Code Rate Research Articles

Construction and application of polar codes in OFDM underwater acoustic communication

A polar-coded orthogonal frequency-division multiplexing (OFDM) underwater acoustic communication system was developed, and a Monte Carlo (MC) method for constructing optimal polar codes was proposed to improve the performance of the system in this study. Several optimal polar codes with different code lengths and rates were constructed for a shallow-water acoustic channel. Simulations showed that the polar codes constructed using the MC method rendered superior performance than those constructed using the Bhattacharyya parameter and the Gaussian approximation method. In addition, shallow-water acoustic communication experiments were conducted at Xiamen port. The results show that the developed polar-coded OFDM communication system has excellent performance with 196 out of 200 frames achieving error-free transmission, which is much greater than the performance (157 out of 200) of the LDPC-coded OFDM communication system.

Efficient Linear and Affine Codes for Correcting Insertions/Deletions

This paper studies linear and affine error-correcting codes for correcting synchronization errors such as insertions and deletions. We call such codes linear/affine insdel codes. Linear codes that can correct even a single deletion are limited to having an information rate at most (achieved by the trivial two fold repetition code). Previously, it was (erroneously) reported that more generally no nontrivial linear codes correcting deletions exist, i.e., that the -fold repetition codes and its rate of are basically optimal for any . We disprove this and show the existence of binary linear codes of length and rate just below capable of correcting insertions and deletions. This identifies rate as a sharp threshold for recovery from deletions for linear codes and reopens the quest for a better understanding of the capabilities of linear codes for correcting insertions/deletions. We prove novel outer bounds and existential inner bounds for the rate vs. (edit) distance trade-off of linear insdel codes. We complement our existential results with an efficient synchronization-string-based transformation that converts any asymptotically good linear code for Hamming errors into an asymptotically good linear code for insdel errors. Last, we show that the -rate limitation does not hold for affine codes by giving an explicit affine code of rate which can efficiently correct a constant fraction of insdel errors.

Network Coding Rate Region With Delay and Reliability Constraint

In this paper, we consider an end-to-end loss network with a limited delay and investigate the maximum network coding rate achievable under a given block length and error probability. We first formulate block network coding for reliable data transmission as an optimization problem and then analyze the throughput, success probability and delay in terms of block length and packet loss probability for block network coding. Results show that the coding rate gradually approaches the capacity 1 – ε as the delay increases, where ε is the packet loss probability. When feedback is allowed in the limited delay, the rate increases in a faster way compared with no retransmission.

The Impacts of Neutron Star Structure and Base Heating on Type I X-Ray Bursts and Code Comparison

Type I X-ray bursts are rapidly brightening phenomena triggered by thermonuclear burning on the accreting layers of a neutron star (NS). The light curves represent the physical properties of NSs and the nuclear reactions on the proton-rich nuclei. The numerical treatments of the accreting NS and physics of the NS interior are not established, which shows uncertainty in modeling for observed X-ray light curves. In this study, we investigate theoretical X-ray burst models compared with burst light curves with GS 1826-24 observations. We focus on the impacts of the NS mass and radius and base heating on the NS surface using the MESA code. We find a monotonic correlation between the NS mass and the parameters of the light curve. The higher the mass, the longer the recurrence time and the greater the peak luminosity. While the larger the radius, the longer the recurrence time, the peak luminosity remains nearly constant. In the case of increasing base heating, both the recurrence time and peak luminosity decrease. We also examine the above results with a different numerical code, HERES, based on general relativity and consider the central NS. We find that the burst rate, energy, and strength are almost the same in two X-ray burst codes by adjusting the base heat parameter in MESA (the relative errors ≲5%), while the duration and rise times are significantly different between (the relative error is possibly ∼50%). The peak luminosity and the e-folding time change irregularly between two codes for different accretion rates.

Improving the error performance of offset pulse position modulation using Reed–Solomon error correction code and low-density parity

An innovative performance study of an offset pulse-position modulation (OPPM) scheme is presented in this work with Reed–Solomon (RS) and low-density parity-checking (LDPC). The main aim is to resolve the errors of OPPM three using an RS or LDPC as a sporadic set of forward error correction (FEC). In this regard, the separate FEC has been utilized with coding that is based on multi-level, and waveform shaping based on the trellis. To systematically conduct this research, the greatest transmission efficiency that associated with the optimum RS code rates at different fiber normalization bandwidths is evaluated. Furthermore, the transmission efficiencies, channel extension, as well as the required number of photons per pulse of OPPM before and after the integration with RS or LDPC are compared. The results indicate an enhancement of mitigating the system's bit error rate and delivering more error-free data to the receiver in the occasion of applying the optimal settings of the RS or LDPC.

Transformer-Based Detection for Highly Mobile Coded OFDM Systems.

This paper is concerned with mobile coded orthogonal frequency division multiplexing (OFDM) systems. In the high-speed railway wireless communication system, an equalizer or detector should be used to mitigate the intercarrier interference (ICI) and deliver the soft message to the decoder with the soft demapper. In this paper, a Transformer-based detector/demapper is proposed to improve the error performance of the mobile coded OFDM system. The soft modulated symbol probabilities are computed by the Transformer network, and are then used to calculate the mutual information to allocate the code rate. Then, the network computes the codeword soft bit probabilities, which are delivered to the classical belief propagation (BP) decoder. For comparison, a deep neural network (DNN)-based system is also presented. Numerical results show that the Transformer-based coded OFDM system outperforms both the DNN-based and the conventional system.

Non-Gaussian Reconciliation for Continuous-Variable Quantum Key Distribution

Non-Gaussian modulation can improve the performance of continuous-variable quantum key distribution (CV QKD). For Gaussian-modulated coherent-state CV QKD, photon subtraction can realize non-Gaussian modulation, which can be equivalently implemented by non-Gaussian postselection. However, non-Gaussian reconciliation has not been deeply researched, which is one of the key technologies in CV QKD. In this paper, we propose a non-Gaussian reconciliation method to obtain identical keys from non-Gaussian data. Multidimensional reconciliation and multiedge-type low-density parity-check codes (MET LDPC) are used in a non-Gaussian reconciliation scheme, where the layered belief propagation decoding algorithm of MET LDPC codes is used to reduce the decoding complexity. Furthermore, we compare the error-correction performance of Gaussian data and non-Gaussian data. The results show that the error-correction performance of non-Gaussian data is better than Gaussian data, where the frame error rate can be reduced by 50 % for code rate 0.1 at SNR of 0.1554 and the average iteration number can be reduced by 25 %.

Generalized Singleton Bound and List-Decoding Reed–Solomon Codes Beyond the Johnson Radius

In this paper we take a combinatorial approach to the problem of list-decoding, which allows us to determine the precise relation (up to the exact constant) between the decoding radius, list size, and code rate. We prove a generalized Singleton bound for a given list size, and conjecture that the bound is tight for most Reed–Solomon (RS) codes over large enough finite fields. We also show that the conjecture holds true for list sizes 2 and 3, and as a by product show that most RS codes with a rate of at least 1/9 are list-decodable beyond the Johnson radius. Last, we give the first explicit construction in the literature of such RS codes. The main tools used in the proof are a new type of linear dependency between codewords of a code that are contained in a small Hamming ball, and a surprising connection between list-decoding and the notion of cycle space in graph theory. Both of them are new, and may be of independent interest.

Adaptive Coded Modulation for OFDM System

This paper studies the adaptive coded modulation for coded OFDM system using punctured convolutional code, channel estimation, equalization and SNR estimation. The channel estimation based on block type pilot arrangement is performed by sending pilots at every sub carrier and using this estimation for a specific number of following symbols. Signal to noise ratio is estimated at receiver and then transmitted to the transmitter through feedback channel ,the transmitter according to the estimated SNR select appropriate modulation scheme and coding rate which maintain constant bit error ratelower than the requested BER. Simulation results show that better performance is confirmed for target bit error rate (BER) of (10-3) as compared to conventional modulation schemes, the convolutional coded modulation offers a SNR gains of 5 dB compared to uncoded state at BER of 10-3. The proposed adaptive OFDM scheme maintains fixed BER under changing channel conditions.

Jamming of LoRa PHY and Countermeasure

LoRaWAN forms a one-hop star topology where LoRa nodes send data via one-hop uplink transmission to a LoRa gateway. If the LoRa gateway can be jammed by attackers, it may not be able to receive any data from any nodes in the network. Our empirical study shows that although the LoRa physical layer (PHY) is robust and resilient by design, it is still vulnerable to synchronized jamming chirps. Potential protection solutions (e.g., collision recovery, parallel decoding) may fail to extract LoRa packets if an attacker transmits synchronized jamming chirps at higher power. To protect the LoRa PHY from such attacks, we propose a new protection method that can separate LoRa chirps from jamming chirps by leveraging their difference in power domain. We note that the new protection solution is orthogonal to existing solutions that leverage the chirp misalignment in the time domain or the frequency disparity in the frequency domain. We conduct experiments with COTS LoRa nodes and software-defined radios with varied experiment settings such as different spreading factors, bandwidths, and code rates. Results show that synchronized jamming chirps at high power can jam all previous solutions, whereas our protection solution can effectively protect LoRa gateways from the jamming attacks.

Delirium is under-reported in discharge summaries and in hospital administrative systems: a systematic review

Background Accurate recording of delirium in discharge summaries (DS) and hospital administrative systems (HAS) is critical for patient care. Objective To systematically review studies reporting the frequency of delirium documentation and coding in DS and HAS, respectively. Method We searched Medline, Embase, PsycINFO and Web of Science databases from inception to 23 June 2021. Eligibility criteria included requiring the term delirium in DS or HAS. Screening and full-text reviews were performed independently by two reviewers. Risk of bias (RoB) was assessed using the Effective Public Health Practice Project tool. Results The search yielded 7,910 results; 24 studies were included. The studies were heterogeneous in design and size (N=25 to 809,512). Mean age ranged from 57 to 84 years. Four studies reported only overall DS documentation and HAS coding in whole hospital or healthcare databases. Twenty studies used additional delirium ascertainment methods (e.g. chart review) in smaller patient subsets. Studies reported either DS figures only (N=8), HAS figures only (N=11), or both (N=5). Documentation rates in DS ranged from 0.1% to 64%. Coding rates in HAS ranged from 1.5% to 49%. Some studies explored the impact of race, and nurse versus physician practice. No significant differences were reported for race; one study reported that nurses showed higher documentation rates in DS relative to physicians. Most studies (N=22) had medium to high RoB. Conclusion Delirium is a common and serious medical emergency, yet studies show considerable under-documentation and under-coding in healthcare systems. This has important implications for patient care and service planning. Healthcare systems need to take action to reach satisfactory delirium documentation and coding rates.

On the construction of new toric quantum codes and quantum burst-error-correcting codes

A toric quantum error-correcting code construction procedure is presented in this work. A new class of an infinite family of toric quantum codes is provided by constructing a classical cyclic code on the square lattice $${\mathbb {Z}}_{q}\times {\mathbb {Z}}_{q}$$ for all odd integers $$q\ge 5$$ and, consequently, new toric quantum codes are constructed on such square lattices and from geometrically uniform codes regardless of whether q can be represented as a sum of two squares. Furthermore, this work supplies for each q the polyomino shapes that tessellate the corresponding square lattices and, consequently, tile the lattice $${\mathbb {Z}}^{2}$$ . The quantum channel without memory to be considered for these constructed toric quantum codes is symmetric, since the $${\mathbb {Z}}^{2}$$ -lattice is autodual. Moreover, we propose a quantum interleaving technique by using the constructed toric quantum codes, which shows that the code rate and the coding gain of the interleaved toric quantum codes are better than the code rate and the coding gain of Kitaev’s toric quantum codes for $$q=2n+1$$ , where $$n\ge 2$$ , and of an infinite class of Bombin and Martin-Delgado’s toric quantum codes. In addition to the proposed quantum interleaving technique that improves such parameters, it can be used for burst-error correction in errors which are located, quantum data stored and quantum channels with memory.

Adaptive Parameters for LoRa-Based Networks Physical-Layer.

Sub-GHz communication provides long-range coverage with low power consumption and reduced deployment cost. LoRa (Long-Range) has emerged, among existing LPWAN (Low Power Wide Area Networks) technologies, as a promising physical layer alternative to provide ubiquitous connectivity to outdoor IoT devices. LoRa modulation technology supports adapting transmissions based on parameters such as carrier frequency, channel bandwidth, spreading factor, and code rate. In this paper, we propose SlidingChange, a novel cognitive mechanism to support the dynamic analysis and adjustment of LoRa network performance parameters. The proposed mechanism uses a sliding window to smooth out short-term variations and reduce unnecessary network re-configurations. To validate our proposal, we conducted an experimental study to evaluate the performance concerning the Signal-to-Noise Ratio (SNR) parameter of our SlidingChange against InstantChange, an intuitive mechanism that considers immediate performance measurements (parameters) for re-configuring the network. The SlidingChange is compared with LR-ADR too, a state-of-the-art-related technique based on simple linear regression. The experimental results obtained from a testbed scenario demonstrated that the InstanChange mechanism improved the SNR by 4.6%. When using the SlidingChange mechanism, the SNR was around 37%, while the network reconfiguration rate was reduced by approximately 16%.

Performance Improvement of CDMA Wireless Sensor Networks in Low SNR Channels Based on Raptor Codes

Low signal to noise ratio (SNR) channels require careful design of communication systems in order to operate reliably in such extreme channels. Special measures and techniques must be considered when designing communication systems for such environments to counteract the effect of high noise power. Channel coding is a powerful tool to aid against adverse channel conditions including low SNR. Coupling channel coding with a spreading technique can further strengthen the performance of communication systems. Hence, we studied the performance of a system that combines Raptor codes with direct sequence code division multiple access (DS-CDMA) in low SNR scenarios. The studied design can operate in a wide range of low SNR values. Simulation results show that the system can offer satisfactory BER performance at different code rates. Also, combining Raptor codes with DS-CDMA showed an improvement of approximately 6 dB when compared with other schemes using DS-CDMA in low SNR conditions.

Impact of colocated behavioral health on OB-GYN clinicians' rate of perinatal behavioral health diagnosis and psychotropic prescription

ObjectiveTo examine the association of colocated behavioral health(BH) care with rates of OB-GYN clinician coding of BH diagnoses and BH medications. MethodUsing 2 years of EMR data from perinatal individuals treated across 24 OB-GYN clinics, we tested the hypothesis that colocated BH care would increase rates of OB-GYN BH diagnoses and psychotropic prescription. ResultsPsychiatrist integration(0.1 FTE) was associated with 45.7% higher odds of OB-GYN coding for BH diagnoses and BH clinician integration was associated with 25% lower odds of OB-GYN BH diagnosis and 37.7% lower odds of BH medication prescription. Non-white patients had 28–74% and 43–76% lower odds of having a BH diagnosis and a BH medication ordered, respectively. The most common diagnoses were anxiety and depressive disorders(60%) and the most prescribed BH medications were SSRIs(86%). ConclusionsOB-GYN clinicians made fewer BH diagnoses and prescribed fewer psychotropics after 2.0 FTE BH clinician integration, a possible indication of external referrals for BH treatment. Non-white patients received BH diagnoses and medications less often than white patients. Future research in real world implementation of BH integration in OB-GYN clinics should examine fiscal strategies that support BH care manager-OB-GYN collaboration as well as methods to ensure equitable delivery of BH care.

New LP-Based Upper Bounds in the Rate-Vs.-Distance Problem for Binary Linear Codes

We develop a new family of linear programs, that yield upper bounds on the rate of binary linear codes of a given distance. Our bounds apply <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">only to linear codes</i> . Delsarte’s LP is the weakest member of this family and our LP yields increasingly tighter upper bounds on the rate as its control parameter increases. Numerical experiments show significant improvement compared to Delsarte. These convincing numerical results, and the large variety of tools available for asymptotic analysis, give us hope that our work will lead to new improved asymptotic upper bounds on the possible rate of linear codes. A slightly prior work by Coregliano, Jeronimo and Jones offers a closely related family of linear programs which converges to the true bound. Here we provide a new proof of convergence for the same LPs.

Adaptive transmission construction based on polar codes

In actual communication scenarios, wireless transmission channels have the nature of heterogeneity. In order to ensure that data can be transmitted with high reliability and low delay, this paper designs a quasi-optimal polar code that can adapt to various channel environments, which called Q-polar code. Based on the polarization theory of polar codes and the channel state information (CSI), the index set of polar codes is designed and constructed to perform data transmission tasks. The simulation results show that the bit error rate (BER) performance of proposed scheme can be improved compared with traditional polar code, especially when the code length N is small and the code rate is large.

Sparse spike trains and the limitation of rate codes underlying rapid behaviours.

Animals live in dynamic worlds where they use sensorimotor circuits to rapidly process information and drive behaviours. For example, dragonflies are aerial predators that react to movements of prey within tens of milliseconds. These pursuits are likely controlled by identified neurons in the dragonfly, which have well-characterized physiological responses to moving targets. Predominantly, neural activity in these circuits is interpreted in context of a rate code, where information is conveyed by changes in the number of spikes over a time period. However, such a description of neuronal activity is difficult to achieve in real-world, real-time scenarios. Here, we contrast a neuroscientists' post-hoc view of spiking activity with the information available to the animal in real-time. We describe how performance of a rate code is readily overestimated and outline a rate code's significant limitations in driving rapid behaviours.

Design of Polar Codes and PAC Codes for SCL Decoding

The performance of a code under the maximum-likelihood (ML) decoder highly depends on the weight enumerating function (WEF). However, how to compute efficiently the WEF of a polar code or a polarization-adjusted convolutional (PAC) code is still an open problem. For the design of stand-alone polar codes, we consider enumerating the number of minimum-weight non-zero codewords of the polar code. The block error rate (BLER) under the ML decoder can be approximated as a function of the minimum weight of non-zero codewords and its multiplicity. On the other hand, for the design of PAC codes, we consider enumerating the WEF averaged over the ensemble of random PAC codes. The ML-BLER upper bound can be represented as a function of the WEF. The bit-channel selection algorithms for polar codes and PAC codes are proposed, which take both utilization of the polarization effect and the ML decoding performance as selection criteria. Simulation results show that the proposed stand-alone polar codes are competitive when the block length gets larger. Also, simulation results show that the proposed PAC codes yield excellent performance for a wide range of code rates and block lengths and outperform the 5G polar codes.

A Construction of Maximum Distance Profile Convolutional Codes With Small Alphabet Sizes

Convolutional codes are essential in a wide range of practical applications due to their efficient non-algebraic decoding algorithms. In this paper, we first propose a new family of matrices over finite fields by combining Vandermonde and Moore matrices. Using favourable properties of the matrices in this new family enables us to construct a new family of convolutional codes with memory 1 and maximum distance profile. It is notable that the alphabet sizes of this new family of convolutional codes with maximum distance profile can be kept significantly smaller than those in the literature. Keeping the code rate to a constant, the alphabet size is roughly the square root of the previously best-known value.