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Among numerous dynamic scheduling strategies for low‐density parity‐check codes, many of them are of high complexity due to repetitive computation and ordering of belief residuals. To address these challenges, two novel approaches are proposed: the derived informed variable‐to‐check residual belief propagation and the derived variable‐node and variable‐to‐check‐edge residual belief propagation for low‐density parity‐check codes. Simulation results show that the derived dynamic scheduling exhibits a substantial gain of approximately 0.15 dB in signal‐to‐noise ratio over the non‐derived one with considerably lower decoding complexity when targeting a bit‐error rate of 10−4. [ABSTRACT FROM AUTHOR]

In recent years, much research has been devoted to free-space optical communication (FSO). The unregulated spectrum, low implementation costs, and robust security of FSO systems all are of great importance which lead to a wide range of applications for FSO links, from terrestrial communications to satellite communications. However, the fundamental limitation with FSO links is atmospheric turbulence (AT) caused by fading, significantly reducing link performance. Random phenomena are the best characteristic of atmospheric turbulence caused by changes in the air's refractive index over time. Numerous probability density functions of the AT models were presented to model the randomness in AT channels. The Log-Normal (LN) channel model is for weak atmospheric turbulence, while the Gamma–Gamma (G–G) channel is selected for moderate and strong atmospheric turbulence. The impacts of geometric losses, attenuation due to weather, and errors due to misalignment are addressed using LN and G–G channels. Channel coding is one of the possible solutions for mitigating such FSO channel impairments as the low-density parity check (LDPC) codes. In this article, the Weighted Bit Flipping (Algorithm (1)), Implementation Efficient Reliability Ratio Weighted Bit Flipping (Algorithm (2)), and Min-Sum (Algorithm (3)) algorithms are compared and evaluated against FSO atmospheric turbulence channels. In addition, two novel algorithms are proposed to enhance the complexity or Bit Error Rate performance of LDPC decoding over FSO channels. The results showed an impressive improvement of the coded FSO system by employing the proposed algorithms compared to the existing LDPC decoders for FSO communications from the point of all comparison parameters. [ABSTRACT FROM AUTHOR]

In this article, a graph-theoretic method (taking advantage of constraints among sets associated with the corresponding parity-check matrices) is applied for the construction of a double low-density parity-check (D-LDPC) code (also known as LDPC code pair) in a joint source-channel coding (JSCC) system. Specifically, we pre-set the girth of the parity-check matrix for the LDPC code pair when jointly designing the two LDPC codes, which are constructed by following the set constraints. The constructed parity-check matrices for channel codes comprise an identity submatrix and an additional submatrix, whose column weights can be pre-set to be any positive integer numbers. Simulation results illustrate that the constructed D-LDPC codes exhibit significant performance improvement and enhanced flexible frame length (i.e., adaptability under various channel conditions) compared with the benchmark code pair. [ABSTRACT FROM AUTHOR]

Although extensive optimization of encoding and decoding schemes for joint source-channel coding (JSCC) systems has been conducted, efficient optimization schemes are still required for designing and optimizing the linking matrix between variable nodes of the source code and check nodes of the channel code. A scheme has been proposed for design and optimization of linking matrix with multi-edges by analyzing the performance of the JSCC system using the joint protograph extrinsic information transfer algorithm to calculate decoding thresholds. The proposed scheme incorporates structural constraints and is effective in designing and optimizing the multi-edges in linking matrix for the JSCC system. Experimental results have demonstrated that the designed and optimized linking matrix significantly improves the performance of the JSCC system. Furthermore, the proposed scheme reduces the complexity of the solution space for the optimized example. [ABSTRACT FROM AUTHOR]

In this paper, we consider a slot-controlled coded compressed sensing protocol for unsourced massive random access (URA) that concatenates a shared patterned Reed–Muller (PRM) inner codebook to an outer error-correction code. Due to the limitations of the geometry-based decoding algorithm in single-sequence settings and due to the message interference that may result in decreased decoding performance under multi-sequence circumstances, a list PRM projection algorithm and an iterative list PRM projection algorithm are proposed to supplant the signal detector associated with the inner PRM sequences in this paper. In detail, we first propose an enhanced path-saving algorithm, called list PRM projection detection, for use in single-user scenarios that maintains multiple candidates during the first few layers so as to remedy the risk of spreading errors. On this basis, we further propose an iterative list PRM projection algorithm for use in multi-user scenarios. The vectors for PRM codes and channel coefficients are jointly detected in an iterative manner, which offers significant improvements regarding the convergence rate for signal recovery. Furthermore, the performances of the proposed algorithms are analyzed mathematically, and we verify that the theoretical simulations are consistent with the numerical simulations. Finally, we concatenate the inner PRM codes that employ iterative list detection in two practical error-correction outer codes. According to the simulation results, we conclude that the packetized URA with the proposed iterative list projection detection works better than benchmarks in terms of the number of active users it can support in each slot and the amount of energy needed per bit to meet an expected error probability. [ABSTRACT FROM AUTHOR]

A 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. [ABSTRACT FROM AUTHOR]

The graph autoencoder (GAE) is a powerful graph representation learning tool in an unsupervised learning manner for graph data. However, most existing GAE-based methods typically focus on preserving the graph topological structure by reconstructing the adjacency matrix while ignoring the preservation of the attribute information of nodes. Thus, the node attributes cannot be fully learned and the ability of the GAE to learn higher-quality representations is weakened. To address the issue, this paper proposes a novel GAE model that preserves node attribute similarity. The structural graph and the attribute neighbor graph, which is constructed based on the attribute similarity between nodes, are integrated as the encoder input using an effective fusion strategy. In the encoder, the attributes of the nodes can be aggregated both in their structural neighborhood and by their attribute similarity in their attribute neighborhood. This allows performing the fusion of the structural and node attribute information in the node representation by sharing the same encoder. In the decoder module, the adjacency matrix and the attribute similarity matrix of the nodes are reconstructed using dual decoders. The cross-entropy loss of the reconstructed adjacency matrix and the mean-squared error loss of the reconstructed node attribute similarity matrix are used to update the model parameters and ensure that the node representation preserves the original structural and node attribute similarity information. Extensive experiments on three citation networks show that the proposed method outperforms state-of-the-art algorithms in link prediction and node clustering tasks. [ABSTRACT FROM AUTHOR]

A key component of the joint source-channel coding (JSCC) scheme based on double low-density parity-check (D-LDPC) codes is the introduction of a linking matrix between the source LDPC code and channel LDPC code, by which the decoding information including the source redundancy and channel state information can be transferred iteratively. However, the linking matrix is a fixed one-to-one mapping, i.e., an identity matrix in a conventional D-LDPC code system, which may not take full advantage of the decoding information. Therefore, this paper introduces a general linking matrix, i.e., a non-identity linking matrix, connecting the check nodes (CNs) of the source LDPC code and the variable nodes (VNs) of the channel LDPC code. Further, the encoding and decoding algorithms of the proposed D-LDPC coding system are generalized. A joint extrinsic information transfer (JEXIT) algorithm is derived for calculating the decoding threshold of the proposed system with a general linking matrix. In addition, several general linking matrices are optimized with the aid of the JEXIT algorithm. Finally, the simulation results demonstrate the superiority of the proposed D-LDPC coding system with general linking matrices. [ABSTRACT FROM AUTHOR]

Recently, a mesh model-based merging (M 3 ) method and four basic graph models were proposed to construct the double protograph low-density parity-check (P-LDPC) code pair of the joint source channel coding (JSCC). Designing the protograph (mother code) of the P-LDPC code with both a good waterfall region and lower error floor is a challenge, and few works have existed until now. In this paper, the single P-LDPC code is improved to further verify the availability of the M 3 method, and its structure is different from the channel code in the JSCC. This construction technique yields a family of new channel codes with lower power consumption and higher reliability. The structured design and better performance demonstrate that the proposed code is hardware-friendly. [ABSTRACT FROM AUTHOR]

In its most elementary form, compressed sensing studies the design of decoding algorithms to recover a sufficiently sparse vector or code from a lower dimensional linear measurement vector. Typically it is assumed that the decoder has access to the encoder matrix, which in the combinatorial case is sparse and binary. In this paper we consider the problem of designing a decoder to recover a set of sparse codes from their linear measurements alone, that is without access to encoder matrix. To this end we study the matrix factorisation task of recovering both the encoder and sparse coding matrices from the associated linear measurement matrix. The contribution of this paper is a computationally efficient decoding algorithm, Decoder-Expander Based Factorisation, with strong performance guarantees. Under mild assumptions on the sparse coding matrix and by deploying a novel random encoder matrix, we prove that Decoder-Expander Based Factorisation recovers both the encoder and sparse coding matrix at the optimal measurement rate with high probability and from a near optimal number of measurement vectors. In addition, our experiments demonstrate the efficacy and computational efficiency of our algorithm in practice. Beyond compressed sensing, our results may be of interest for researchers working in areas as diverse as linear sketching, coding theory, matrix compression and dictionary learning. [ABSTRACT FROM AUTHOR]

Polar codes are one of the most effective methods of error correction coding. Currently, these codes are used in 5G communication systems and are the main candidate for 6G. Symmetry plays an important role in coding and decoding algorithms for polar codes. Modulation and multiple access methods are the basis for a physical layer along with error correction codes. Non-Orthogonal Multiple Access (NOMA) methods are a promising technology for future telecommunication systems. They allow the increase of both spectral efficiency and the quantity of subscribers of a communication system. In this paper, we consider a communication system with polar codes, traditional orthogonal multiple access (OMA), and NOMA. The channel with multipath propagation, which can be defined by the Rayleigh channel model, is especially difficult to transmit. We propose a method for adapting signals with polar codes to a channel state based on the analysis of channel matrix and permutation of logical subchannels. The results obtained demonstrate efficiency compared to classical solutions and do not really increase the computational complexity of signal processing and decoding. [ABSTRACT FROM AUTHOR]

In this paper, we propose a modified adaptive belief propagation (ABP) algorithm, which is referred to as the random ABP (R-ABP) algorithm, for decoding short channel codes adopted in the fifth generation (5G) New Radio (NR) wireless systems. Based on the cyclic redundancy check (CRC) concatenation structure of 5G channel codes, we can take partial or even all CRC bits into iterative R-ABP decoding to improve the error correction performance, while the error detection capability can still be guaranteed by the remaining CRC bits and a proposed threshold-based acceptance criterion. We call this improved R-ABP decoding the threshold-and-CRC-aided R-ABP (TCA-R-ABP) decoding. The simulation results show that our proposed TCA-R-ABP algorithm outperforms the state-of-the-art decoding algorithms for many 5G low-density parity-check (LDPC) and polar codes. Moreover, the proposed TCA-R-ABP algorithm leads to a unified decoder for LDPC and polar codes, which has the potential to be a lower-complexity decoder over the combination of the belief propagation (BP) and CRC-aided successive cancellation list (CA-SCL) decoders. [ABSTRACT FROM AUTHOR]

This paper studies the secrecy coding analysis achieved by the self-jamming technique in the presence of an eavesdropper by considering a short-packet Full-Duplex (FD) transmission developed based on iterative blind or semi-blind channel estimation and advanced decoding algorithms. Indeed, the legitimate receiver and eavesdropper can simultaneously receive the intended signal from the transmitter and broadcast a self-jamming or jamming signal to the others. Unlike other conventional techniques without feedback, the blind or semi-blind algorithm applied at the legitimate receiver can simultaneously estimate, firstly, the Self-Interference (SI) channel to cancel the SI component and, secondly, estimate the propagation channel, then decode the intended messages by using 5G Quasi-Cyclic Low-Density Parity Check (QC-LDPC) codes. Taking into account the passive eavesdropper case, the blind channel estimation with a feedback scheme is applied, where the temporary estimation of the intended channel and the decoded message are fed back to improve both the channel estimation and the decoding processes. Only the blind algorithm needs to be implemented in the case of a passive eavesdropper because it achieves sufficient performances and does not require adding pilot symbols as the semi-blind algorithm. In the case of an active eavesdropper, based on its robustness in the low region of the Signal-to-Noise Ratio (SNR), the semi-blind algorithm is considered by trading four pilot symbols and only requiring the feedback for channel estimation processes in order to overcome the increase in noise in the legitimate receiver. The results show that the blind or semi-blind algorithms outperform the conventional algorithm in terms of Mean Square Error (MSE), Bit Error Rate (BER) and security gap ( S g ). In addition, it has been shown that the blind or semi-blind algorithms are less sensitive to high SI and self-jamming interference power levels imposed by secured FD transmission than the conventional algorithms without feedback. [ABSTRACT FROM AUTHOR]

Most synchronization error correction codes deal with random independent insertion and deletion errors without correlation. In this paper, we propose a probabilistic channel model with correlated insertion and deletion (CID) errors to capture the data dependence applicable to the bit-patterned media recording (BPMR) system. We also investigate the error performance and decoding complexity of a concatenated LDPC-marker code over the CID channel. Furthermore, we modify the forward backward decoding algorithm to make it suitable for the CID channel, and elaborate it based on a two-dimensional state transition diagram. Compared with the conventional marker coding scheme dealing with random errors, the concatenated LDPC-marker code takes into account the dependence between synchronization errors, improves the error performance, and reduces the decoding complexity. The BER performance of the concatenated LDPC-marker code is improved by more than 50% on average, and the decoding time is reduced by nearly 35% when the LDPC code (n = 4521, k = 3552) and the marker code (Nm = 2, Nc = 30) are used over the CID channel. [ABSTRACT FROM AUTHOR]

Channel coding technology is indispensable in digital communication systems. In noncooperative contexts, the identification of the channel codes of the synchronous scrambler is essential. In this paper, a new algorithm that directly uses a soft decision sequence for blind reconstruction of the synchronous scrambler is proposed. First, considering imbalanced signal sources and the principle of scrambling and descrambling the synchronous scrambler, the error-containing equation of the synchronous scrambler is established. Second, the average check conformity is introduced to complete the check relationship detection. Then, based on the statistical characteristics of the average check conformity, the corresponding discrimination threshold is established, and the reconstruction of the feedback polynomial of the synchronous scrambler is completed by traversing the possible primitive polynomials. Finally, the verification equation is determined by the method of subsection optimization, which greatly reduces the number of initial states that need to be traversed; this is critical for scramblers with high-order feedback polynomials (i.e., when the order of the feedback polynomial is greater than 15). Simulations show that the algorithm can effectively reconstruct the synchronous scrambler under imbalanced signal sources. Moreover, the proposed algorithm offers improved performance with about 1–2 dB gain at low signal-to-noise ratios compared with existing methods, and its computational complexity is reasonable. [ABSTRACT FROM AUTHOR]

This paper presents an online perturbed and directed neural-evolutionary (Online-PDNE) decoding algorithm for polar codes, in which the perturbation noise and online directed neuro-evolutionary noise sequences are sequentially added to the received sequence for re-decoding if the standard polar decoding fails. The new decoding algorithm converts uncorrectable received sequences into error-correcting regions of their decoding space for correct decoding by adding specific noises. To reduce the decoding complexity and delay, the PDNE decoding algorithm and sole neural-evolutionary (SNE) decoding algorithm for polar codes are further proposed, which provide a considerable tradeoff between the decoding performance and complexity by acquiring the neural-evolutionary noise in an offline manner. Numerical results suggest that our proposed decoding algorithms outperform the other conventional decoding algorithms. At high signal-to-noise ratio (SNR) region, the Online-PDNE decoding algorithm improves bit error rate (BER) performance by more than four orders of magnitude compared with the conventional simplified successive cancellation (SSC) decoding algorithm. Furthermore, in the mid-high SNR region, the average normalized complexity of the proposed algorithm is almost the same as that of the SSC decoding algorithm, while preserving the decoding performance gain. [ABSTRACT FROM AUTHOR]

Reed-Muller (RM) codes have recently regained some interest in the context of low latency communications and due to their relation to polar codes. RM codes can be constructed based on the Plotkin construction. In this work, we consider concatenated codes based on the Plotkin construction, where extended Bose-Chaudhuri-Hocquenghem (BCH) codes are used as component codes. This leads to improved code parameters compared to RM codes. Moreover, this construction is more flexible concerning the attainable code rates. Additionally, new soft-input decoding algorithms are proposed that exploit the recursive structure of the concatenation and the cyclic structure of the component codes. First, we consider the decoding of the cyclic component codes and propose a low complexity hybrid ordered statistics decoding algorithm. Next, this algorithm is applied to list decoding of the Plotkin construction. The proposed list decoding approach achieves near-maximum-likelihood performance for codes with medium lengths. The performance is comparable to state-of-the-art decoders, whereas the complexity is reduced. [ABSTRACT FROM AUTHOR]

This work gives an explicit construction of a family of error correcting codes for the binary deletion channel and for the Poisson repeat channel. In the binary deletion channel with parameter $p$ (${\mathrm {BDC}}_{p}$) every bit is deleted independently with probability $p$. A lower bound of $(1-p)/9$ is known on the capacity of the ${\mathrm {BDC}}_{p}$ , yet no explicit construction is known to achieve this rate. We give an explicit family of codes of rate $(1-p)/16$ , for every $p$. This improves upon the work of Guruswami and Li (2018) that gave a construction of rate $(1-p)/120$. The codes in our family have polynomial time encoding and decoding algorithms. Another channel considered in this work is the Poisson repeat channel with parameter $\lambda $ (PRC $_{\lambda }$) in which every bit is replaced with a discrete Poisson number of copies of that bit, where the number of copies has mean $\lambda $. We show that our construction works for this channel as well. As far as we know, this is the first explicit construction of an error correcting code for PRC $_{\lambda }$. [ABSTRACT FROM AUTHOR]

An end-to-end joint source–channel (JSC) encoding matrix and a JSC decoding scheme using the proposed bit flipping check (BFC) algorithm and controversial variable node selection-based adaptive belief propagation (CVNS-ABP) decoding algorithm are presented to improve the efficiency and reliability of the joint source–channel coding (JSCC) scheme based on double Reed–Solomon (RS) codes. The constructed coding matrix can realize source compression and channel coding of multiple sets of information data simultaneously, which significantly improves the coding efficiency. The proposed BFC algorithm uses channel soft information to select and flip the unreliable bits and then uses the redundancy of the source block to realize the error verification and error correction. The proposed CVNS-ABP algorithm reduces the influence of error bits on decoding by selecting error variable nodes (VNs) from controversial VNs and adding them to the sparsity of the parity-check matrix. In addition, the proposed JSC decoding scheme based on the BFC algorithm and CVNS-ABP algorithm can realize the connection of source and channel to improve the performance of JSC decoding. Simulation results show that the proposed BFC-based hard-decision decoding (BFC-HDD) algorithm (ζ = 1) and BFC-based low-complexity chase (BFC-LCC) algorithm (ζ = 1, η = 3) can achieve about 0.23 dB and 0.46 dB of signal-to-noise ratio (SNR) defined gain over the prior-art decoding algorithm at a frame error rate (FER) = 10 − 1 . Compared with the ABP algorithm, the proposed CVNS-ABP algorithm and BFC-CVNS-ABP algorithm achieve performance gains of 0.18 dB and 0.23 dB, respectively, at FER = 10 − 3 . [ABSTRACT FROM AUTHOR]

A novel time-varying channel adaptive low-complexity chase (LCC) algorithm with low redundancy is proposed, where only the necessary number of test vectors (TVs) are generated and key equations are calculated according to the channel evaluation to reduce the decoding complexity. The algorithm evaluates the error symbol numbers by counting the number of unreliable bits of the received code sequence and dynamically adjusts the decoding parameters, which can reduce a large number of redundant calculations in the decoding process. We provide a simplified multiplicity assignment (MA) scheme and its architecture. Moreover, a multi-functional block that can implement polynomial selection, Chien search and the Forney algorithm (PCF) is provided. On this basis, a high-efficiency LCC decoder with adaptive error-correcting capability is proposed. Compared with the state-of-the-art LCC (TV = 16) decoding, the number of TVs of our decoder was reduced by 50.4% without loss of the frame error rate (FER) performance. The hardware implementation results show that the proposed decoder achieved 81.6% reduced average latency and 150% increased throughput compared to the state-of-the-art LCC decoder. [ABSTRACT FROM AUTHOR]

In this paper, a simplified successive cancellation (SC) decoding algorithm for polar codes on insertion/deletion error channels is proposed. First, the SC decoding is designed to decode polar codes on insertion/deletion channels and the joint weight distribution is derived to measure the occurrence probability of different scenarios. Some scenarios with small occurrence probability can be pruned to obtain lower decoding complexity with negligible performance loss. Inspired by this, a fixed pruning strategy (FPS) is proposed to reduce the decoding complexity, which can prune as many scenarios as possible with the given performance requirement. By exploiting the periodicity of the joint weight distribution, the upper bound of the block error rate of the pruned SC decoding is derived. Furthermore, according to the convergence of the upper bound, a dynamic self-adjusting pruning strategy is designed to further reduce the decoding complexity and improve the flexibility of the pruning algorithm. Simulation results show that the decoding complexity of the proposed pruning-based decoding algorithms is significantly reduced compared to the state-of-the-art scenario simplified SC decoding algorithm. [ABSTRACT FROM AUTHOR]

High-rate product codes (PCs) and staircase codes (SCs) are ubiquitous codes in high-speed optical communication achieving near-capacity performance on the binary symmetric channel. Their success is mostly due to very efficient iterative decoding algorithms that require very little complexity. In this paper, we extend the density evolution (DE) analysis for PCs and SCs to a channel with ternary output and ternary message passing, where the third symbol marks an erasure. We investigate the performance of a standard error-and-erasure decoder and of its simplification using DE. The proposed analysis can be used to find component code configurations and quantizer levels for the channel output. We also show how the use of even-weight BCH subcodes as component codes can improve the decoding performance at high rates. The DE results are verified by Monte-Carlo simulations, which show that additional coding gains of up to 0.6dB are possible by ternary decoding, at only a small additional increase in complexity compared to traditional binary message passing. [ABSTRACT FROM AUTHOR]

Zero-shot learning (ZSL) aims to learn a classifier for unseen classes by exploiting both training data from seen classes and external knowledge. In many visual tasks such as image classification, a set of high-level attributes that describe the semantic properties of classes are used as the external knowledge to bridge seen and unseen classes. While the attributes are usually treated equally by previous ZSL studies, we observe that the contribution of different attributes varies significantly over model training. To adaptively exploit the discriminative information embedded in different attributes, we propose a novel encoder–decoder framework with attention mechanism on the attribute level for zero-shot learning. Specifically, by mapping the visual features into a semantic space, the more discriminative attributes are emphasized with larger attention weights. Further, the attentive attributes and the class prototypes are simultaneously decoded to the visual space so that the hubness problem can be eased. Finally, the labels are predicted in the visual space. Extensive experiments on multiple benchmark datasets demonstrate that our proposed model achieves a significant boost over several state-of-the-art methods for ZSL task and comparative results for generalized ZSL task. [ABSTRACT FROM AUTHOR]

Deletion errors are notoriously difficult to correct. The capacity of the binary deletion channel is not yet fully known, and there is no completely satisfactory solution even to the specific problem of correcting only two deletion errors. In this paper, we show that polarization theory, along with the powerful methods of polar coding and successive-cancellation decoding, can be extended to channels with deletion errors. Our results further generalize to channels corrupted by insertion errors and/or combinations of insertions and deletions. It was recently proposed to correct deletion errors using polar codes designed for the BEC, precoded with a sufficiently powerful CRC code. In this approach, in order to correct ${d}$ deletions in a codeword of length ${n}$ , successive-cancellation decoding is run separately for each of the $\binom {n}{d}$ possible deletion patterns, while treating the deleted symbols as erasures. The resulting complexity of decoding is ${O}\bigl ({n}^{d+1}\log {n}\bigr)$. In contrast, we develop herein a natural generalization of successive-cancellation decoding to channels with deletion errors. Our algorithm is based on the recursive structure of polar codes, processing the channel output in ${m} = \log _{2} {n}$ decoding layers, just like the conventional successive-cancellation decoder. Every node in each decoding layer propagates its uncertainty about the deletion pattern to the nodes in the next layer and, eventually, the correct deletion pattern becomes visible at the decoder output, with high probability. This makes it possible to consider at most $\binom {d+2}{2}$ scenarios at each node, and the overall decoding complexity is only ${O}\bigl ({d}^{3} {n} \log {n}\bigr)$ , which scales polynomially rather than exponentially with the number of deletions. Based on the proposed algorithm, we also investigate the channel polarization phenomenon. We are able to prove weak polarization where the number of deletions ${d}$ is small, i.e. ${d}={o}({n})$. We also conjecture the strong polarization for when ${d}={O}(1)$ and provide some evidence to support this conjecture. The strong polarization, if proven, implies that our coding scheme achieves the capacity of any binary-input symmetric channel which furthermore introduces a constant number of deletions. [ABSTRACT FROM AUTHOR]

Analysis of the current state and development of wireless communication systems, such as first generation 1G, second generation 2G, third generation 3G, fourth generation 4G LTEAdvanced, fifth generation 5G, Wi-Max and Wi-Fi, shows the need application of information technologies that allow efficient data transmission in real time. In such systems, ensuring a given level of reliability of information transmission is carried out through the use of information technology adaptation and coding. With increasing noise levels, existing methods of ensuring the reliability of information based on correction codes do not provide the specified indicators of the efficiency of information transmission. With restrictions on code parameters, in systems with adaptation, in the case of increasing noise levels to a certain value, ensuring the specified characteristics of the reliability of information becomes impossible. Therefore, the question arises of the use of turbo codes and their multilevel parametric adaptation. In the case of reverse data decoding, there is a need for a priori information on the plausibility functions of the received data, taking into account the procedure of decoding algorithms based on probabilistic decoding, namely for turbo codes. It is possible to form estimates of uncertainty of information during decoding, to minimize these estimates by choosing the rules of decision using the methods of parametric adaptation and to ensure the reliability of information transfer. [ABSTRACT FROM AUTHOR]

A joint channel estimation and channel coding scheme is presented for channels with memory using polar codes. Unlike the conventional approach of first estimating all channel parameters and then performing channel decoding separately, the proposed scheme incorporates a subset of reliable estimates of channel parameters into the decoding procedure and computes decoding metrics averaged over the statistical behavior of the channel. Specifically, decoding algorithms for finite-state Markov channels of any order, for the Gauss-Markov channel and for flat-fading channels are presented. Further, by adapting list decoding to identify reliably-decoded bits within a codeword, channel estimation and decoding steps are performed iteratively to boost the reliability of channel estimation as well as error correction. In order to improve the performance even further, a new pilot arrangement scheme is developed that utilizes the structure of polar codes and sends pilot symbols embedded within the polar codewords. This construction can be viewed as a new family of shortened polar codes that can be of independent interest. Simulation results demonstrate the benefit of the proposed approach compared to existing solutions. [ABSTRACT FROM AUTHOR]

Decoding of polar codes, a class of capacity-achieving channel codes, typically requires the perfect knowledge of channel parameter in advance. This paper aims to investigate how to decode polar codes when channel parameter is unknown. Specifically, we study a generalized Gilbert-Elliott channel model, which assumes that the channel switches between a finite number of states. On the platform of Soft CANcellation (SCAN), which is a low-complexity iterative decoding algorithm of polar codes superior to the widely-used Successive Cancellation (SC) decoder, we propose three adaptive algorithms, i.e., Sliding-Window SCAN (SWSCAN), Weighted-Window SCAN (W2SCAN), and Linear-Weighting SCAN (LWSCAN). These adaptive SCAN decoders are seeded with a coarse estimate of channel state, and after each SCAN iteration, the decoders progressively refine the estimate of channel state. Experimental results demonstrate that the proposed adaptive SCAN decoders outperform the original SCAN decoder and other competitors. [ABSTRACT FROM AUTHOR]

The coding problem for wiretap channels (WTCs) with causal and/or non-causal channel state information (CSI) available at the encoder (Alice) and/or the decoder (Bob) is studied, particularly focusing on achievable secret-message secret-key (SM-SK) rate pairs under the semantic security criterion. One of our main results is summarized as on causal inner bounds for SM-SK rate pairs, which follows immediately by leveraging the unified seminal theorem for WTCs with non-causal CSI at Alice that has been recently established by Bunin et al.. The only thing to do here is just to re-interpret the latter non-causal scheme in a causal manner by restricting the range of auxiliary random variables appearing in non-causal encoding to a subclass of auxiliary random variables for the causal encoder. This technique is referred to as “plugging.” Then, we are able to dispense with the block-Markov encoding scheme used in the previous works by Chia and El Gamal, Fujita, and Han and Sasaki and then extend all the known results on achievable rates. The other main results include the exact SM-SK capacity region for WTCs with non-causal CSI at “both” Alice and Bob (), a “tighter” causal SM-SK outer bound for state-reproducing coding schemes with CSI at Alice (), and the exact SM-SK capacity region for degraded WTCs with causal/non-causal CSI at both Alice and Bob (). [ABSTRACT FROM AUTHOR]

In this paper, we propose a new method to design low-density parity-check Hadamard (LDPC-Hadamard) codes — a type of ultimate-Shannon-limit approaching channel codes. The technique is based on applying Hadamard constraints to the check nodes in a generalized protograph-based LDPC code, followed by lifting the generalized protograph. We name the codes formed protograph-based LDPC Hadamard (PLDPC-Hadamard) codes. We also propose a modified Protograph Extrinsic Information Transfer (PEXIT) algorithm for analyzing and optimizing PLDPC-Hadamard code designs. The proposed algorithm further allows the analysis of PLDPC-Hadamard codes with degree- 1 and/or punctured nodes. We find codes with decoding thresholds ranging from −1.53 dB to −1.42 dB. At a BER of 10−5, the gaps of our codes to the ultimate-Shannon-limit range from 0.40 dB (for rate = 0.0494) to 0.16 dB (for rate = 0.003). Moreover, the error performance of our codes is comparable to that of the traditional LDPC-Hadamard codes. Finally, the BER performances of our codes after puncturing are simulated and compared. [ABSTRACT FROM AUTHOR]

Known for their capacity-achieving abilities and low complexity for both encoding and decoding, polar codes have been selected as the control channel coding scheme for 5G communications. To satisfy the needs of high throughput and low latency, belief propagation (BP) is chosen as the decoding algorithm. However, it suffers from worse error performance than that of cyclic redundancy check (CRC)-aided successive cancellation list (CA-SCL). Recently, convolutional neural network-aided bit-flipping (CNN-BF) is applied to BP decoding, which can accurately identify the erroneous bits to achieve a better error rate and lower decoding latency than prior critical-set bit-flipping (CS-BF) mechanism. However, successive BF, having better error correction capability, has not been explored in CNN-BF since the more complicated flipping strategy is out of the scope of supervised learning. In this work, by using imitation learning, a convolutional neural network-aided tree-based multiple-bits BF (CNN-Tree-MBF) mechanism is proposed to explore the benefits of multiple-bits BF. With the CRC information as additional input data, the proposed CNN-BF model can further reduce 5 flipping attempts. Besides, a tree-based flipping strategy is proposed to avoid useless flipping attempts caused by wrongly flipped bits. From the simulation results, our approach can outperform CS-BF and reduce flipping attempts by 89% when code length is 64, code rate is 0.5 and SNR is 1 dB. It also achieves a comparable block error rate (BLER) as CA-SCL. [ABSTRACT FROM AUTHOR]

We propose a new class of efficient decoding algorithms for Reed-Muller (RM) codes over binary-input memoryless channels. The algorithms are based on projecting the code on its cosets, recursively decoding the projected codes (which are lower-order RM codes), and aggregating the reconstructions (e.g., using majority votes). We further provide extensions of the algorithms using list-decoding. We run our algorithm for AWGN channels and Binary Symmetric Channels at the short code length (≤ 1024) regime for a wide range of code rates. Simulation results show that in both low code rate and high code rate regimes, the new algorithm outperforms the widely used decoder for polar codes (SCL+CRC) with the same parameters. The performance of the new algorithm for RM codes in those regimes is in fact close to that of the maximal likelihood decoder. Finally, the new decoder naturally allows for parallel implementations. [ABSTRACT FROM AUTHOR]

Low-Density Parity-Check (LDPC) codes are widely used from hard-disk systems to satellite communications. Sliding-Window Belief Propagation (SWBP) is an effective decoding algorithm of LDPC codes for time-varying channels and demonstrates near-optimal performance in many experiments. However, to adaptively find the best window size, SWBP may need very long computing time. Inspired by Graphics Processing Unit and Compute Unified Device Architecture, in this paper we propose a novel method to address the issue of SWBP's computing complexity. Different from sequential SWBP, we simultaneously compute the metrics of different window sizes in parallel, which enables us to quickly find the best window size. We use coalesced memory access to accelerate reading and writing processes. Registers and shared memory are also considered in our program to reduce memory latency. On the GTX 1080Ti platform, experimental results show that parallel SWBP can achieve about 14 × to 118 × speedup ratio for different regular LDPC codes, and about 8 × to 120 × speedup ratio for different irregular LDPC codes, respectively. According to the trend of our experiments, we strongly believe that, as the length of LDPC codes increases, a higher speedup ratio can be obtained. [ABSTRACT FROM AUTHOR]

A general time-varying feedback coding scheme is proposed for $M$ -user fully connected symmetric Gaussian interference channels. Based on the analysis of the general coding scheme, we prove a theorem which gives a criterion for designing good time-varying feedback codes for Gaussian interference channels. The proposed scheme improves the Suh-Tse and Kramer inner bounds of the channel capacity for the cases of weak and not very strong interference when $M=2$. This capacity improvement is more significant when the signal-to-noise ratio (SNR) is not very high. In addition, our coding scheme can be proved mathematically and numerically to outperform the Kramer code for $M\geq 2$ when the SNR is equal to the interference-to-noise ratio (INR). Besides, the generalized degrees-of-freedom (GDoF) of our proposed coding scheme can be proved to be optimal in the all network situations (very weak, weak, strong, very strong) for any $M$. The numerical results show that our coding scheme can attain better performance than the Suh-Tse coding scheme for $M=2$ or the Mohajer-Tandon-Poor lattice coding scheme for $M > 2$. Furthermore, the simplicity of the encoding/decoding algorithms is another strong point of our proposed coding scheme compared with the Suh-Tse coding scheme when $M=2$ and the Mohajer-Tandon-Poor lattice coding scheme when $M > 2$. More importantly, our results show that an optimal coding scheme for the symmetric Gaussian interference channels with feedback can be achieved by only using marginal posterior distributions under a better cooperation strategy between transmitters. [ABSTRACT FROM AUTHOR]

Low density parity check (LDPC) code is a kind of linear block code with excellent performance which is proposed by Dr. Gallager. It overcomes the shortcomings of other error correcting codes and it is the nearest channel code from Shannon limit at the present discover. The decoding algorithms of LDPC code can reduce the decoding delay by the parallel decoding structure, so this has caused great concern in many fields. In recent years more and more scholars begin to study LDPC code, this makes the coding and decoding algorithms of LDPC code improved continuously. LDPC code has been widely used in many fields such as optical fiber communication, digital watermarking, underwater communication and deep space communication because of its excellent performance. Non-binary LDPC code has better performance compared with binary LDPC code. In this paper, FFT-BP decoding algorithm of non-binary LDPC code is studied, and on this basis, we proposed an improved FFT-BP algorithm. The improved decoding algorithm can effectively reduce the average iteration number. Finally, we achieved encode and decode algorithm of non-binary LDPC code with FPGA. [ABSTRACT FROM AUTHOR]

In recent times, many advanced wireless communication systems have adopted channel coding schemes to ease secure transmission and reception of wireless data over noisy perturbed channel conditions. Channel coding approaches using low-density parity-check (LDPC) codes are most interesting and fastest growing research areas in the domain of wireless communications. Due to its widespread popularity, adaptability and parallelism for cost-effective hardware implementations, LDPC codes are widely endorsed in a number of wireless communication standards. Over the years, many low complex decoding algorithms using LDPC codes were introduced to improve the data reliability of many wireless applications. This work introduces an efficient and robust offset min-sum decoding scheme for optimal decoding of LDPC codes. This improved approach introduces a new offset correction factor to suppress the error propagation during the approximation of high precision soft values within the given range boundary of signal strength-to-background noise ratio (SNR). The experimental results illustrate the competitive advantage of the proposed algorithm over several popular algorithms in terms of error rate performance, complexity reductions and convergence speed. [ABSTRACT FROM AUTHOR]

We explore several new converse bounds for classical communication over quantum channels in both the one-shot and asymptotic regimes. First, we show that the Matthews-Wehner meta-converse bound for entanglement-assisted classical communication can be achieved by activated, no-signaling assisted codes, suitably generalizing a result for classical channels. Second, we derive a new efficiently computable meta-converse on the amount of classical information unassisted codes can transmit over a single use of a quantum channel. As applications, we provide a finite resource analysis of classical communication over quantum erasure channels, including the second-order and moderate deviation asymptotics. Third, we explore the asymptotic analogue of our new meta-converse, the $\Upsilon $ -information of the channel. We show that its regularization is an upper bound on the classical capacity, which is generally tighter than the entanglement-assisted capacity and other known efficiently computable strong converse bounds. For covariant channels, we show that the $\Upsilon $ -information is a strong converse bound. [ABSTRACT FROM AUTHOR]

Evaluating the block error rate of a digital communication system is usually done using the Monte Carlo (MC) simulation method. The main drawback of the Monte Carlo method is the need of a huge sample size for estimating low error rates. Other methods commonly used are the importance sampling technique and the quasi-analytical method. This paper introduces the metric star domain decoder model and shows that many practical decoders fall into this category. The main result is the introduction of a novel SNR-invariant quasi-analytical technique for estimating the block error rate of a communication link over the geodesic channel model (a generalization of a vast number of commonly used channels, including binary symmetric channel, BEC, and AWGN channel) with a metric star domain decoder used at the receiver. This technique outperforms the Monte Carlo and importance sampling methods in both accuracy and speed. It is shown that our quasi-analytical method is at least $10^{3}$ times faster than MC and 10 times faster than IS for the same accuracy. [ABSTRACT FROM AUTHOR]

The fundamental limits of communication over state-dependent discrete memoryless channels with noiseless feedback are studied, under the assumption that the communicating parties are allowed to use variable-length coding schemes. Various cases are analyzed, with the employed coding schemes having either bounded or unbounded codeword lengths, and with state information revealed to the encoder and/or decoder in a strictly causal, causal, or non-causal manner. In each of these settings, necessary and sufficient conditions for positivity of the zero-error capacity are obtained, and it is shown that, whenever the zero-error capacity is positive, it equals the conventional vanishing-error capacity. Moreover, it is shown that the vanishing-error capacity of state-dependent channels is not increased by the use of feedback and variable-length coding. Both these kinds of capacities of state-dependent channels with feedback are thus fully characterized. [ABSTRACT FROM AUTHOR]

Two independent data streams are to be transmitted over a noisy discrete memoryless channel with noiseless (ideal) feedback. Errors are tolerated only in the second stream, provided that they occur with vanishing probability. The rate of the error-free stream cannot, of course, exceed the channel’s zero-error feedback capacity, and nor can the sum of the streams’ rates exceed the channel’s Shannon capacity. Using a suitable coding scheme, these necessary conditions are shown to characterize all the achievable rate pairs. Planning for the worst channel behavior—as is needed to achieve zero-error communication—and planning for the typical channel behavior—as is needed to communicate near the Shannon limit—are thus not incompatible. It is further shown that feedback may be beneficial for the multiplexing problem even on channels on which it does not increase the zero-error capacity. [ABSTRACT FROM AUTHOR]

Given a collection of strings, each with an associated probability of occurrence, the guesswork of each of them is their position in a list ordered from most likely to least likely, breaking ties arbitrarily. The guesswork is central to several applications in information theory: average guesswork provides a lower bound on the expected computational cost of a sequential decoder to decode successfully the transmitted message; the complementary cumulative distribution function of guesswork gives the error probability in list decoding; the logarithm of guesswork is the number of bits needed in optimal lossless one-to-one source coding; and the guesswork is the number of trials required of an adversary to breach a password protected system in a brute-force attack. In this paper, we consider memoryless string sources that generate strings consisting of independent and identically distributed characters drawn from a finite alphabet, and characterize their corresponding guesswork. Our main tool is the tilt operation on a memoryless string source. We show that the tilt operation on a memoryless string source parametrizes an exponential family of memoryless string sources, which we refer to as the tilted family of the string source. We provide an operational meaning to the tilted families by proving that two memoryless string sources result in the same guesswork on all strings of all lengths if and only if their respective categorical distributions belong to the same tilted family. Establishing some general properties of the tilt operation, we generalize the notions of weakly typical set and asymptotic equipartition property to tilted weakly typical sets of different orders. We use this new definition to characterize the large deviations for all atypical strings and characterize the volume of tilted weakly typical sets of different orders. We subsequently build on this characterization to prove large deviation bounds on guesswork and provide an accurate approximation of its probability mass function. [ABSTRACT FROM AUTHOR]

We analyze a class of vector multiple access channels with additive noise, where the sum of the dimensions of the transmitted signals matches that of the received signal. We first focus on the case without power constraints, in the Poltyrev sense, using point process techniques. We find the Poltyrev capacity region for noise processes that are independent and identically distributed over channel uses. For each rate vector strictly in the Poltyrev capacity region, we study, for each subset of the transmitters, the exponent of the decay in block length of the smallest possible probability that decoding results in error for each transmitter in that subset. In the case of independent and identically distributed Gaussian noise, with arbitrary positive definite covariance matrix, we derive random coding exponents for each type of error event—these are lower bounds to the true error exponents. This also leads to random coding error exponents in the traditional power-constrained case, where the power constraint at each transmitter is defined by an arbitrary positive definite matrix. [ABSTRACT FROM AUTHOR]

We extend the notion of list decoding to ratio list decoding which involves a list decoder whose list size is specified as a function of the number of messages $M_{n}$ and the block length $n$. We present the necessary and sufficient conditions on $M_{n}$ for the existence of code sequences which enable reliable list decoding with respect to the desired list size $L(M_{n},n)$. It is shown that the ratio-capacity, defined as the supremum of achievable normalized logarithms of the ratio $r(M_{n},n)=M_{n}/L(M_{n},n)$ , is equal to the Shannon channel capacity $C$ , for both stochastic and deterministic encoding. Allowing for random list size, we are able to deduce some properties of identification codes, where the decoder’s output can be viewed as a list of messages corresponding to decision regions that include the channel output. We further address the regime of mismatched list decoding, in which the list constitutes of the codewords that accumulate the highest score values (jointly with the channel output) according to some given function. We study the case of deterministic encoding and mismatched ratio list decoding. We establish similar necessary and sufficient conditions for the existence of code sequences which enable reliable mismatched list decoding with respect to the desired list size $L(M_{n},n)$ , and we show that the ratio-capacity with mismatched decoding is equal to the mismatch capacity. Focusing on the case of an exponential list size $L_{n}=e^{n \Theta }$ , its comparison with ordinary mismatched decoding shows that the increase in capacity is by $\Theta $ bits per channel used for all channels and decoding metrics. Several properties of the average error probability in the setup of mismatched list decoding with deterministic list size are provided. [ABSTRACT FROM AUTHOR]

The performance of maximum-likelihood (ML) decoding on the binary erasure channel for finite-length low-density parity-check (LDPC) codes from two random ensembles is studied. A tightened union-type upper bound on the ML decoding error probability based on the precise coefficients of the average weight spectrum is presented. For LDPC codes from the Gallager ensemble and the Richardson–Urbanke ensemble, new upper bounds on the ML decoding performance based on computing the rank of submatrices of the code parity-check matrix are derived. A new lower bound on the ML decoding threshold followed from the latter error probability bound is obtained. An improved lower bound on the error probability for codes with a known estimate on the minimum distance is presented as well. A new low-complexity near-ML decoding algorithm for quasi-cyclic LDPC codes is proposed and simulated. Its performance is compared to the simulated belief propagation and ML decoding performance and simulated performance of the best known improved iterative decoding techniques, as well as, with the derived upper bounds on the ML decoding performance and with decoding thresholds obtained by the density evolution technique. [ABSTRACT FROM AUTHOR]

A new method is presented for low-complexity near-maximum-likelihood (ML) decoding of low-density parity-check (LDPC) codes over the additive white Gaussian noise channel. The proposed method termed belief-propagation–list erasure decoding (BP-LED) is based on erasing carefully chosen unreliable bits performed in case of BP decoding failure. A strategy of introducing erasures into the received vector and a new erasure decoding algorithm are proposed. The new erasure decoding algorithm, called list erasure decoding, combines ML decoding over the BEC with list decoding applied if the ML decoder fails to find a unique solution. The asymptotic exponent of the average list size for random regular LDPC codes from the Gallager ensemble is analyzed. Furthermore, a few examples of irregular quasi-cyclic LDPC as well as randomly constructed regular LDPC codes of short and moderate lengths are studied by simulations and their performance is compared to the tightened upper bound on the LDPC ensemble-average performance and the upper bound on the average performance of random linear codes under ML decoding. A comparison of the BP decoding and BP-LED performance of the WiMAX standard codes and performance of the near-ML BEAST decoding are presented. The new algorithm is applied to decoding a short nonbinary (NB) LDPC code over extensions of the binary Galois field. The obtained simulation results are compared to the tightened upper bound on the ensemble-average performance of the binary image of regular NB LDPC codes. [ABSTRACT FROM AUTHOR]

A construction of a channel code by using a source code with decoder side information is introduced. The encoder and decoder pair of any source code can be used for the construction. Constrained-random-number generators, which generate random numbers satisfying a condition specified by a function and its value, are used to construct stochastic encoders and decoders. The result suggests that we can divide the channel coding problem into the problems of channel encoding and source decoding with side information. [ABSTRACT FROM AUTHOR]

Due to the rapid advancement in processing power and camera quality of mobile devices, research on the display-to-camera (D2C) communication channel has recently received increasing attention. Unlike the traditional QR Code, the unobtrusive D2C communication scheme normally serves both the human eyes and the mobile camera in commercial advertisements. Thus, attention should be paid to both unobtrusiveness and reliability of the design of a D2C communication scheme. In this paper, 2D barcodes with unobtrusive embedding in the blue channel are proposed in image and video formats to yield the robust and unobtrusive (RU) code and video-based RU (vRU) code, respectively. The proposed RU code is featured with a modulation scheme in blue channel that leverages several important properties of the human visual system; such as insensitivity toward the yellow-blue chrominance component, the proximity principle, and the oblique effect. Both RU code and vRU code employ a low-density-parity-check code for intra-frame channel coding. In addition, vRU code adopts an erasure-correcting Reed–Solomon code for inter-frame channel coding. Under a high perceptual quality constraint (multiscale structural similarity (MS-SSIM) ≈ 0.95), RU code achieves a demodulation bit error probability of 3.84%, which is an order of magnitude smaller than that of the existing picture-embedding 2D barcodes. Meanwhile, under a similar perceptual quality requirement (MS-SSIM ≈ 0.95 for each video frame), the goodput of vRU code is reported to be as high as 34.33 kbps under practical settings, e.g., a display frame rate of 30 fps and a capture frame rate of 42 fps. [ABSTRACT FROM AUTHOR]

With the rise of critical machine-to-machine applications, next generation wireless communication systems must meet challenging requirements with respect to latency and reliability. A key question in this context relates to channel state estimation, which allows the transmitter to adapt the code rate to the channel state. In this paper, we characterize the tradeoff between the training sequence length and data codeword length: shorter channel estimation leaves more time for the payload transmission but reduces the estimation accuracy and causes more decoding errors. Using lower coding rates can mitigate this effect, but may result in a higher backlog of data at the transmitter. In order to optimize the training sequence length and the rate adaptation scheme with respect to the delay performance, we employ queuing analysis on top of accurate models of the physical layer. We obtain an analytically tractable solution to the problem by deriving a closed-form approximation for the decoding error probability due to imperfect channel knowledge and finite-blocklength channel coding. The optimized training sequence length and rate adaptation strategy can reduce the delay violation probability by an order of magnitude, compared with suboptimal strategies that do not consider the delay constraints. [ABSTRACT FROM AUTHOR]