Convolutional Codes Research Articles

Minimal encoders of convolutional codes with general cyclic structures

Roos’ direct sum decomposition of a cyclic convolutional code based upon a suitable construction of a minimal encoder is extended to a broader class of convolutional codes endowed with additional algebraic structure. The two (equivalent) usual concepts of a convolutional code are taken into account, as a vector space and as a module.

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.

A Rank-Iteration Based Blind Identification Method for Convolutional Codes

A blind identification technology of channel coding has received increasing attentions in recent years. In this letter, we focus on blind identification of convolutional codes without a candidate set. To improve the blind identification accuracy, a novel rank-iteration based blind identification algorithm for convolutional codes is proposed in this paper. Specifically, a weight-dependent threshold for the Binary Symmetric Channel (BSC) channel is firstly proposed to calculate the rank of a received data matrix more accurately. Then, we propose a new iterative operation that repeats the Gauss-Jordan Elimination Through Pivoting (GJETP) algorithm for several times, and select the smallest rank as the rank of the data matrix. Employing this strategy, the rank of a rank-deficient matrix in noisy environments can be close to its noiseless rank. Further, a rank-deficient threshold is introduced to amend the rank of the full-rank matrix after the end of the whole iterative process, which can reduce the rank deviation of the full-rank matrix. Finally, the effectiveness of the proposed method is verified by simulations and comparisons.

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.

Tensor completion via convolutional sparse coding with small samples-based training

Tensor data often suffer from missing value problems due to the complex high-dimensional structure while acquiring them. To complete the missing information, lots of Low-Rank Tensor Completion (LRTC) methods have been proposed, most of which depend on the low-rank property of tensor data. In this way, the low-rank component of the original data could be recovered roughly. However, the shortcoming is that the detailed information can not be fully restored, no matter the Sum of the Nuclear Norm (SNN) nor the Tensor Nuclear Norm (TNN) based methods. On the contrary, in the field of signal processing, Convolutional Sparse Coding (CSC) can provide a good representation of the high-frequency component of the image, which is generally associated with the detail component of the data. To this end, we propose two novel methods, LRTC-CSC-I and LRTC-CSC-II, which adopt CSC as a supplementary regularization for LRTC to capture the high-frequency components. Therefore, the LRTC-CSC methods can not only solve the missing value problem but also recover the details. Moreover, the regularizer CSC can be trained with small samples due to the sparsity characteristic. Extensive experiments show the effectiveness of LRTC-CSC methods, and quantitative evaluation indicates that the performance of our models are superior to state-of-the-art methods.

Design of Ternary Convolutional Code using Reconfigurable Architecture

The need for trustworthy and efficient digital data transmission and storage systems has increased in recent years. The demand to handle and store digital information has grown in the business sector, the military, and the government as a direct result of the widespread availability of high-speed, large-scale data networks. This requirement must be met in order for the design of these systems to keep up with the rapid pace set by communication and computer technologies. When trying to overcome the variable degradation in real time, one of the most important factors to consider is the dependability of the broadband communication channel. Therefore, the use of convolutional codes and other channel-coding strategies is an essential component of any broadband communication system. DSL, WLAN, and 3G standards all require different configurations of convolutional coding, each of which must achieve a specific level of coding performance despite operating at a unique data rate (constraint length and code rate) Therefore, from the perspective of channel-coding techniques, hardware implementations for the development of an encoder are essential. This encoder should be able to support multiple networks using a reconfigurability approach and should be able to function across a variety of standards. Additionally, flexibility and hardware performance should both be prioritised. This calls for forward error control coding with reconfigurable logic, which provides high-speed, low-power dynamically dedicated hardware architectures under a number of speed/power performance constraints at different time intervals that can function within a variety of channel conditions. The ternary computation system has a number of benefits, the most notable of which are the availability of a high data rate, improved spectral efficiency, enhanced coverage, and lower latency. As a result, there is a growing demand for ternary-based systems that use convolutional encoders as a result of developments in technology

Deep residual constrained reconstruction via learned convolutional sparse coding for low-dose CT imaging

Low-dose computed tomography (LDCT) holds great potential to reduce radiation dose damage. However, LDCT degrades the signal-to-noise ratio (SNR) of projection and compromises the reconstruction image quality. This paper proposes a deep residual-constrained reconstruction (DRCR) framework via learned convolutional sparse coding (LCSC) for LDCT imaging. DRCR consists of multiple iteration blocks, and each iteration contains three modules: image update, residual correction and convolution representation modules. First, the image update module updates the reconstruction image with a DL-based prior constraint. Then, the residual correction module attempts to accurately estimate the residual features after mapping the projection errors into the image domain. Finally, the LCSC network is applied for feature map and filter updating to further constrain the image update process. To further improve the performance of DRCR, the perceptual losses of the image domain and projection domain are considered in the optimized model. The results obtained on two datasets show the competitive performance of the proposed framework, with a 0.5 dB PSNR margin, 0.007 SSIM margin, and 1.7 FID margin on the MAYO dataset and a 0.5 dB PSNR margin, 0.011 SSIM margin and 2.4 FID margin on the UIH dataset.

On the improvements of successive cancellation Creeper decoding for polar codes

In this paper, an improvement for successive cancellation (SC) decoding is presented for polar codes. This improvement is based on applying Creeper approach that was used to decode convolutional codes. The proposed decoder combines a stack and a Fano approaches, allowing to significantly decrease complexity of Successive Cancellation Fano decoder at the cost of a slight increase in space complexity. We also show how to combine the SC-Creeper decoding with a bit-flipping approach to further improve the performance of SC-Creeper due to introducing additional decoding attempts.Simulation results show that the proposed SC-Creeper and SC-Creeper Flip decoders with carefully selected parameters have the same performance as both CRC-aided Successive Cancellation List decoder with list size 8 and Fano decoder, while having much smaller complexity.

Implementation of Novel Block and Convolutional Encoding Circuit Using FS-GDI

A novel implementation of Block and Convolutional encoding circuits approach using Gate Input Diffusion-Full Swing (FS-GDI) and Complementary Metal Oxide Semiconductor (CMOS) logic styles has been presented. Performance analysis of the proposed encoding circuits has been performed using Cadence Virtuoso (CV) S/W package. The performance metrics of FS-GDI-based encoding circuits have been compared with traditional CMOS-based designs. The proposed encoding circuits involve Block Hamming (15, 11), Convolutional (2, 1, 3), and Recursive Systematic Convolutional (2, 1, 2) encoding circuits; these presented circuits are simulated and tested using a word length of 11 bits. The simulation experiments revealed that the proposed implemented circuits achieve delay time improving by 27.91% and 33.27% for Hamming (15, 11) and Convolutional (2, 1, 3) codes, respectively. The simple proposed RSC encoder performs better than the Convolutional (2, 1, 3) due to shorter constraint length and less H/W complexity. On the other hand, the Transistor Count-Hardware (TC-H/W) is enhanced by 50% for the Block and Convolutional encoding based on employing area-efficient FS-GDI-XOR gate. From the analysis of the results, the proposed designs achieve efficient power and delay optimization of Hamming and Convolutional encoding utilizing the FS-GDI logic style. Also, it is clear that the characteristics of the proposed encoding circuits are vital and effective in the digital signal processing circuits and encoding/decoding schemes implementation in low-power wireless networks.

A pyroshock signal characterization method based on shock-waveform dictionary

In space engineering, devices (including products) need to work in pyroshock environments during their complete service life. The verification of the full compatibility of vulnerable devices with the pyroshock environment is necessary. Shock response spectrum (SRS) as the current shock specification tool in space engineering has many limitations. However, an SRS curve may be associated with different pyroshock signals that can cause different effects. Therefore, there is a great need to develop characterization methods for pyroshock signals. In this paper, the shock-feature relevant waveform is used as the basis function to approximate pyroshock signals. A parametric dictionary design method is proposed using a random search strategy, in which the designed dictionaries are close to equiangular tight frames. The pyroshock approximation problem is turned into a multi-objective optimization problem and solved by a modified convolutional sparse coding algorithm. Reconstructed signals approach pyroshock not only in the time domain but also in the SRS domain. Parameters of shock-waveforms can be used for pyroshock characterization, simplification, comparison and tracking. The superiority of the proposed methods is validated by the analyses of a pyroshock signal measured in-flight.

Construction of High-Rate Convolutional Codes Using Dual Codes

In this study, we consider techniques for searching high-rate convolutional code (CC) encoders using dual code encoders. A low-rate (R = 1/n) CC is a dual code to a high-rate (R = (n - 1)/n) CC. According to our past studies, if a CC encoder has a high performance, a dual code encoder to the CC also tends to have a good performance. However, it is not guaranteed to have the highest performance. We consider a method to obtain a high-rate CC encoder with a high performance using good dual code encoders, namely, high-performance low-rate CC encoders. We also present some CC encoders obtained by searches using our method.

Probabilistic Shaping for Trellis-Coded Modulation With CRC-Aided List Decoding

This paper applies probabilistic amplitude shaping (PAS) to cyclic redundancy check (CRC)-aided tail-biting trellis-coded modulation (TCM). CRC-TCM-PAS produces practical codes for short block lengths on the additive white Gaussian noise (AWGN) channel. In the transmitter, equally likely message bits are encoded by a distribution matcher (DM) generating amplitude symbols with a desired distribution. A CRC is appended to the sequence of amplitude symbols, and this sequence is then encoded and modulated by TCM to produce real-valued channel input signals. This paper proves that the sign values produced by the TCM are asymptotically equally likely to be positive or negative. The CRC-TCM-PAS scheme can thus generate channel input symbols with a symmetric capacity-approaching probability mass function. The paper provides an analytical upper bound on the frame error rate of the CRC-TCM-PAS system over the AWGN channel. This FER upper bound is the objective function used for jointly optimizing the CRC and convolutional code. Additionally, this paper proposes a multi-composition DM, which is a collection of multiple constant-composition DMs. The optimized CRC-TCM-PAS systems achieve frame error rates below the random coding union (RCU) bound in AWGN and outperform the short-blocklength PAS systems with various other forward error correction codes studied in Coşkun et al. (2019).

Fast list decoders for polarization‐adjusted convolutional (PAC) codes

AbstractA latest coding scheme named polarization‐adjusted convolutional (PAC) codes is shown to approach the dispersion bound for the code (128,64) under list decoding. However, to achieve the near‐bound performance, the list size of list decoding needs to be excessively large, which leads to insufferable time complexity. In this paper, to improve the speed of list decoding, fast list decoders for PAC codes are proposed. Four types of constituent nodes are defined and fast list decoding algorithms are provided for each of them. Simulation results present that fast list decoding with three types of constituent nodes can yield exactly the same error‐correction performance as list decoding, and reduce more than 50% time steps for the code (128,64). Moreover, fast list decoding with four types of constituent nodes can further reduce decoding complexity with negligible performance degradation.

Noncoherent Demodulation and Decoding via Polynomial Zeros Modulation for Pilot-Free Short Packet Transmissions over Multipath Fading Channels

With the advent of the Internet of Things (IoT), short packet transmissions will dominate the future wireless communication. However, traditional coherent demodulation and channel estimation schemes require large pilot overhead, which may be highly inefficient for short packets in multipath fading scenarios. This paper proposes a novel pilot-free short packet structure based on the association of modulation on conjugate-reciprocal zeros (MOCZ) and tail-biting convolutional codes (TBCC), where a noncoherent demodulation and decoding scheme is designed without the channel state information (CSI) at the transceivers. We provide a construction method of constellation sets and demodulation rule for M-ary MOCZ. By deriving low complexity log-likelihood ratios (LLR) for M-ary MOCZ, we offer a reasonable balance between energy and bandwidth efficiency for joint coding and modulation scheme. Simulation results show that our proposed scheme can attain significant performance and throughput gains compared to the pilot-based coherent modulation scheme over multipath fading channels.

Hyper-Dimensional Modulation for Robust Short Packets in Massive Machine-Type Communications

In this paper, we introduce Hyper-Dimensional Modulation (HDM) for massive machine-type communications (mMTC). HDM enables robust communication of short packets by spreading information bits across many elements in a hyper-dimensional vector and superimposing a set of such non-orthogonal vectors. The proposed CRC-aided K-best decoding algorithm for HDM can achieve a very low packet error rate (PER) in additive white Gaussian noise (AWGN) channels for short packets. Furthermore, extended decoding algorithms are proposed to combat overwhelming interference in an mMTC network. Comprehensive simulation and real-world experiment results show that HDM outperforms sparse superposition codes in AWGN channels and state-of-the-art short codes such as polar and tail-biting convolutional codes in interference-heavy channels for short packet transmissions.

Rethinking 1D convolution for lightweight semantic segmentation.

Lightweight semantic segmentation promotes the application of semantic segmentation in tiny devices. The existing lightweight semantic segmentation network (LSNet) has the problems of low precision and a large number of parameters. In response to the above problems, we designed a full 1D convolutional LSNet. The tremendous success of this network is attributed to the following three modules: 1D multi-layer space module (1D-MS), 1D multi-layer channel module (1D-MC), and flow alignment module (FA). The 1D-MS and the 1D-MC add global feature extraction operations based on the multi-layer perceptron (MLP) idea. This module uses 1D convolutional coding, which is more flexible than MLP. It increases the global information operation, improving features' coding ability. The FA module fuses high-level and low-level semantic information, which solves the problem of precision loss caused by the misalignment of features. We designed a 1D-mixer encoder based on the transformer structure. It performed fusion encoding of the feature space information extracted by the 1D-MS module and the channel information extracted by the 1D-MC module. 1D-mixer obtains high-quality encoded features with very few parameters, which is the key to the network's success. The attention pyramid with FA (AP-FA) uses an AP to decode features and adds a FA module to solve the problem of feature misalignment. Our network requires no pre-training and only needs a 1080Ti GPU for training. It achieved 72.6 mIoU and 95.6 FPS on the Cityscapes dataset and 70.5 mIoU and 122 FPS on the CamVid dataset. We ported the network trained on the ADE2K dataset to mobile devices, and the latency of 224 ms proves the application value of the network on mobile devices. The results on the three datasets prove that the network generalization ability we designed is powerful. Compared to state-of-the-art lightweight semantic segmentation algorithms, our designed network achieves the best balance between segmentation accuracy and parameters. The parameters of LSNet are only 0.62 M, which is currently the network with the highest segmentation accuracy within 1 M parameters.

Hybrid HMM Decoder for Convolutional Codes by Joint Trellis-Like Structure and Channel Prior

The anti-interference capability of wireless links is a physical layer problem for edge computing. Although convolutional codes have inherent error correction potential due to the redundancy introduced in the data, the performance of the convolutional code is drastically degraded due to multipath effects on the channel. In this paper, we propose the use of a Hidden Markov Model (HMM) for the reconstruction of convolutional codes and decoding by the Viterbi algorithm. Furthermore, to implement soft-decision decoding, the observation of HMM is replaced by Gaussian mixture models (GMM). Our method provides superior error correction potential than the standard method because the model parameters contain channel state information (CSI). We evaluated the performance of the method compared to standard Viterbi decoding by numerical simulation. In the multipath channel, the hybrid HMM decoder can achieve a performance gain of 4.7 dB and 2 dB when using hard-decision and soft-decision decoding, respectively. The HMM decoder also achieves significant performance gains for the RSC code, suggesting that the method could be extended to turbo codes.

On Tail-Biting Polarization-Adjusted Convolutional (TB-PAC) Codes and Small-Sizes List Decoding

Polarization-adjusted convolutional (PAC) coding is a good concatenation of convolutional codes and polar codes. For short block-length codes ( <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$N\leq 128$ </tex-math></inline-formula> ), PAC codes with a sequential decoding or a list decoding with large list-sizes ( <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$L\geq 128$ </tex-math></inline-formula> ) can achieve better block-error-rate (BLER) performance than polar codes with CRC-aided list decoding. However, the PAC codes have no BLER performance advantage when the list decoding is with small list-sizes ( <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$L\leq 8$ </tex-math></inline-formula> ). In this letter, tail-biting PAC (TB-PAC) coding is proposed, in which tail-biting convolutional pre-transformation is applied. A multi-round list decoding with small list-sizes is provided for TB-PAC codes, in which an early-stopping method is designed to control the number of rounds. In each round, the tail-biting bits are assigned various initial path-values and also used as a check at the end, which helps the correct path be distinguishable. The proposed small-sizes list decoding can help the TB-PAC codes achieve much better BLER performance than the polar/PAC codes.

Concatenated Codes for Multiple Reads of a DNA Sequence

Decoding sequences that stem from multiple transmissions of a codeword over an insertion, deletion, and substitution channel is a critical component of efficient deoxyribonucleic acid (DNA) data storage systems. In this paper, we consider a concatenated coding scheme with an outer nonbinary low-density parity-check code or a polar code and either an inner convolutional code or a time-varying block code. We propose two novel decoding algorithms for inference from multiple received sequences, both combining the inner code and channel to a joint hidden Markov model to infer symbolwise a posteriori probabilities (APPs). The first decoder computes the exact APPs by jointly decoding the received sequences, whereas the second decoder approximates the APPs by combining the results of separately decoded received sequences and has a complexity that is linear with the number of sequences. Using the proposed algorithms, we evaluate the performance of decoding multiple received sequences by means of achievable information rates and Monte-Carlo simulations. We show significant performance gains compared to a single received sequence. In addition, we succeed in improving the performance of the aforementioned coding scheme by optimizing both the inner and outer codes.

Concatenated turbo polar-convolutional codes based on soft cancellation algorithm

This paper presents the Parallel and Serial Concatenated Turbo Polar-Convolutional Codes (CTPCCs) to improve the performance of polar codes in the finite code length regime. Both proposed concatenated codes use the Systematic Polar Code (SPC) and Recursive Systematic Convolutional (RSC) code as constituent codes. The iterative decoding algorithms of the proposed systems consist of a Soft Cancellation (SCAN) decoder with a single internal iteration for the SPC and SOVA or LogMap decoder for the RSC code. The simulation results show that the performance of the Parallel Concatenated Turbo Polar-Convolutional Code (PCTPCC) at low signal-to-noise ratios (SNRs) is better than that of the Serial Concatenated Turbo Polar-Convolutional Code (SCTPCC) and also better than the performance of other Turbo Polar Codes (TPCs). At BER=10−2, the proposed PCTPCC with SOVA and LogMap algorithms has about 0.3 dB and 0.25 dB performance gains over the SCTPCC models, respectively. In the high SNR regions, the performance of the SCTPCC with the LogMap algorithm significantly outperforms that of other models. At BER=10−6, the proposed SCTPCC models with SOVA and LogMap algorithms outperform the PCTPCC model by gains of 0.3 dB and 0.25 dB, respectively. The PCTPCC model with the SOVA decoder is superior to other models in terms of complexity.