Convolutional Codes Research Articles

LidarCSNet: A Deep Convolutional Compressive Sensing Reconstruction Framework for 3D Airborne Lidar Point Cloud

Lidar scanning is a widely used surveying and mapping technique ranging across remote-sensing applications involving topological, and topographical information. Typically, lidar point clouds, unlike images, lack inherent consistent structure and store redundant information thus requiring huge processing time. The Compressive Sensing (CS) framework leverages this property to generate sparse representations and accurately reconstructs the signals from very few linear, non-adaptive measurements. The reconstruction is based on valid assumptions on the following parameters- (1) sampling function governed by sampling ratio for generating samples, and (2) measurement function for sparsely representing the data in a low-dimensional subspace. In our work, we address the following motivating scientific questions- Is it possible to reconstruct dense point cloud data from a few sparse measurements? And, what could be the optimal limit for CS sampling ratio with respect to overall classification metrics? Our work proposes a novel Convolutional Neural Network based deep Compressive Sensing Network (named LidarCSNet) for generating sparse representations using publicly available 3D lidar point clouds of the Philippines. We have performed extensive evaluations for analysing the reconstruction for different sampling ratios {4%, 10%, 25%, 50% and 75%} and we observed that our proposed LidarCSNet reconstructed the 3D lidar point cloud with a maximum PSNR of 54.47 dB for a sampling ratio of 75%. We investigate the efficacy of our novel LidarCSNet framework with 3D airborne lidar point clouds for two domains - forests and urban environment on the basis of Peak Signal to Noise Ratio, Haussdorf distance, Pearson Correlation Coefficient and Kolmogorov-Smirnov Test Statistic as evaluation metrics for 3D reconstruction. The results relevant to forests such as Canopy Height Model and 2D vertical profile are compared with the ground truth to investigate the robustness of the LidarCSNet framework. In the urban environment, we extend our work to propose two novel 3D lidar point cloud classification frameworks, LidarNet and LidarNet++, achieving maximum classification accuracy of 90.6% as compared to other prominent lidar classification frameworks. The improved classification accuracy is attributed to ensemble-based learning on the proposed novel 3D feature stack and justifies the robustness of using our proposed LidarCSNet for near-perfect reconstruction followed by classification. We document our classification results for the original dataset along with the point clouds reconstructed by using LidarCSNet for five different measurement ratios - based on overall accuracy and mean Intersection over Union as evaluation metrics for 3D classification. It is envisaged that our proposed deep network based convolutional sparse coding approach for rapid lidar point cloud processing finds huge potential across vast applications, either as a plug-and-play (reconstruction) framework or as an end-to-end (reconstruction followed by classification) system for scalability.

Research on image super-resolution algorithm based on mixed deep convolutional networks

The existing image processing methods had aimed at the problems of blurred image reconstruction, large noise, and poor visual perception. The improved image super-resolution algorithm based on mixed deep convolutional networks is proposed in the paper. Firstly, the proposed method can shrink the low-resolution image to the specified size in upsampling phase. Secondly, it can extract features from low-resolution images. It sends the extracted initial features into the convolutional coding and decoding structure for image features. Thirdly, the feature extraction and calculation in high-dimensions are performed using dilated convolution in reconstruction layer. The high-resolution image had been reconstructed. The proposed method had been compared with state-of-arts on Set5, Set14, BSD100, and Urban100 datasets. The experimental results can show that the Peak Signal-to-Noise Ratio is increased by some ranges, and the Structural Similarity is increased by some effective percentage points.

Twisted-Pair Superposition Transmission

We propose in this paper a new coding scheme called twisted-pair superposition transmission (TPST). The encoding is to “mix together” a pair of basic codes by superposition, while the decoding can be implemented as a successive cancellation list decoding algorithm. The most significant features of the TPST code are its predictable performance that can be estimated numerically from the basic codes and its flexible construction in the sense that it can be easily adapted to different coding rates. To construct good TPST codes in the finite length regime, we propose two design approaches – rate allocation and partial superposition. By taking tail-biting convolutional codes (TBCC) as basic codes, we show by numerical results that the constructed TPST-TBCCs have performance close to the random coding union bound in the short length regime.

Efficient and Robust Distributed Matrix Computations via Convolutional Coding

Distributed matrix computations - matrix-matrix or matrix-vector multiplications - are well-recognized to suffer from the problem of stragglers (slow or failed worker nodes). Much of prior work in this area is (i) either sub-optimal in terms of its straggler resilience, or (ii) suffers from numerical problems, i.e., there is a blow-up of round-off errors in the decoded result owing to the high condition numbers of the corresponding decoding matrices. Our work presents a convolutional coding approach to this problem that removes these limitations. It is optimal in terms of its straggler resilience, and has excellent numerical robustness as long as the workers' storage capacity is slightly higher than the fundamental lower bound. Moreover, it can be decoded using a fast peeling decoder that only involves add/subtract operations. Our second approach has marginally higher decoding complexity than the first one, but allows us to operate arbitrarily close to the storage capacity lower bound. Its numerical robustness can be theoretically quantified by deriving a computable upper bound on the worst case condition number over all possible decoding matrices by drawing connections with the properties of large block Toeplitz matrices. All above claims are backed up by extensive experiments done on the AWS cloud platform.

Performance study of a serial relay CC-OGSM-SD free space optical system based on an M distribution model

This paper proposes a novel, to the best of our knowledge, convolutional coding (CC)-optical generalized spatial modulation (OGSM)-spatial diversity (SD) serial relay system under M distribution. In this work, two types of SD schemes are considered both at the relay node and receiver, and the decode-and-forward (DF) relay transmission protocol is adopted. Taking into account the combined effects of path loss, pointing error, and atmospheric turbulence, the closed-form expressions for the average bit error rate (ABER) of the serial relay uncoded and CC-OGSM-SD free space optical (FSO) system are derived using Meijer's G-function. On the basis of theoretical derivation, the ABER of the proposed system and other common multiple input multiple output schemes in FSO systems are compared through simulation. In addition, the effects of the number of relay nodes, link distance between relays, and different OGSM configurations, SD schemes, and coding rates on the ABER of the system are also analyzed via simulation. Monte Carlo simulations indicate the correctness of the numerical results. The simulation results show that the serial relay CC-OGSM-SD FSO system has lower ABER and higher spectral efficiency.

Low Complexity Modified Viterbi Decoder with Convolution Codes for Power Efficient Wireless Communication

Low Complexity Modified Viterbi Decoder with Convolution Codes for Power Efficient Wireless Communication

Convolutional Sparse Coding Using Pathfinder Algorithm-Optimized Orthogonal Matching Pursuit With Asymmetric Gaussian Chirplet Model in Bearing Fault Detection

Sparse representation has been widely used in bearing fault impact detection, which can find the impact that best matches the fault waveform from the pre-defined dictionary and recover the fault impulse waveform. However, the current dictionary of sparse representation and the efficiency of sparse representation algorithm need to be improved. In order to accurately detect the fault impulse in the original signal, a convolutional sparse coding using pathfinder algorithm-optimized orthogonal matching pursuit with asymmetric Gaussian chirplet model (CSC-OAGCM) is proposed in this paper. A new time-frequency atom prototype, AGCM, is used to match the fault impulse waveform. The specific application steps of the proposed algorithm are as follows: Firstly, a convolution dictionary is constructed with atoms generated by AGCM. Subsequently, based on the convolution dictionary, a pathfinder algorithm-optimized orthogonal matching pursuit algorithm is used to solve the sparse representation and optimize the atomic parameters to achieve the best approximation of the original signal. In other words, the proposed method detects the convolutional sparse patterns in the signal. A simulation signal, two sets of mixed signals of experimental data collected from the experimental platform and an axle box vibration signal collected from the actual operating train are used to verify the effectiveness of proposed method. Additionally, the spectral kurtosis and empirical wavelet transform are also used to process these signals, and their processing results are compared with those obtained by the proposed method to demonstrate the superiority of the proposed method.

Iterative Threshold Channel Estimation in ORGV Convolutional Code MISO-OFDM System

ABSTRACT In the orthogonal frequency division multiplexing (OFDM) transmission system, when the digital symbols are transmitted in the wireless channel, it would be affected by a lot of noise interference due to the unsatisfactory condition characteristics of the wireless channel itself, therefore, the symbol error and bit error would be generated. To achieve a certain bit error rate (BER) under the condition of known signal-to-noise ratio (SNR), convolutional channel coding and block interleaver should be utilized to further reduce the BER. Moreover, convolutional code is almost utilized in all wireless communication systems. This paper proposes a convolutional code channel estimation method in multiple-input single-output (MISO)-based OFDM (MISO-OFDM) system with frequency-shift m-sequence (FSMS) as guard interval (GI) for avoiding inter-symbol interference (ISI). The proposed space-frequency block code (SFBC) MISO-OFDM system achieves higher transmit diversity gains and better BER performance. Simulation results verify that the proposed iterative threshold channel estimation (ITCE) method in octal representation generation vector (ORGV) convolutional code 4 × 1 MISO-OFDM system provides good BER and normalized mean squared error (NMSE) performance with significant coding gains in both static and dynamic multipath channels.

Improving bit error-rate based on adaptive Bose-Chaudhuri Hocquenghem concatenated with convolutional codes

Several algorithms have been proposed to avoid the error floor region, such as the concatenation codes that requires high computational demands in addition to high complexity. This paper proposes a technique based on using cascaded BCH and convolutional codes that leads to better error correction performance. Moreover, an adaptive method based on sensing the channel's noise to determine the number of the parity bits that will be added to the used BCH that reduces the consumed bandwidth and the transmitted parity bits is presented. A further enhancement is fulfilled by using parallel processing branches, resulting in reducing the consumed time and speed up the performance. The results show that the proposed code presents a better performance. A high reduction in the number of cycles that will be used in the encoding and decoding compared with the classical method and finally a flexible parity bits method based on the signal-to-noise ratio of the channel that reduced the parity bits which leads to reduce the consumed bandwidth. The MATLAB simulation and the field programmable gate array (FPGA) implementation will be provided in this paper to validate the proposed concept.

Tight Upper Bound on the Bit Error Rate of Convolutional Codes over Correlated Nakagami-<i>m</i> Fading Channels

Tight Upper Bound on the Bit Error Rate of Convolutional Codes over Correlated Nakagami-<i>m</i> Fading Channels

Comparison of BCH Code Performance in LTE-Advanced Cooperative System in Suburban, Urban and Rural Environment Based on WINNER II Channel Model

Multi-path fading is a severe issue that causes fluctuations in the amplitudes of the received signals. For combating this issue, several researchers have used cooperative communication in the Long-Term Evolution (LTE)-advanced system. To further decrease the degradative effects of transmitted signals, various error correction techniques can be used to recover the erroneous components, especially when the channel has been deep fading. The paper investigates the general performance of the Convolutional Codes (CC) in the LTE-advanced cooperative system and compare it with the Bose-Chaudhuri-Hocquenghem (BCH) codes. The comparison is based on WINNER II project as the channel model between the nodes in the two coding processes. To validate the advantages of BCH code, the process were tested on three different environments; a suburban macro-cell, urban macro-cell, and the rural micro-cell with prior study to understand the appropriate relay height in every environment. Path loss models for each environment were derived and proposed as part of the proposed simulation framework. Conducted simulation studies based on bit error rate and direct connection showed that the use of the CC and the BCH codes in a relay technologies could significantly increase the system performance. It was noted that the performance of the system which used BCH nodes was better than the system using CC nodes in an LTE-advanced cooperative system.

Construction of LDPC convolutional codes via difference triangle sets

In this paper, a construction of (n,k,delta ) LDPC convolutional codes over arbitrary finite fields, which generalizes the work of Robinson and Bernstein and the later work of Tong is provided. The sets of integers forming a (k, w)-(weak) difference triangle set are used as supports of some columns of the sliding parity-check matrix of an (n,k,delta ) convolutional code, where nin {mathbb {N}}, n>k. The parameters of the convolutional code are related to the parameters of the underlying difference triangle set. In particular, a relation between the free distance of the code and w is established as well as a relation between the degree of the code and the scope of the difference triangle set. Moreover, we show that some conditions on the weak difference triangle set ensure that the Tanner graph associated to the sliding parity-check matrix of the convolutional code is free from 2ell -cycles not satisfying the full rank condition over any finite field. Finally, we relax these conditions and provide a lower bound on the field size, depending on the parity of ell , that is sufficient to still avoid 2ell -cycles. This is important for improving the performance of a code and avoiding the presence of low-weight codewords and absorbing sets.

Low complexity iterative decoding of Reed–Solomon convolutional concatenated codes

SummaryThe power limitation is the predominant challenge for achieving a reliable communication transmission for aerospace systems. Therefore, it is appealing to use robust channel coding techniques with a low decoding complexity. The robust forward error correction scheme that uses a Reed–Solomon as an outer code concatenated with a convolutional code as an inner code is an attractive scheme whose applications are widely used in wireless and space communications. However, iterative soft‐decision decoding of that concatenated code is still an open research challenge. This paper proposes a reduced complexity iterative decoding algorithm for this concatenated coding scheme. The soft‐output adaptive Viterbi algorithm with a dynamic discarding threshold has been adopted to decode the inner convolutional code while the outer decoder will be based on a bit‐level modified Chase algorithm. We have used the Hamming metric instead of the Euclidean metric, which is not only much less complex but also overcomes the lack of channel information on the outer decoder input. Simulation results using the proposed soft information exchange decoding mechanism show that a considerable performance enhancement over the classical decoding scheme as well as a significant reduction in complexity over the existing decoding algorithms that use an iterative process to decode this concatenated coding scheme. The adaptive decoding of the inner convolutional code can gain a complexity reduction of 90% after 5 iterations compared to the soft‐output Viterbi algorithm while maintaining the small performance loss from the maximum a posteriori decoding algorithm.

An Embedding Strategy Using Q-Ary Convolutional Codes for Large and Small Payloads

Matrix embedding (ME) code is a commonly used steganography technique, which uses linear block codes to improve embedding efficiency. However, its main disadvantage is the inability to perform maximum likelihood decoding due to the high complexity of decoding large ME codes. As such, it is difficult to improve the embedding efficiency. The proposed q-ary embedding code can provide excellent embedding efficiency and is suitable for various embedding rates (large and small payloads). This article discusses that by using perforation technology, a convolutional code with a high embedding rate can be easily converted into a convolutional code with a low embedding rate. By keeping the embedding rate of the (2, 1) convolutional code unchanged, convolutional codes with different embedding rates can be designed through puncturing.

Non-continuous Orthogonal Frequency Division Multiplexing Satellite Communication Model and Analysis of Interference to Authorized System

With the aim at improving the efficiency of satellite communication spectrum utilization, this paper proposes a non-continuous orthogonal frequency division multiplexing (NC-OFDM) satellite communication model based on convolutional code and LDPC code. We further analyze the bit error rate performance of the NC-OFDM system and evaluates the interference of the authorized system. Simulation experiment results show that NC-OFDM model can significantly improve the spectrum utilization of satellite communication, which can achieve spectrum compatibility with authorized users by adopting adaptive channel access and spectrum sensing technologies.

Manifold Gradient Descent Solves Multi-Channel Sparse Blind Deconvolution Provably and Efficiently

Multi-channel sparse blind deconvolution, or convolutional sparse coding, refers to the problem of learning an unknown filter by observing its circulant convolutions with multiple input signals that are sparse. This problem finds numerous applications in signal processing, computer vision, and inverse problems. However, it is challenging to learn the filter efficiently due to the bilinear structure of the observations with respect to the unknown filter and inputs, as well as the sparsity constraint. In this paper, we propose a novel approach based on nonconvex optimization over the sphere manifold by minimizing a smooth surrogate of the sparsity-promoting loss function. It is demonstrated that manifold gradient descent with random initializations will probably recover the filter, up to scaling and shift ambiguity, as soon as the number of observations is sufficiently large under an appropriate random data model. Numerical experiments are provided to illustrate the performance of the proposed method with comparisons to existing ones.

List Decoding of Arıkan's PAC Codes.

Polar coding gives rise to the first explicit family of codes that provably achieve capacity with efficient encoding and decoding for a wide range of channels. However, its performance at short blocklengths under standard successive cancellation decoding is far from optimal. A well-known way to improve the performance of polar codes at short blocklengths is CRC precoding followed by successive-cancellation list decoding. This approach, along with various refinements thereof, has largely remained the state of the art in polar coding since it was introduced in 2011. Recently, Arıkan presented a new polar coding scheme, which he called polarization-adjusted convolutional (PAC) codes. At short blocklengths, such codes offer a dramatic improvement in performance as compared to CRC-aided list decoding of conventional polar codes. PAC codes are based primarily upon the following main ideas: replacing CRC codes with convolutional precoding (under appropriate rate profiling) and replacing list decoding by sequential decoding. One of our primary goals in this paper is to answer the following question: is sequential decoding essential for the superior performance of PAC codes? We show that similar performance can be achieved using list decoding when the list size L is moderately large (say, ). List decoding has distinct advantages over sequential decoding in certain scenarios, such as low-SNR regimes or situations where the worst-case complexity/latency is the primary constraint. Another objective is to provide some insights into the remarkable performance of PAC codes. We first observe that both sequential decoding and list decoding of PAC codes closely match ML decoding thereof. We then estimate the number of low weight codewords in PAC codes, and use these estimates to approximate the union bound on their performance. These results indicate that PAC codes are superior to both polar codes and Reed–Muller codes. We also consider random time-varying convolutional precoding for PAC codes, and observe that this scheme achieves the same superior performance with constraint length as low as .

Blind Recognition of Forward Error Correction Codes Based on a Depth Distribution Algorithm

Forward error correction codes (FEC) are one of the vital sections of modern communication systems; therefore, recognition of the coding type is an important issue in non-cooperative communication. At present, the recognition of FEC codes is mainly concentrated in the field of semi-blind identification with known types of codes. However, based on information asymmetry, the receiver cannot know the types of channel coding previously used in non-cooperative systems such as cognitive radio and remote sensing of communication. Therefore, it is important to recognize the error-correcting encoding type with no prior information. Although the traditional algorithm can also recognize the type of codes, it is only applicable to the case without errors, and its practicability is poor. In the paper, we propose a new method to identify the types of FEC codes based on depth distribution in non-cooperative communication. The proposed algorithm can effectively recognize linear block codes, convolutional codes, and Turbo codes under a low error probability level, and has a higher robustness to noise transmission environment. In addition, an improved matrix estimation algorithm based on Gaussian elimination was adopted in this paper, which effectively improves the parameter identification in a noisy environment. Finally, we used a general framework to unify all the reconstruction algorithms to simplify the complexity of the algorithm. The simulation results show that, compared with the traditional algorithm based on matrix rank, the proposed algorithm has a better anti-interference performance. The method proposed is simple and convenient for engineering and practical applications.

Minimal State-Space Representation of Convolutional Product Codes

In this paper, we study product convolutional codes described by state-space representations. In particular, we investigate how to derive state-space representations of the product code from the horizontal and vertical convolutional codes. We present a systematic procedure to build such representation with minimal dimension, i.e., reachable and observable.

On a class of modal Θ-valent convolutional codes

The notions of mΘ codes, mΘ linear codes and mΘ cyclic codes are defined in [4]; [5]; [6]. In this note, we plan to define a notion of mΘ convolutional code on the mΘ field .