of the L candidates are

compared. Out of all the candidates who pass the CRC, the decoded codeword is selected as the most

trustworthy candidate. If all candidates fail the CRC, the technique simply selects the candidate with the

highest route dependability.

3.4. LATENCY AND THROUGHPUT

To evaluate the latency boost from the novel algorithm and implementation, we compare two unrolled

decoders with an LLR-based SC-list decoder developed in accordance with the technique described in

[6] in Table I. The first unrolled decoder, also called the "unrolled SC-list," does not rely on any specific

set of constituent decoders. The second is called "unrolled Dec-SPC-4," and it incorporates all of the

component decoders we have covered so far while limiting the number of SPC decoders to four. When

the SC-list decoder is unrolled, we find that decoding time is cut by more than half. Latency is reduced

to between 63% (L = 2) and 18.9% (L = 32) of the unrolled SC-list decoder when the rate-0, rate-1,

repetition, and SPC-4 constituent decoders are used. In comparison to SC-list decoding, the suggested

decoding strategy and implementation yield a performance boost of between 18.4 and 11.9% for list

sizes of 2 and 32, respectively.

The impact of the unrolled decoder is more noticeable for shorter lists, while the impact of the new

constituent decoders is greater for longer lists.

When there is no limitation on the length of the individual SPC decoders, as in the case of "Unrolled

Dec-SPC-4+" in Table I, the latency for the recommended decoder is also shown. Turning on these

longer constituent decoders decreases latency by 14% and 18% for L = 2 and L = 8, respectively. We do

not advise using SPC-8+ component decoders because of the drastic decrease in error-correction

performance for L >= 8. Consequently, we do not guarantee the lag associated with such a decoder

setup. The proposed decoder has a roughly linear decrease in throughput in function of L. At L = 32 and

433 s of latency, the data rate is 4 Mbps. Performance can be improved with adaptive decoding by using

a Fast-SSC decoder prior to the list decode. The results of this method's throughput are shown for L = 8

and L = 32 in Table II. According to (17), when the throughput for L = 8 and 32 is equal, the effect of

the list decoder on throughput diminishes, and the Fast-SSC performs better at 4.5 dB.

4. COMPARATIVE ANALYSIS

Table 1. Latency (in µsec) for various decoding methods of polar code.

Decoder

2 8 32

SC-List 558 1450 5145

Unrolled SC-

list

193 (2.9×) 564(2.6×) 2294(2.2×)

Unrolled Dec

SPC-4

30.4(18.4×) 97.5(14.9×) 433(11.9×)

Unrolled Dec

SPC-4+

26.3(21.2×) 80.2(18.1×) N/A

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Table 2. When calculating 524,280 information bits, the suggested list decoder's information throughput and latency were compared to those

of the ldpc decoders of [32].

5. CONCLUSION

This article will help the reader understand and implement the polar code encoding process in

accordance with the 5G wireless systems standard, as well as simulate it for practise. This encoding

chain exemplifies the 3GPP standards body's efforts to support a variety of code lengths and speeds

while satisfying the various code criteria for the eMBB control channel, such as low description

complexity and low encoding complexity. Insights into the consideration given to the receiver side

during the standardisation process are provided. So long as cutting-edge hardware and decoders are

used, the encoder was designed to allow for the decoder to be generated with a tolerable level of

complexity and perform at the required latency. But now it is possible to optimise decoding complexity

or improve error-rate performance by developing new decoding structures or principles.

We also investigated potential delays introduced by various decoding strategies, including successive

cancellation (SC) decoding, successive cancellation flip (SCF) decoding, and successive cancellation

list (SCL) decoding. Additionally, we conducted latency analyses to determine the relative merits of

each decoding technique. Decoding algorithms can be tweaked to improve delay and throughput.

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