Channel Polarization Research Articles

Algorithmization and Hardware Implementation of Polar Coding for 5G Telecommunications

Abstract The article explores a recursive algorithm for determining Bhattacharyya parameters, which is a measure of the degree of channel polarization for telecommunications with polar coding. A method is given for determining the positions of information and fixed bits in a polar code. The principles of constructing a polar encoder and a polar decoder successive cancellation are considered. The Field-Programmable Gate Array implementation of the successive cancellation list decoder is considered. Experimental studies of the construction of a polar code using Gaussian approximation have been carried out. The influence of the design signal-to-noise ratio on the bit error rate of telecommunications with polar codes has been studied. The use of multi-position modulation in telecommunications with polar codes has been studied. It is expected that the results obtained will be useful in hardware and software implementation of 5G telecommunications with polar coding.

PCC Polar Codes for Future Wireless Communications: Potential Applications and Design Guidelines

The main limitation of polar codes is that the channel polarization is insufficient in the context of short and moderate codeword length, resulting in a degradation of error correction performance. Promising solutions can be found in the recently proposed parity-check-concatenated (PCC) polar codes, which exploit the scattered parity bits to improve the error correction capability substantially. Owing to this benefit, PCC polar codes constitute an appealing paradigm of channel coding and have been deemed a critical technology of the control channel coding for 5G mobile communication. As an emerging channel coding, its potentiality has yet to be thoroughly investigated. To unleash the eminent benefits of the PCC polar codes, in this article, we present a comprehensive overview, including its innovative construction of encoding, low-complexity decoding, advanced evolution variants, and potential application scenarios, as well as its future design guidelines.

Polar-coded channel polarization for reducing complexity of soft-decision forward error correction

To reduce the computational complexity of soft-decision (SD) forward error correction (FEC), we propose a polar coding method with a low-complexity successive cancellation decoder. Polar coding induces channel polarization in which two bit-channels with lower and higher reliabilities are polarized. Only the less-reliable bit-channels are protected by SD-FEC, whereas the more-reliable bit-channels are offloaded, reducing the complexity of SD-FEC decoding. The degradation of the bit error ratio (BER) performance can be suppressed by designing the polar encoder structures for the successive cancellation decoder. We numerically demonstrate that the proposed method manages to both reduce the computational complexity by half and suppress the BER performance degradation by less than 0.6 dB, compared with the conventional method using only the SD-FEC.

Experimental demonstration of 17.5 Gb/s physical layer key distribution over 100 km fiber link based on channel physical intrinsic property and polarization reciprocity.

Secure key distribution (SKD) schemes based on fiber channel reciprocity provide information-theoretic security as well as a simple symmetric structure. However, the nonlinear effects and backscattering effects introduced during the bidirectional transmission process degrade the channel reciprocity. Recent unidirectional SKD schemes avoid non-reciprocal factors but require additional negotiation mechanisms to aggregate the transmitter and receiver data. Here, we propose a unidirectional SKD scheme based on channel physical intrinsic property and polarization reciprocity. The designed loopback structure constructs asymmetry between legitimate and illegitimate parties while aggregating data. The deployment of a broadband chaotic entropy source significantly improves the key generation rate (KGR). In the experiment, the KGR reaches 17.5 Gb/s, and the distribution distance reaches 100 km.

Ab initio theory of the nonequilibrium adsorption energy

While first-principles calculations of electrode-molecule adsorption play an indispensable role in obtaining atomic-level understanding in surface science and electrochemistry, a significant challenge remains because the adsorption energy is well-defined only in equilibrium. Herein, a theory to calculate the electric enthalpy for electrified interfaces is formulated within the multi-space constrained-search density functional theory (MS-DFT), which provides the nonequilibrium total energy of a nanoscale electrode-channel-electrode junction. An additional MS-DFT calculation for the electrode-only counterpart that maintains the same bias voltage allows one to identify the internal energy of the channel as well as the electric field and the channel polarization, which together determine the electric enthalpy and the nonequilibrium adsorption energy. Application of the developed scheme to the water-Au and water-graphene interface models shows that the Au and graphene electrodes induce very different behaviors in terms of the electrode potential-dependent stabilization of water configurations. The theory developed here will be a valuable tool in the ongoing effort to obtain atomic-scale understanding of bias-dependent molecular reorganizations in electrified interfaces.

AN IMPROVED POLARIZATION WEIGHTS CONSTRUCTION FOR POLAR CODES

Polar codes proposed by Arikan based on channel polarization have been proven to achieve Symmetric Binary-Discrete Input Memoryless Channels capacity. 3GPP has also chosen the Polar codes as the error correction code in the fifth mobile communication system (5G New Radio - 5G NR) with a maximum codeword length of 1024 bits. The design of the code based on the reliability of the synthetic channels has been researched with many different methods to satisfy the requirements demanded in the application of 5G NR. The Polar codes design requirements are ease of implementation, low decoding complexity, and high performance in error correction. This paper has proposed a method of designing Polar codes by determining a synthetic channels reliability index sequence based on the Polarization Weights (PW) method called the Improved Polarization Weights (IPW) method. The simulation results show that the error correction performance of the code designed according to IPW is better than the code structure selected for 5G NR and designed according to the original PW method.

Effect of device size on conduction channel effective width and polarization Coulomb field scattering intensity of split-gate AlGaN/GaN heterostructure field-effect transistors

In this study, the ungated AlGaN/GaN devices with special mesa structures were designed. The hypothesis of effective width expansion was tested experimentally by using ungated samples with different sizes, and an empirical expression for calculating the conduction channel effective width was given according to the experimental results. Finally, split-gate AlGaN/GaN heterostructure field-effect transistors (HFETs) with different gate lengths were prepared, and the channel electron mobility of split-gate samples was calculated by using the empirical expression and polarization Coulomb field (PCF) scattering theoretical model. The results showed that, for split-gate AlGaN/GaN HFETs, with the increase in the gate length, the total amount of additional polarization charges underneath the gate increases, resulting in the enhancement of the PCF scattering intensity.

Simple and Fast Polarization Tracking Algorithm for Continuous-Variable Quantum Key Distribution System Using Orthogonal Pilot Tone

To reduce the influence of random channel polarization variation, especially fast polarization perturbation, for continuous-variable quantum key distribution (CV-QKD) systems, a simple and fast polarization tracking algorithm is proposed and experimentally demonstrated. The algorithm is implemented by an orthogonal pilot tone scheme, one of the pilot tones is used for estimating the polarization rotation angle, and the other one is used for compensating the polarization perturbation introduced phase noise. Meanwhile, residual effects are compensated precisely with the help of a real-valued FIR filter. In this case, the excess noise introduced by polarization perturbation is effectively suppressed. Experimental results show that the polarization scrambling rate ≥12.57 krad/s can be tracked by using the proposed algorithm, and a good estimated parameters performance is achieved. Compared to conventional polarization tracking algorithms such as the constant modulus algorithm (CMA), experimental results show that the polarization tracking capability of the proposed algorithm is significantly improved. Furthermore, much faster polarization tracking performance is evaluated by digital simulations, and the simulation results show that about 188.50 Mrad/s can be tracked by the proposed algorithm. Thus, our method provides effective technology for the practical application of fiber-based CV-QKD.

Analysis of the Encoding and Decoding Process of Polar Code

This paper briefly introduces the history of channel coding from the hamming code to the newest polar code. Then it introduces that the polar code is the only one that can reach the Shannon limit. With such a crucial technique, this study set it as the core research target of this article. After pointing out the target and the content of the polar code, this paper explains the core principle, which is the channel polarization theory. It also contains channel polarization's two components, the channel combining and splitting theory. In the main part, this paper explains the encoding and decoding of polar code in detail based on the polarization theory. It analyzes the whole process of polar code using examples with multiple inputs. And at last, the result of the likelihood ratio and channel capacity is obtained, which can be utilized to compute the relevant parameters to evaluate the efficiency of encoding and decoding and other rates.

Multi‐Channel Image Encryption Based on an All‐Dielectric Metasurface Incorporating Near‐Field Nanoprinting and Far‐Field Holography

AbstractMetasurfaces that can efficiently control the light‐field characteristics have shown many advantages in ultra‐compact, high‐resolution, and high‐concealment optical imaging such as nanoprinting and holography. The development of metasurfaces with multiple functions operating at multiple wavelengths can promote the progress of optical imaging with high information storage and encryption densities. Here, an all‐dielectric metasurface is proposed for multi‐channel image encryption in the near field by controlling the amplitude distribution based on Marius’ law and for holographic imaging in the far field by controlling the phase distribution based on the Pancharatnam–Berry phase. This metasurface can realize the pattern imaging of 12 channels by independently regulating the three‐wavelength channel and different polarization modes. The metasurface achieves independent control of the amplitude, phase, polarization, and wavelength of the incident light wave, improving the storage capacity of information and its encryption security level. The proposed multichannel metasurface provides an effective solution for high‐capacity optical encryption and information storage applications.

Channel polarization of two-dimensional-input quantum symmetric channels

Channel polarization of two-dimensional-input quantum symmetric channels

Conditional Entropy-Based Construction of Multilevel Polar-Coded Modulation With Probabilistic Shaping

Code construction is a critical issue for polar-coded systems to ensure competitive performance. In this letter, we propose a conditional entropy-based method to construct multilevel polar-coded modulation (MLC-PCM) with probabilistic shaping. More specifically, we allocate the bit positions in accordance with their conditional entropies induced by channel and source polarization. We show that a surrogate channel can be used to determine the frozen set in each component polar code efficiently. The remaining positions are assigned to the information and shaping bits by the source Bhattacharyya parameter, where the shaping bits are used to achieve non-uniform channel inputs. Approximate bounds are also derived to evaluate the decoding error probability of the probabilistically shaped MLC-PCM.

NIR Mitochondrial Fluorescent Probe for Visualizing SO2/Polarity in Drug Induced Inflammatory Mice

SO2 and polarity are important microenvironmental parameters in cells, which are closely related to physiological activities in organisms. The intracellular levels of SO2 and polarity are abnormal in inflammatory models. To this end, a novel near-infrared fluorescent probe BTHP that can simultaneously detect SO2 and polarity was studied. BTHP can sensitively detect polarity change with emission peak change from 677 to 818 nm. BTHP can also detect SO2 with fluorescence change from red to green. After addition of SO2, the fluorescence emission intensity ratio I517/I768 of the probe increased by about 33.6 times. BTHP can determine bisulfite in single crystal rock sugar with high recovery rate (99.2%-101.7%). Fluorescence imaging of cells showed that BTHP could better target mitochondria and monitor exogenous SO2 in A549 cells. More importantly, BTHP has been successfully used for dual channel monitoring SO2 and polarity in drug-induced inflammatory cells and mice. In particular, the probe showed increased green fluorescence with the generation of SO2 and increased red fluorescence with the decrease of polarity in inflammatory cells and mice.

Performance analysis of Polar Codes in a Visible Light Communication System

One of the vital entity of any communication systems is Channel coding, which leads to the design of high performance codes for future wireless systems having low complexity encoder and decoder design. These systems will have a requirement of operating in highly reliable conditions, maximum throughput, and low and high code rates and to work with short and long information messages. Polar codes are one of the promising error correcting channel codes that can be used in these situations to obtain maximum throughput and coding gain in a communication systems because of their capacity approaching performance and finds interests in Satellite communication and 4G/5G services. These codes uses the concept of channel polarization to be constructed. The work proposed in this paper focusses on the Bit Error Rate evaluation and analysis of the Polar codes using traditional approach and Deep learning approach. The feedforward deep learning networks using different activation functions were used for the Deep learning approach. The Successive Cancellation algorithm and its variant using List decoding were used as traditional decoding methodology. The results obtained using Deep learning approach were satisfactory and was matching as per the traditional decoding.

High-order harmonic generation in orthogonal IR and XUV pulses: XUV-initiated channel separation and polarization control

Single-atom high-order harmonic generation (HHG) induced by an intense linearly polarized infrared (IR) field and assisted by a perturbative extreme ultraviolet (XUV) short pulse with linear polarization is analyzed in perpendicular geometry. It is shown that for the case of the initial $p$ state, the two independent projections of the laser-induced dipole are formed by two independent physical channels, which are responsible for IR-induced HHG and XUV-initiated HHG. This property of the laser-induced dipole is utilized for polarization control of the generated radiation. An alternative scheme for studying XUV-initiated HHG is proposed.

Channel Polarization Scheme for Ocean Turbulence Channels in Underwater Visible Light Communication

Underwater wireless communication technology plays an important role in marine environment monitoring and ecological protection. Underwater optical wireless communications (UWOCs) can currently achieve a transmission distance of hundreds of meters, and the rate can reach hundreds of Mbps or even Gbps, with low power consumption and high-speed features. In addition, UWOC also has the advantages of a small transceiver size and strong anti-electromagnetic interference ability, which is especially suitable for scenarios where underwater volume and power consumption are relatively limited. However, UWOC systems face problems such as unstable transceiver ends, ocean turbulence, and so on, resulting in reduced communication reliability and limited transmission distance. Establishing a stable and reliable communication link is critical to extending the communication distance of the UWOC system. In this paper, a model of ocean turbulence channels is established based on the power spectrum inversion method. The transmission characteristics of orbital angular momentum (OAM) light in an ocean turbulence channel are studied, then the mode selection of OAM light is determined. At the same time, the polarization coding technique is applied to the underwater OAM communication system for the first time. The simulation results show that this scheme can effectively extend the communication distance and reduce the system bit error rate.

A golden decade of polar codes: From basic principle to 5G applications

After the pursuit of seventy years, the invention of polar codes indicates that we have found the first capacity-achieving coding with low complexity construction and decoding, which is the great breakthrough of the coding theory in the past two decades. In this survey, we retrospect the history of polar codes and summarize the advancement in the past ten years. First, the primary principle of channel polarization is investigated such that the basic construction, coding method and the classic successive cancellation (SC) decoding are reviewed. Second, in order to improve the performance of the finite code length, we introduce the guiding principle and conclude five design criteria for the construction, design and implementation of the polar code in the practical communication system based on the exemplar schemes in the literature. Especially, we explain the design principle behind the concatenated coding and rate matching of polar codes in 5G wireless system. Furthermore, the improved SC decoding algorithms, such as SC list (SCL) decoding and SC stack (SCS) decoding etc., are investigated and compared. Finally, the research prospects of polar codes for the future 6G communication system are explored, including the optimization of short polar codes, coding construction in fading channels, polar coded modulation and HARQ, and the polar coded transmission, namely polar processing. Predictably, as a new coding methodology, polar codes will shine a light on communication theory and unveil a revolution in transmission technology.

Joint Design of Polar Coding and Physical Network Coding for Two-User Downlink Non-Orthogonal Multiple Access.

In this paper, we propose a joint polar coding and physical network coding (PNC) for two-user downlink non-orthogonal multiple access (PN-DNOMA) channels, since the successive-interference-cancellation-aided polar decoding cannot be optimal for finite blocklength transmissions. In the proposed scheme, we first constructed the XORed message of two user messages. Then, the XORed message was superimposed with the message of the weak User 2 for broadcast. By doing so, we can utilize the PNC mapping rule and polar decoding to directly recover the message of User 1, while at User 2, we equivalently constructed a long-length polar decoder to obtain its user message. The channel polarization and decoding performance can be greatly improved for both users. Moreover, we optimized the power allocation of the two users with their channel conditions by considering the user fairness and the performance. The simulation results showed that the proposed PN-DNOMA can achieve performance gains of about 0.4-0.7 dB over the conventional schemes in two-user downlink NOMA systems.

UAV-Correlated MIMO Channels: 3-D Geometrical-Based Polarized Model and Capacity Analysis

The unmanned aerial vehicle (UAV) communication with the multiple-input–multiple-output (MIMO) system has attracted lots of attention to improve spectral efficiency and channel capacity. The large antenna spacing is often required to reduce the spatial correlation between subchannels. However, this requirement cannot be well satisfied in practical scenarios due to the limited dimension of UAV platforms. Therefore, polarization diversity is a promising approach for UAV MIMO systems. In this work, we propose a three-dimensional (3-D) geometrical-based polarized model for UAV-correlated MIMO channels. By utilizing the geometrical theory of polarization, we describe the channel depolarization caused by the terrestrial scattering environment based on the multicylinder geometrical model and then acquire the channel polarization function and polarized channel impulse response (CIR). Furthermore, we investigate the impact of the key factors, such as the UAV tilt rotation, cross-polarization, and limited antenna spacing on the UAV MIMO channel capacity. To validate the proposed UAV channel model, we compare the spatial correlations of the numerical simulation and UAV field measurement results for the co- and cross-polarized channels, and the close agreements between them are observed. This work can provide useful guidance and support for the design and performance evaluation of UAV communication networks.

Analysis and optimization of polarization effect of telescope group of channel polarization spectrometer

Analysis and optimization of polarization effect of telescope group of channel polarization spectrometer