Polar Codes Research Articles

Prevention and control of ship-source pollution in the Arctic shipping routes: challenges and countermeasures

Ship-source pollution is one of the important contributors to marine environment pollution. Because the legal status of the Arctic shipping routes is not clear, there is a considerable degree of dispute in the application of the rules on the prevention and control of ship-source pollution. The increased melting of sea ice undermines the legal legitimacy of the “ice-covered areas” clause under the United Nations Convention on the Law of the Sea. The conflict between the application of the Polar Code and “ice-covered areas” will also reach an initial conclusion in the context of melting sea ice. However, the inadequacy of ship-source pollution rules in the Polar Code hampers its application, which has led to a negative impact on the more active role in the governance of pollution from Arctic shipping. For replying to the Challenges in the prevention of ship-source pollution in Arctic shipping routes, the relevant rules of the Polar Code need to be further improved, while a more binding HFO ban according to ship types needs to be applied. Therefore, a more important role in the future Arctic governance mechanism will be played by the enhanced enforcement of the Polar Code, meanwhile, the target for uniform international regulation of preventing and controlling ship-source pollution in Arctic shipping routes should be achieved.

Enhancing channel estimation accuracy in polar-coded MIMO–OFDM systems via CNN with 5G channel models

In this paper, a novel channel estimation technique for multiple-input multiple-output orthogonal frequency-division multiplexing (MIMO–OFDM) systems in fifth generation (5G) networks is proposed, which leverages the power of convolutional neural networks (CNNs) along with the application of polar coding. By employing polar encoding at the transmitter and polar decoding at the receiver, the proposed system enhances error correction performance, reliability, and data transmission rate in 5G networks. A novel optimized CNN-based channel estimation technique, named CNN-CENet, has been integrated into the polar-coded MIMO–OFDM receiver. This integration aims to address the interference and noise challenges in 5G systems. The proposed channel estimation method utilizes multiple layers of CNN to accurately characterize the properties of the real channel by incorporating least squares (LS) estimations. Hence, the proposed CNN-CENet provides an accurate estimation of the channel coefficients, enabling efficient signal detection at the receiver. The MATLAB simulation has been conducted using deep learning and 5G toolboxes to obtain results for various channel parameters. These results are then compared with the LS and minimum mean square error (MMSE) methods for performance evaluation. The proposed model surpasses the performance of the LS and MMSE methods, achieving a significant 95.6% reduction in mean square error (MSE) compared to LS and a substantial 59.7% reduction compared to MMSE. Additionally, it delivers notable bit error rate (BER) reductions of 59.8% and 53.2% for LS and MMSE, respectively, in low mobility scenarios, and 57.4% and 48.5% reductions in high mobility scenarios. This improvement leads to enhanced reliability and overall system efficiency.

Review of schemes for transport-geographical zoning of the Arctic water area

The retrospective and modern schemes for geographic and transport zoning of the Arctic and the Northern Sea Route are examined. The historical research method, which consists in identifying and analyzing documented facts, historical processes and their logic in terms of clarifying development, is used. There are several stages in the formation of zones and areas in the waters of the Arctic seas. The time period chosen for the review is from the beginning of the 19th century to the present in chronological order. International relations, national legal and natural conditions, and country characteristics are taken into account. The evolution of the organizational structure for managing the operation of the transport system of the Northern Sea Route, from the creation of the first administration to the present day, is considered. The countries of the Arctic Council have not yet developed a uniform approach to such tasks as the classification of ice (ice conditions) and requirements for the design of a vessel (ship ice class). Most countries use the definitions from the Polar Code. Individual countries apply their own rules and classification. The Russian Federation, for example, when choosing criteria for the admission of ships, uses both the national classification (Arc4-Arc9) and the Baltic one (Ice1-Ice3), while recognizing the ice classes of ships according to the International Association of Classification Societies. The results of a comparison of the Arctic Council countries on the presence of signs for development of transport-geographical zoning and navigation management in the Polar waters are presented. In conclusion, a list of tasks, the solution of which will contribute to the future transition from geographical to transport zoning of the Northern Sea Route and the Polar waters as a whole, is provided.

Reversible Data Hiding in Encrypted Images Based on Binary Symmetric Channel Model and Polar Code

For vacating-room-after-encryption reversible data hiding in encrypted images (VRAE RDHEI), an essential problem is how to address potential errors in data extraction and image recovery. This problem significantly limits the capacities of the existing VRAE RDHEI methods. To solve the problem while losing as little capacity as possible, in this paper, a novel method is proposed that uses the ideas of noisy channel model and channel code. By designing the data hiding mechanism appropriately, the embedding and extraction of data in the proposed method can be equivalent to the input and output of a virtual binary symmetric channel (BSC) model, so that the errors in data extraction are equivalent to the bit transitions in BSC. Based on the virtual BSC model, polar code is used to encode the secret data in the data hider's side. With the help of polar code, the receiver can decode the extracted bits containing errors to obtain correct secret data, then recover the error-free original image based on the corrected secret data. The experimental results proved that, compared with the existing VRAE methods, the proposed method can significantly improve the capacity and the quality of the decrypted images under the premise of complete reversibility.

Cyclic redundancy check-aided successive cancellation-based polar decoders

<span>Research on channel coding for network transmission using polar codes has produced excellent results. By removing error redundancy from the decoding process, cyclic redundancy check (CRC) is frequently used by researchers to increase a system’s performance. In prior research, the application of decoder algorithms for polar codes was examined but not thoroughly compared. For the general capabilities of the previously proposed algorithms to be ascertained, it is crucial to analyze the employment of polar decoders especially successive cancellation (SC)-based polar decoders and the use of CRC in additive white gaussian noise (AWGN). Hence, this paper analyzes the performance of CRC with SC-based polar decoders in AWGN. In the simulation setup, (256,128) polar codes and CRCs with three-bit sizes (6, 8 and 11) were utilized. SC-based polar decoders, such as SC, soft-output cancellation, SC list (SCL) and simplified SC, were applied at the decoder part. The outcomes show that CRC-aided SC-based polar decoders reduced redundancy error. Among all the decoders, the SCL decoder with 11-bits CRC performed well when the normalized signal-to-noise ratio was high. Based on the analysis, removing errors at the highest level is possible using a suitable CRC size for SC-based polar decoders.</span>

Many-to-One Mapping Based Truncated Probabilistic Shaped 64-QAM for Metro Transmissions Enabled by Polar Code

Many-to-One Mapping Based Truncated Probabilistic Shaped 64-QAM for Metro Transmissions Enabled by Polar Code

Scalable Polar Code Construction for Successive Cancellation List Decoding: A Graph Neural Network-Based Approach

Scalable Polar Code Construction for Successive Cancellation List Decoding: A Graph Neural Network-Based Approach

A Novel Polar Code Construction for Magnetic Induction-Based Wireless Underground Communications

A Novel Polar Code Construction for Magnetic Induction-Based Wireless Underground Communications

Polar code-based cryptosystem: comparative study and analysis of efficiency

<p><span>This review paper aims to examine the use of polar codes in public key cryptosystems, providing a comprehensive overview of the state-of-the-art in this field at present. This study thoroughly searches databases such as IEEE Xplore, Scopus, and the ACM digital library to locate relevant research articles. In this study, we demonstrate the use of polar codes in public key cryptography and provide valuable insights for researchers interested in this field of research. The paper identifies several areas for further research and development, such as improved security and reliability of polar code-based cryptosystems. An analysis of the review highlights the major challenges and open research questions in this area, including the need for efficient key generation algorithms and the trade-offs between security and performance. An analysis of various existing encryption techniques as well as their security proofs is provided in the tables.</span></p>

A Note on the Mixing Factor of Polar Codes.

Over binary-input memoryless symmetric (BMS) channels, the performance of polar codes under successive cancellation list (SCL) decoding can approach maximum likelihood (ML) algorithm when the list size L is greater than or equal to 2MF, where MF, known as mixing factor of code, represents the number of information bits before the last frozen bit. Recently, Yao et al. showed the upper bound of the mixing factor of decreasing monomial codes with length n=2m and rate R≤12 when m is an odd number; moreover, this bound is reachable. Herein, we obtain an achievable upper bound in the case of an even number. Further, we propose a new decoding hard-decision rule beyond the last frozen bit of polar codes under BMS channels.

New Structure of Channel Coding: Serial Concatenation of Polar Codes

In this paper, we introduce a new coding and decoding structure for enhancing the reliability and performance of polar codes, specifically at low error rates. We achieve this by concatenating two polar codes in series to create robust error-correcting codes. The primary objective here is to optimize the behavior of individual elementary codes within polar codes. In this structure, we incorporate interleaving, a technique that rearranges bits to maximize the separation between originally neighboring symbols. This rearrangement is instrumental in converting error clusters into distributed errors across the entire sequence. To evaluate their performance, we proposed to model a communication system with seven components: an information source, a channel encoder, a modulator, a channel, a demodulator, a channel decoder, and a destination. This work focuses on evaluating the bit error rate (BER) of codes for different block lengths and code rates. Next, we compare the bit error rate (BER) performance between our proposed method and polar codes.

An Improved Bit-Flipping Algorithm of Successive Cancellation List Decoding for Polar Codes

Polar codes, as the coding scheme for the control channel in fifth-generation mobile communication technology (5G), have attracted widespread attention since their proposal. As a mainstream decoding algorithm for polar codes, the successive cancellation list (SCL) decoder usually improves the error correction performance by increasing the list size, but this method suffers from the problems of high decoding complexity. To address this problem, this paper proposes a layered-search bit-flipping (LS-SCLF) decoding algorithm based on SCL decoding. Firstly, a new flip-bit metric is proposed, which derives a formula to approximate the probability of an error occurring in an information bit. This formula introduces a perturbation parameter to improve the calculation accuracy. Secondly, a compromise scheme for determining the perturbation parameter is proposed. The scheme uses Monte Carlo simulation to determine an optimized parameter for the precise positioning of the first erroneous decoded bit under different decoding conditions. Finally, a layered search strategy is adopted to sequentially search the erroneous decoded bits from the low order to high order, which can correct up to multiple bits at the same time. Simulation results show that the proposed algorithm achieves improved error correction performance with a slight increase in decoding complexity compared to the generalized SCL-Flip (GSCLF) decoding algorithm. This algorithm also achieves a good balance between the error correction performance and decoding complexity.

A comprehensive study on the synchronization procedure in 5G NR with 3GPP-compliant link-level simulator

The 5G New Radio synchronization procedure is the first step that the user must complete to access the mobile network. It mainly consists of the detection of the primary and secondary synchronization signals (PSS and SSS, respectively) and the decoding of the physical broadcast channel (PBCH). Our goal is to provide a comprehensive study of the synchronization procedure and investigate different techniques and approaches, through the implementation of a 5G New Radio-compliant simulator. Of significant interest is the investigation of impairments such as the fading channel, the frequency offset, and the delay spread. The results are provided in terms of detection probability for the PSS and SSS detection, and in terms of block error rate for the PBCH. From the data collected, there is evidence that choosing M-sequences for the PSS leads to an appreciably robust solution against frequency offset. The structure of the Gold sequences for SSS generation can be exploited to reduce the detection complexity, and different approaches can be chosen to improve reliability against delay spread. Moreover, the polar coding for 5G PBCH outperforms the former 4G coding technique, but they are still sensible to frequency offset. Finally, the simulator functionalities are validated through real captures of 5G signals.

Analysis and application research on key issues of channel coding

Channel coding plays a crucial role in enhancing the reliability and efficiency of communication systems, particularly when transmission channels are disrupted by noise and interference. This paper presents an in-depth review of various channel coding techniques, their applications, and future research directions. Key topics discussed include prevalent channel coding methods, such as repetition codes, convolutional codes, LDPC codes, turbo codes, and polar codes. The paper also delves into the selection of suitable channel coding parameters and their applications in digital TV, mobile and satellite communications, unmanned aerial vehicle data links, speech communication, and underwater acoustic channels. Moreover, the paper explores the performance analysis and comparison of different channel coding techniques, shedding light on their strengths and weaknesses. Lastly, the paper identifies emerging trends and challenges in channel coding research, providing valuable insights for researchers and practitioners in the field of communication systems. By examining these techniques and future directions, this comprehensive overview aims to contribute to the development of more robust and efficient channel coding schemes for a wide range of communication applications.

Polarization-adjusted convolutional (PAC) codes as a concatenation of inner cyclic and outer polar- and Reed-Muller-like codes

Polarization-adjusted convolutional (PAC) codes are a new family of linear block codes that can perform close to the theoretical bounds in the short block-length regime. These codes combine polar coding and convolutional coding. In this study, we show that PAC codes are equivalent to a new class of codes consisting of inner cyclic codes and outer polar- and Reed-Muller-like codes. We leverage the properties of cyclic codes to establish that PAC codes outperform polar- and Reed-Muller-like codes in terms of minimum distance.

16QAM OFDM-PON based on polar code and CCDM joint chaotic encryption.

A new optical transmitting scheme based on chaotic constant component distribution matcher (CCDM) and Polar coding was proposed. The data is first encrypted by Polar coding using a five-dimensional chaotic sequence. Then the encrypted data is divided into two paths to perform chaotic CCDM encryption operations with different schemes. Finally, the two channels are merged, and the subcarriers are scrambled. The transmission experiment of 16QAM-OFDM signal on 2 km seven-core fiber is conducted to verify the scheme's feasibility. The experimental results show that the received optical power of all ONUs is less than -15dBm when the BER of all ONUs is reduced to less than 10-3. In addition, the key space of the proposed system reaches 1085, and the security performance is further enhanced. The advantages of BER and safety performance make this two-path chaotic encrypted OFDM-PON with an optimistic application prospect in the current optical transmission systems.

High-Quality and Low-Complexity Polar-Coded Radio-Wave Encrypted Modulation Utilizing Multipurpose Frozen Bits

In recent years, physical layer security (PLS), which utilizes the inherent randomness of wireless signals to perform encryption at the physical layer, has attracted attention. We propose chaos modulation as a PLS technique. In addition, a method for encryption using a special encoder of polar codes has been proposed (PLS-polar), in which PLS can be easily achieved by encrypting the frozen bits of a polar code. Previously, we proposed a chaos-modulated polar code transmission method that can achieve high-quality and improved-security transmission using frozen bit encryption in polar codes. However, in principle, chaos modulation requires maximum likelihood sequence estimation (MLSE) for demodulation, and a large number of candidates for MLSE causes characteristic degradation in the low signal-to-noise ratio region in chaos polar transmission. To address this problem, in this study, we propose a versatile frozen bit method for polar codes, in which the frozen bits are also used to reduce the number of MLSE candidates for chaos demodulation. The numerical results show that the proposed method shows a performance improvement by 1.7 dB at a block error rate of 10-3 with a code length of 512 and a code rate of 0.25 compared with that of conventional methods. We also show that the complexity of demodulation can be reduced to 1/16 of that of the conventional method without degrading computational security. Furthermore, we clarified the effective region of the proposed method when the code length and code rate were varied.

Construction of Polar Codes Based on Memetic Algorithm

As an emerging coding technique chosen by the 5th generation wireless systems (5G) standardization process, polar coding has attracted the attention of both academia and industry in recent years. The currently used construction methods of polar code are generally based on the reliability of each polarized sub-channel, which directly correspond to the Successive Cancellation (SC) decoding algorithm. However, much less is known about the optimal construction of polar codes under more sophisticated decoding methods such as the Successive Cancellation List (SCL) decoding. There is currently no perfect theory to derive the optimal construction for the SCL decoding to the best of our knowledge, because finding such optimal construction of SCL is considered to be a hard problem for normal choices of the list size. To address this problem, in this paper we turn to evolutionary computation, and propose a memetic algorithm by incorporating prior knowledge obtained from both the channel estimation of the SC-profile and the codeword weight evaluation of the RM-profile, shorted as MA-SCRM. The potential constructions of polar codes are expressed as binary sequences which are processed as the individuals of the population in MA-SCRM. Based on the prior knowledge obtained from the SC-profile and the Reed-Muller-profile, we design special initialization and evolutional operators for polar codes construction. An elitism archive is also introduced to maintain promising constructions and accelerate the convergence of the algorithm. For the SCL decoding, MA-SCRM obtains polar-coding constructions that are more excellent than the SC decoder construction in the sense of block error probability. Compared with the SC decoding construction method, MA-SCRM can reduce the block error probability by up to 48.78% for the original block error rate around <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$10^{-2}$</tex-math></inline-formula> , and more improvement can be observed for lower original block error rate.

A construction method of arbitrary-length polar codes

A construction method of arbitrary-length polar codes

Pre-Configured Error Pattern Ordered Statistics Decoding for CRC-Polar Codes.

In this paper, we propose a pre-configured error pattern ordered statistics decoding (PEPOSD) algorithm and discuss its application to short cyclic redundancy check (CRC)-polar codes. Unlike the traditional OSD that changes the most reliable independent symbols, we regard the decoding process as testing the error patterns, like guessing random additive noise decoding (GRAND). Also, the pre-configurator referred from ordered reliability bits (ORB) GRAND can better control the range and testing order of EPs. An offline-online structure can accelerate the decoding process. Additionally, we also introduce two orders to optimize the search order for testing EPs. Compared with CRC-aided OSD and list decoding, PEPOSD can achieve a better trade-off between accuracy and complexity.