Channel Polarization Research Articles

Simulation of Ultra-Fast Dynamics Effects in Resonant Inelastic X-ray Scattering of Gas-Phase Water.

Resonant inelastic soft X-ray scattering maps for the water molecule are simulated by combining quantum chemical calculations of X-ray spectroscopy with ab initio molecular dynamics. The resonant inelastic scattering intensity is computed using the Kramers-Heisenberg formalism, which accounts for channel interference and polarization anisotropy. Algebraic diagrammatic construction and density functional theory-based approaches for the calculation of the X-ray transition energies and transition dipole moments of the absorption and emission processes are explored. Conformational sampling of both ground and core-excited intermediate states allows the effects of ultrafast dynamics on the computed maps to be studied. Overall, it is shown how resonant inelastic scattering maps can be simulated with a computationally efficient protocol that can be extended to investigate larger systems.

Concatenated Coding Schemes for High Areal Density Bit-Patterned Media Magnetic Recording

This paper proposes a new concatenated error correction coding scheme for 2-D magnetic recording (TDMR). The designed concatenated coding scheme consists of outer codes as binary polar codes and an inner code as non-binary low-density parity-check (LDPC) code. These error-correcting codes (ECCs) are considered to achieve large coding gains with small bandwidth expansion in the presence of intersymbol interference and inter-track interference. Polar codes have attracted much attention as one of the ECCs that provably achieve the optimal symmetric capacity of memoryless channels with an explicit construction and are decoded by the successive-cancellation decoding algorithm, whose computational complexity is comparatively low. Using systematic polar codes, we are able to design proper low-complexity ECCs with run-length-limited constraints for any TDMR schemes based on the selection criterion (which is called channel polarization ) for choosing parity and information symbols by the magnitude of the approximately calculated mutual information amount regarding each recorded symbol in a codeword. Concretely, the concatenated coding schemes are designed for four-track and three-track recording, and the block error rate (BER) performances of 2-D partial response equalized signal processing schemes with proposed concatenated ECCs for bit-patterned media recording are evaluated. As a result, it shows that the BER performances of the proposed schemes are superior to that of the conventional scheme using a 1-D high rate binary LDPC code.

Universal Construction for Polar Coded Modulation

Recently, the polarization weight (PW), independent of transmission channel, is proposed to construct the polar codes based on the partial orders (POs) of the polarized bit channels (PBCs). In this paper, we propose a general PW (GPW) to solve the universal construction of the multilevel coding polar-coded modulation (MLC-PCM). In the same way, we first study the POs in the MLC-PCM. For the MLC-PCM, the $2^{m}$ -ary modulation can be decomposed into $m$ correlated modulated bit channels (MBCs). Then, each MBC group can be further transformed into a series of PBCs by using the conventional channel polarization. Based on this structure of two-stage channel polarization, we find four types of POs. For the PBCs polarized from the same MBCs, we establish two types of POs to indicate the reliability order of some PBCs. Furthermore, for the PBCs polarized from different MBCs, we explore other two types of POs to reveal the relative order of the PBCs. The general PW (GPW), including the influence of the two-stage channel polarization, is defined to construct the polar codes in the MLC-PCM. Finally, the simulation results are given to verify the effectiveness of the proposed GPW in the MLC-PCM.

Joint Source-Channel Polarization With Side Information

As an extension of source polarization and channel polarization, this paper considers joint source-channel polarization, which results in a joint source-channel coding (JSCC) scheme using a quasi-uniform systematic polar code (SPC). In this JSCC scheme, the source with side information is encoded as a systematic polar codeword and only parity bits are transmitted through the channel. The indices of systematic bits are quasi-uniform, which enable the source and the channel to be jointly polarized to either a high entropy part or a low entropy part. The analysis reveals that the quasi-uniform SPC cannot be constructed via original polar coding. To solve this problem, additional bit-swap coding is introduced to modify original polar coding and construct this kind of SPCs. The proposed JSCC scheme can asymptotically approach the information-theoretical limit. For the noiseless channel, the proposed scheme is degraded into classic Slepain-Wolf coding or lossless source coding based on parity approach.

Novel dual channel polarization interference imaging system

The interference images with fixed spectral resolution can be obtained by using the existing static polarization-difference imaging system because the optical path of the system cannot be changed flexibly. However, for different detection targets, the spectral resolution of the system determined by the optical path difference must be appropriate. To satisfy a variety of application requirements, a novel dual channel polarization-difference interference imaging system (DPDⅡS), based on the lateral shear of the wide-field-of-view Savart polariscope (WSP) and the modulated Savart polariscope (MSP), is presented. The two-dimensional space images of a target and orthogonal interference images can be obtained by adjusting the MSP under different lateral displacements simultaneously. In addition, the remarkable characteristics of the system avoid spilling over rays and optimizing the system optical path effectively. In this paper, by using the Jones matrix, the system structure is demonstrated and the theoretical principle of DPDⅡS is analyzed in detail. The amplitudes of the four beams from the MSP and the interference intensity expressions of the coherent light are derived. Then the splitting characteristics of the Savart polariscope (SP) and WSP are presented. It is concluded that the WSP has better shear ability than SP and the WSP can optimize the optical path effectively compared with Wollaston prism in the DPDⅡS. The change ranges of the optical path difference and lateral displacement produced by the MSP for structure angles =/3, /4, /6 are analyzed in detail. The reconstructed orthogonal interferograms and the experimental interferograms under 632.8 nm monochromatic light for dMSP=1.00, 1.10, 1.20, 1.30 mm are obtained. A comparison between the experimental interference images and the simulated images proves that the interference fringes with different resolutions can be obtained simultaneously by adjusting the MSP. Meanwhile, the light intensities of the double optical paths are approximately equal and the same optical path difference is generated for the dual channel with the movement of MSP. The experimental results are consistent with the theoretical analyses. The spatial images of parallel and vertical components are detected under 632.8 nm polychromatic light. Then the total intensity image and the polarization-difference image are obtained through data processing. The conclusion that the polarization difference intensity image has a high resolution compared with the polarization intensity image is presented. The study has reference significance and practical value for the dual channel polarization interference imaging system.

Polarization of the Rényi Information Dimension With Applications to Compressed Sensing

In this paper, we show that the Hadamard matrix acts as an extractor over the reals of the Renyi Information Dimension (RID), in an analogous way to how it acts as an extractor of the discrete entropy over finite fields. More precisely, we prove that the RID of an i.i.d. sequence of mixture random variables polarizes to the extremal values of 0 and 1 (corresponding to discrete and continuous distributions) when transformed by a Hadamard matrix. Furthermore, we prove that the polarization pattern of the RID admits a closed form expression and follows exactly the Binary Erasure Channel (BEC) polarization pattern in the discrete setting. We discuss the applications of the RID polarization to Compressed Sensing of i.i.d. sources. In particular, we use the RID polarization to construct a family of deterministic ±1-valued sensing matrices for Compressed Sensing. We run numerical simulations to compare the performance of the resulting matrices with that of the random Gaussian and the random Hadamard matrices. The results indicate that the proposed matrices afford competitive performances, while being explicitly constructed.

Polar Channel Coding Schemes for Two-Dimensional Magnetic Recording Systems

This paper proposes new two-dimensional magnetic recording (TDMR) systems using polar channel coding as practical error correction coding. It is known that the time and space complexities of the encoding/decoding algorithms based on polar channel coding are $\mathcal {O}(N \log N)$ , where $N$ is the codeword (block) length. If we compare the error-correction performance of a polar code with that of a low-density parity-check (LDPC) code in the same rate, it is known that the polar code has a longer length and its decoder still has a lower implementation complexity than the LDPC decoder. Therefore, relatively low-complexity coding schemes are preferable for any TDMR systems under high rates and relatively long codeword lengths. In this paper, the proposed TDMR system serially concatenates a two-dimensional (2-D) modulation code with one-dimensional (1-D) polar codes in each down-track direction. These element polar codes are designed on the fundamentals of the channel polarization theory, which are applied for channels with memory. Actually, it evaluates the performance of the signal processing scheme with concatenated coding and generalized partial response equalization for the proposed TDMR system using bit-patterned media by computer simulations. As a result, it shows that the block error rate performance of the proposed TDMR system with the 2-D modulation and polar channel coding schemes is superior to that of the 1-D system with the conventional 1-D high rate modulation and LDPC coding schemes.

Polarization of a Point-to-Point Channel by a Multiple Access Channel: A New Method for Different Channel Polarization

The polar coding method which was proposed by Arikan is mentioned. In this article, we will apply this method for the polarization of a general Multiple Access Channel. It will be shown that the polarization of a general Multiple Access Channel with a point-to-point channel can be given a more achievable rate region in the general form. The encoding and decoding complexity for these codes are $$O (N \cdot \log N)$$ and error probability for them is $$O(2^{{ - (N)^{\beta } }} )$$ like the original channel polarization method. Some numerical examples for the proposed method and the competitors are also given.

Relaxed Polar Codes

Polar codes are the latest breakthrough in coding theory, as they are the first family of codes with explicit construction that provably achieve the symmetric capacity of discrete memoryless channels. Ar{\i}kan's polar encoder and successive cancellation decoder have complexities of $N \log N$, for code length $N$. Although, the complexity bound of $N \log N$ is asymptotically favorable, we report in this work methods to further reduce the encoding and decoding complexities of polar coding. The crux is to relax the polarization of certain bit-channels without performance degradation. We consider schemes for relaxing the polarization of both \emph{very good} and \emph{very bad} bit-channels, in the process of channel polarization. Relaxed polar codes are proved to preserve the capacity achieving property of polar codes. Analytical bounds on the asymptotic and finite-length complexity reduction attainable by relaxed polarization are derived. For binary erasure channels, we show that the computation complexity can be reduced by a factor of 6, while preserving the rate and error performance. We also show that relaxed polar codes can be decoded with significantly reduced latency. For AWGN channels with medium code lengths, we show that relaxed polar codes can have lower error probabilities than conventional polar codes, while having reduced encoding and decoding computation complexities.

Capacity of the broadband dual-orthogonal polarized MIMO Land Mobile Satellite (LMS) channel: Channel modeling and influenced factors analysis

Generally, the channel capacity of a MIMO system is closely related to its Channel Characteristic Matrix (CCM). In most current studies, the CCMs are formed by an independent identical distribution (i.i.d) model with Rayleigh or Rice distribution and nevertheless incomplete and inaccurate to describe a Broadband Dual-orthogonal Polarized MIMO Land Mobile Satellite (BDM-LMS) channel. In this paper, we build up the BDM-LMS channel model combining a 4-states broadband LMS channel model, time selective fading features, Channel Covariance Information (CCI) model and polarization correlation between antennas. Modeling steps of the channel model are introduced. The main emphasis is placed on the effects of the factors on the channel capacity in BDM-LMS system, such as antenna numbers, temporal correlations, terminal environments, elevation angles and polarization correlations between the DPAs. We provide simulation results to illustrate the effects of these factors through comparisons of the transmit rate, Ergodic Capacity and Outage Capacity. Moreover, the MIMO outage capacity advantages, indicating the benefits of MIMO compared with SISO systems under the same channel condition, are also studied under i.i.d and BDM-LMS channel.

Interference Signal Suppression by Polarization Filters under Estimate Error

For the polarization estimate operation of polarization filter, the polarization filter performance is fully analyzed from antenna polarization property, channel amplitude and phase error, channel noise effect and polarization estimate algorithm in four aspects. The validity of polarization filtering is proved under polarization estimate error condition. The study indicated that, adding polarization filter process in radar sensor to cancel interference and evaluate the performances, optimizing the output of polarization channel and processing method is the key point. The polarization estimate precisions will not directly constraint the performance of polarization filtering. The conclusion will be significant to help single polarized radar improving the polarization measurement and anti-interference ability.

Decode‐and‐forward polar coding scheme for receive diversity: a relay partially perfect retransmission for half‐duplex wireless relay channels

Recently, it is shown that the channel polarisation phenomenon of Arikan's polar codes with their original multilevel construction happens in several levels with perfect, partially perfect and useless bit channels. On the basis of this construction, this study aims to illustrate design principles and decoding steps of cooperative decode-and-forward polar coding schemes for half-duplex relay channel. In these schemes, the authors consider the use of relay retransmission of partially perfect bit channels in time-division process. The source node transmits its polar-coded information to both the relay and the destination nodes during the first time slot. For the second transmission period, the relay first decodes the source signal then after reconstruction of the polarisation matrix, the extracted partially perfect bit channels are recoded using another polar code and finally transmitted to the destination node. At destination, the signals received from both source and relay nodes are processed by using multi-stage successive cancellation decoding for retrieving the original information bits. They demonstrate via numerical results that by carefully constructed polarisation matrix at relay node, their cooperative polar coding schemes can achieve better performances than other previous schemes.

Room-Temperature Spin Filtering in Metallic Ferromagnet-Multilayer Graphene-Ferromagnet Junctions.

We report room-temperature negative magnetoresistance in ferromagnet-graphene-ferromagnet (FM|Gr|FM) junctions with minority spin polarization exceeding 80%, consistent with predictions of strong minority spin filtering. We fabricated arrays of such junctions via chemical vapor deposition of multilayer graphene on lattice-matched single-crystal NiFe(111) films and standard photolithographic patterning and etching techniques. The junctions exhibit metallic transport behavior, low resistance, and the negative magnetoresistance characteristic of a minority spin filter interface throughout the temperature range 10 to 300 K. We develop a device model to incorporate the predicted spin filtering by explicitly treating a metallic minority spin channel with spin current conversion and a tunnel barrier majority spin channel and extract spin polarization of at least 80% in the graphene layer in our structures. The junctions also show antiferromagnetic coupling, consistent with several recent predictions. The methods and findings are relevant to fast-readout low-power magnetic random access memory technology, spin logic devices, and low-power magnetic field sensors.

Cascading polar coding and LT coding for radar and sonar networks

In radar and sonar networks, heavy clutter and noise have generated strong impairments to information transmission and processing. Coding techniques have been widely used to cope with various channel noises and thereby to improve transmission performance. In the study, we investigate a novel cascaded coding scheme for systems operating in adverse electromagnetic environments, e.g., underwater acoustic communications (UAC), where the impulsive noise will be inevitable and the bit error ratio (BER) of receiver will be deteriorated greatly. Our cascaded encoding scheme employs the polar code as inner code while the Luby transform (LT) code as outer code. Inspired on a novel conception of channel polarization, the polar code uses a group of idea sub-channels to carry the useful information, while let other bad sub-channels bear no information. By cascading the outer LT code which accomplishes some parity check to the input of inner code, the performance of inner polar code is improved, as the decoding of polar code relies on a successive cancelation technique which is relatively sensitive to initial input. Error correcting performance of the new cascaded code is studied under impulsive noise characterized by a Middleton Class-A model. Simulations validate the proposed cascaded coding scheme. Compared with the popular low-density parity check (LDPC) code, the cascaded scheme can significantly improve the BER performance in the presence of impulsive interference, which also surpasses another cascaded code that is proved to be effective in impulsive noise channel, i.e., cascaded LDPC and LT coding scheme.

Transmission of a 120-GBd PM-NRZ Signal Using a Monolithic Double-Side EML

A 120-GBd polarization multiplexed NRZ (PMNRZ) signal is generated using a monolithic double side electroabsorption modulated distributed feedback (DFB) laser. Using a pre-amplified direct detection receiver and direct detection faster than Nyquist technique, the optical receiver sensitivities of -18.3 and -13.5 dBm are obtained for a 240-Gb/s (a net data rate of 200 Gb/s with 20% soft-decision forward error correction) PM-NRZ signal at back-to-back and after 2-km transmission, respectively. To the best of our knowledge, this is the highest baud rate transmission reported to date for single channel polarization multiplexed signal generated by a single device for short reach applications and the longest transmission distance (2 km) at baud-rate >100 GBd IM/DD system without CD compensation at 1.55 μm.

Implementation of Polar Codes over AWGN and Binary Symmetric Channel

Objectives: Forward Error Correction (FEC) is a mechanism that has been used for years to improve the reliability of digital communications over wireless channels as they are subjected to interference, fading and noise. The goal of FEC is to add some redundant data to the input stream which facilitates the receiver to recognize and correct the errors with no need of sender to transmit the data again. In this paper we have computed bit error rate using polar codes in an Additive White Gaussian Noise Channel (AWGN) and Binary Symmetric Channel (BSC) at different block lengths. Methods/Analysis: Shannon limit states that it is the maximum amount of information that any given channel can carry. Latterly, there have been inventions in Forward Error Correction (FEC) area that allows today's systems to approach the Shannon limit. One such advancement in FEC is Polar Codes which has mathematically proved to attain the Shannon capacity for Binary Discrete Memoryless Channels using the phenomenon of channel polarization which states that by recursively combining and splitting N individual channels, some channels will become completely noiseless and some become noisy. These noiseless channels are then chosen to send information bits. Findings: We have implemented polar codes over BIAWGN and BSC and have calculated their bit error rate's at different channel ranges. The decoder used for decoding polar codes is successive cancellation decoder and it's seen that the performance is not that good at small block lengths but as the block length increases the performance improves when compared with the un-coded data stream. Applications: As polar codes are the first codes that achieve the Shannon capacity, so they seem to be the best solution for discrete memoryless channels which encounter packet failures and other noisy disturbances. Also, apart from channel encoding, polar codes found its applications in lossy and lossless source coding, coding for secrecy, communication over multiple access channels.

Polar Coding for Bit-Interleaved Coded Modulation

A polar coding scheme is proposed for reliable communication over channels with bit-interleaved coded modulation (BICM). In an ideal information-theoretic model, BICM schemes are modeled as a set of multiple binary-input channels that experience different reliabilities. This model is referred to as multichannel . The conventional scheme for encoding information over multi-channels is to encode separately across the individual constituent channels, which requires multiple encoders and decoders. As opposed to the conventional scheme, we take advantage of the recursive structure of polar codes to construct a unified compound polar code. The proposed scheme has a single encoder and decoder and can be used over multi-channels, in particular over channels with BICM. We prove that the scheme achieves the multi-channel capacity with the same error decay rate as in Arikan's polar codes. Furthermore, due to more levels of channel polarization, we obtain a better finite block length performance compared with the separated polarization scheme. This is confirmed through various simulations over the binary erasure channel and with transmissions over additive white Gaussian noise (AWGN) and fast fading channels with BICM and different modulation orders.

Bipolar Conduction in Tin-Oxide Semiconductor Channel Treated by Oxygen Plasma for Low-Power Thin-Film Transistor Application

In this paper, we investigated the bipolar conduction mechanism in thin-film transistors (TFTs) with oxygen plasma treatment on tin-oxide channel. The optimized p-type thin-oxide TFTs showed an on/off ratio of ${>}{\hbox{10}}^{4}$ , a threshold voltage of $-$ 1.05 V, and a field-effect mobility of ${\hbox{2.14}} {\hbox{cm}}^{2}{\cdot}{\hbox{V}}^{-1}{\cdot}{\hbox{s}}^{-1}$ . By increasing the exposure time of oxygen plasma, excess oxygen was incorporated to thin-oxide channel and converted thin monoxide to oxygen-rich n-type thin dioxide, which in turn led to n-type operation. It indicated that oxygen plasma was the critical factor to determine oxygen concentration, oxygen vacancies, metal ions and channel polarity. This proposed oxygen-content tuning through plasma treatment approach shows great promise in simplification of TFT process that can achieve n-type and p-type TFTs under the same device process.

A study on the multi-antenna geometrical depolarization channel modeling

The traditional geometrical depolarization model that single transmitter to single receiver provides a simple method of polarization channel modeling. It can obtain the geometrical depolarization effect of each path if known the antenna configuration, the polarization field radiation pattern and the spatial distribution of scatters. With the development of communication technology, information transmission spectrum is more and more scarce. The original model provides only a single channel polarization state, so the information will be limited that the polarization state carries in the polarization modulation. The research is so significance that how to carries polarization modulation information by using multi-antenna polarization state. However, the present study shows that have no depolarization effect model for multi-antenna systems. In this paper, we propose a multi-antenna geometrical depolarization model. On the basis of a single antenna to calculate the depolarization effect of the model, and through simulation to analysis the main factors that influence the depolarization effect. This article provides a multi-antenna geometrical depolarization channel modeling that can applied to large-scale array antenna, and to some extent increase the speed of information transmission.

Construction of Polar Codes Exploiting Channel Transformation Structure

Polar Codes are the first binary linear codes that provably achieve the symmetric capacity of arbitrary binary-input discrete memoryless channels. Their construction is explicit as implied by the transformations that lead to channel polarization, and low-complexity encoding and decoding methods are available. While being explicitly defined, exact construction is intractable as it depends on calculating channel parameters of channels whose output alphabets grow exponentially in the code length. To overcome this problem, heuristics have been proposed. In this work, we show how to accelerate one popular construction method by introducing two modifications to the channel transformation step, leaving quality of the results unaffected.