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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]

The authors propose encoding and decoding network‐based normalizing flows (EaD‐Flow) for the detection and localization of anomalies in an image. Multiple networks of the EaD‐Flow estimate probability densities of tenor image. The anomaly localization model based on multiple networks shows superior anomaly detection and localization performance. [ABSTRACT FROM AUTHOR]

This letter focuses on improving the error correction performance of the extended min‐sum (EMS) decoding algorithm. Introducing factor/offset modifications in the check node update process of the EMS algorithm can improve the performance. Based on this, the authors propose a novel threshold‐based modified EMS algorithm that introduces the factor/offset in a targeted manner by setting a threshold for the posterior probability. Simulation results show that an additional performance gain of the order of 0.08 dB is obtained with the proposed method without significantly increasing the complexity of the method. [ABSTRACT FROM AUTHOR]

White modules of quick response codes (QR codes) are degraded by dot gain, especially when printed at smaller sizes, which results in more false blacks than false whites in error analysis, and also severely affects decoding ability. To reduce the false blacks generated from printing and to improve code readability, modifying the microstructure of graphic QR codes by reducing the size of the information dots is proposed. Experimental results show that the resultant QR code reduces the number of false blacks and thus the error rate. This method applies to the physical output of both conventional and graphic QR codes. [ABSTRACT FROM AUTHOR]

An efficient joint Viterbi detection and decoding (JVDD) algorithm for a bluetooth low energy (BLE) system is proposed. Since the convolutional coded Gaussian minimum-shift keying (GMSK) signal is specified in the BLE 5.0 standard, two Viterbi processors are needed for detection and decoding. However, the proposed JVDD scheme uses only one Viterbi processor by modifying the branch metric with inter-symbol interference information from GMSK modulation; therefore, the hardware complexity can be significantly reduced without performance degradation. [ABSTRACT FROM AUTHOR]

All test patterns are decoded in the conventional Chase-2 algorithm, but only a few candidate codewords are derived. In this work, a highly efficient Chase-2 decoding algorithm has been proposed, where only the test patterns that can be decoded into distinct candidate codewords are processed. It means that the total number of decoding attempts is reduced from that of the test patterns to that of the candidate codewords, which consequently reduces the complexity, especially in high signal-to-noise ratio (SNR) region. The criterion of the test pattern selection is based on the property of minimum Hamming distance, it can be expected that the proposed algorithm can be applied to all linear block codes without performance degradation compared to the conventional Chase-2 algorithm. [ABSTRACT FROM AUTHOR]

Belief propagation and variants are the usual decoding algorithms for low‐density parity check codes. The successive overrelaxations are applied to increase the convergence speed of the decoding process. Performances are reported and improvements over the reference algorithms are observed. This technique is also compatible with the high‐speed parallel group decoding involved in modern standards such as DVB‐S2. [ABSTRACT FROM AUTHOR]

In a recent study, Li et al. proposed an algorithm for the decoding of binary quadratic residue codes with tiny memory requirements. In this Letter, this algorithm is modified in order to dramatically improve the decoding speed. The case of the (89, 45, 17) binary quadratic residue code is used to illustrate the new algorithm. [ABSTRACT FROM AUTHOR]

The existing thumbnail extraction method generates a thumbnail by reducing the reconstructed frame after a full decoding process. This method is complex and requires considerable time, particularly for higher resolution video. To alleviate these issues, a fast thumbnail extraction method which utilises an intra-prediction mode for high-efficiency video coding (HEVC) is presented. The proposed method reconstructs only the 4×4 boundary pixels needed for a thumbnail image based on the intra-prediction mode. Experimental results indicate that the proposed method significantly reduces the computational complexity and extraction time for a thumbnail image. The visual quality of thumbnail images obtained with this method does not differ significantly from that of images extracted after a full decoding process. [ABSTRACT FROM AUTHOR]

In this Letter, a list decoding algorithm is proposed for the semi-random block-oriented convolutional code (SRBO-CC). To decode each sub-frame, a list of candidates are serially computed until finding a qualified one or achieving maximum list, where the correctness of the decoding candidate is checked by a statistical threshold. Simulation results show that SRBO-CC with list decoding is competitive with polar codes and that the performance-complexity tradeoffs can be achieved by adjusting the statistical threshold. [ABSTRACT FROM AUTHOR]

This Letter introduces a class of fixed-length to variable-length balanced binary line codes. By considering fixed size blocks of source digits, a balanced line code is constructed by appending a minimum number of 0's or 1's to each such block in order to produce words having equal number of 0's and 1's, i.e. balanced words of variable length. By taking into account the design constraint of being easily implementable in practice, the construction introduced achieves high coding efficiency and is at least asymptotically optimal in terms of redundancy. [ABSTRACT FROM AUTHOR]

Error correction performance of finite-length polar codes has been a major concern in the past decade. This Letter presents a method for improving the error correction performance of cyclic redundancy check (CRC)-aided successive cancellation list decoding for polar codes of medium block-lengths with high code rates. In the proposed decoding scheme, a one-time repetition of least reliable bit-channels along with partial protection of the message is employed to correct the error(s) when decoding fails. The results show an improvement of nearly 0.2 dB in error correction performance. [ABSTRACT FROM AUTHOR]

Array-based non-binary (NB) low-density parity-check (LDPC) codes are attractive in practice for their advantages in implementation and performance. However, existing construction of array-based NB LDPC codes is only with the prime number cases. In this Letter, the authors extend the array-based construction to composite numbers to give an explicit construction of structured array-based NB LDPC codes with column weights three, four, and five. The resulting codes have girth at least six. The simulation results show that the proposed structured codes perform as well as the random codes constructed by progressive edge-growth algorithm, when decoded with the Q-ary sum product algorithm and the low-complexity weighted bit-reliability-based decoding algorithm. [ABSTRACT FROM AUTHOR]

Belief propagation and variants are the usual decoding algorithms for low-density parity check codes. The successive overrelaxations are applied to increase the convergence speed of the decoding process. Performances are reported and improvements over the reference algorithms are observed. This technique is also compatible with the high-speed parallel group decoding involved in modern standards such as DVB-S2. [ABSTRACT FROM AUTHOR]

An improved extension method based on protograph extrinsic information transfer (PEXIT) charts is proposed to design ratecompatible quasi-cyclic low-density parity-check (QC-LDPC) codes with more flexible rates and better performance. The masking matrix of the highest-rate code can first be constructed column by column to own the lowest decoding threshold. Then, an extension algorithm is proposed to obtain the masking matrices of lower-rate codes with flexible rates. Finally, the base matrices with small amount of short cycles are designed and the parity-check matrices of rate-compatible QC-LDPC codes are obtained through matrix extension. Simulations show that compared with the existing codes, the proposed codes have more flexible rates while achieving better performance. [ABSTRACT FROM AUTHOR]

Since irregular low-density parity-check (LDPC) codes are known to perform better than regular ones, and to exhibit, like them, the so-called 'threshold phenomenon', this Letter investigates a low-complexity upper bound on belief-propagation decoding thresholds for this class of codes on memoryless binary input additive white Gaussian noise channels, with sum-product decoding. A simplified analysis of the belief-propagation decoding algorithm is used, i.e. consider a Gaussian approximation for message densities under density evolution, and a simple algorithmic method, defined recently, to estimate the decoding thresholds for regular and irregular LDPC codes. [ABSTRACT FROM AUTHOR]

A polar code-based overlapping transmission scheme to improve channel utilisation for Internet of Vehicles is presented. In the presented scheme, different relay nodes (RNs) are allowed to send their packets to the destination node (DN) in the same time slot and frequency band. The signals from RNs to DN are overlapped and hence non-orthogonal. However, the information in the overlapped signals can be recovered by the proposed decoding algorithm. Numerical results show that the decoding algorithm performs well on information recovery in the presented transmission scheme. [ABSTRACT FROM AUTHOR]

Image steganography hides secret information in the cover images so naturally that the existence of hidden data in the stego-image is not recognisable. This Letter proposes a new approach to blind decoding of image steganography using the local entropy distributions of decoded images. The local entropy distributions of incorrectly decoded images are different from those of normal ones because of the abnormal image structures in the erroneously decoded images. This blind decoding in the image steganography is very useful to extract hidden image information because there are enormous least significant bit (LSB)-based steganography methods, and it is very hard to find the methods by observing manipulated LSBs. [ABSTRACT FROM AUTHOR]

In this Letter, a new criterion based on frozen BER (FBER) is proposed to early stop belief propagation (BP) decoding of polar codes. The authors first verify that the behaviour of FBER along with the iteration is almost the same as the information BER. Based on this phenomenon, the authors propose a new criterion by detecting the status of FBER to determine whether the BP decoding is successful or not. To reduce the complexity, only a part of frozen bits transmitted in most reliable frozen sub-channels are considered. Simulation results show that the proposed criterion is more hardware friendly than the existing criteria. [ABSTRACT FROM AUTHOR]

Systematic wireless network coding has been proposed as a potential solution to solve the major drawback of high encoding/decoding complexities of random linear network coding and to increase the decoding capability. However, the complete analysis of the decoding performance has not been fully derived. In this Letter, the authors derive closed-form expressions for the decoding probability under systematic network coding (SNC) over single-hop and multi-hop wireless networks. They validate the analysis by comparing simulation results. Their formulation provides a theoretical analysis for further understanding of the SNC and can be used to improve the current upper bound for the decoding probability. [ABSTRACT FROM AUTHOR]

Since the polar code was discovered by Arikan, many decoding methods have been proposed, one of which is the belief propagation (BP) decoding. Its inherent high parallel level makes it suitable for high-speed applications. A novel BP decoder based on a modified three-by-three kernel matrix is proposed. The corresponding decoding algorithm and frozen bits selection method are presented. The numerical results show that it has a similar error correcting capability compared with the original polar BP decoder. More importantly, the message memory requirement can be reduced from O(N log2 N) to O (N log3 N), and the decoding delay can be reduced accordingly. [ABSTRACT FROM AUTHOR]

A novel optical comparator is proposed for the novel Viterbi-decoding scheme, and the performance of the proposed scheme with the optical comparators is analytically investigated. The net coding gain of the proposed scheme is not degraded compared with conventional scheme, and the proposed scheme could reduce the calculation steps by a factor of ~4/5 of the conventional scheme. [ABSTRACT FROM AUTHOR]

A hard-decision iterative decoding scheme for the Davey–MacKay construction with symbol-level inner decoder is presented. In this scheme, the synchronisation capability of the inner decoder is enhanced by replacing the equal priori probabilities for symbols by the accurate hard-decision feedback information from the outer decoder. Furthermore, the error-correcting capability of the outer decoder is improved and the hard-decision feedback information is updated. Simulation results show that the presented scheme significantly improves the performance and saves the computational time with little performance loss. [ABSTRACT FROM AUTHOR]

Error correction codes are commonly used to protect the data stored in memories from errors. Among the codes used, single error correction double error detection (SEC-DED) codes are probably the most common due to their simplicity. In some applications, the importance of the bits is different, being some of them critical while others can tolerate some errors. This is the case, for example, in some multimedia and signal processing systems. For those applications, unequal error protection (UEP) codes that provide different protection for different bits can be used. In many cases, the bits that require extra protection are only a few. Therefore, it would be convenient to use a traditional code extended to provide additional protection for a few bits. A simple method to derive UEP codes from SEC-DED codes is presented. The proposed UEP codes protect a few bits against double errors and behave as SEC-DED codes for the rest. Encoding and decoding complexity is only slightly larger than that of an SECDED code and the implementation is a simple modification of the SEC-DED implementation. [ABSTRACT FROM AUTHOR]

The optimal strategy of chroma 422 subsampling for Bayer pattern in H.264 video coding is proposed. The state-of-the-art work uses a predetermined conversion method from colour filter array to YCbCr 422. Derived from this structure, first, 64 subsampling methods are designed to exploit more possibilities. Secondly, among which, the four optimal methods are found by the pre-screening process, which show their better performances than the state-of-the-art method by up to 2.57 dB in CPSNR averaged for different videos, demonstrating the practicability of the proposed methods. Finally, for the experiment consisting of the whole conversion and H.264 video encoding/decoding procedures, the proposed optimal methods perform better than the state-of-the-art method under all different operating bitrates and different tested videos, by up to 2.25 dB in BDPSNR. [ABSTRACT FROM AUTHOR]

Novel simplified merged processing element (SMPE) architectures to design a low-complexity successive-cancellation (SC) polar decoder are presented. The proposed SMPE architectures reduce the number of sign-magnitude conversions and switch networks, relative to those of the conventional merged processing element. Synthesis results show that the (1024, 512) SC polar decoder using the proposed SMPE architectures significantly decreases hardware complexity and improves technology scaled normalised throughput, as compared to those of the previously reported architectures. [ABSTRACT FROM AUTHOR]

A simple and effective technique to skip the computation of reliable portions of a frame (windows) for turbo code decoding is proposed. The proposed criterion relies on a very simple approximation of cross-entropy measure by means of thresholding. This criterion features negligible complexity and low-memory requirements. Simulation results show that, in the best case, up to 20% of windows can be skipped with no error-rate degradation. Such a significant computation reduction can be exploited to directly reduce the power consumption as well. [ABSTRACT FROM AUTHOR]

A robust stopping criterion (called online-BER [OB]) that can terminate iterative turbo decoding in a signal-to-noise ratio (SNR) uncertainty environment is proposed. OB is based on the online bit error rate (BER) estimation and the BER thresholds. Both values are used to detect convergence and non-convergence decoder output and also to halt iterative decoding in various SNRs. Unlike other well-known stopping criteria, OB does not depend on SNR information in its stopping rules and hence it is less complex. OB is also more robust than other stopping criteria in a SNR uncertainty environment while being capable of reducing the average iteration number and resulting in less degradation in BER performance. [ABSTRACT FROM AUTHOR]

A novel comparative study of different low-density parity-check (LDPC) coding algorithms and implementation issues through field-programmable gate arrays (FPGAs) technology for wireless vehicular applications is presented. A key development in LDPC codes is the iterative decoding algorithm which uses the belief propagation algorithm. A comprehensive investigation of the performance of different coding schemes was carried out. Four different decoding techniques were tested by computer-based simulations of messages modulated under the binary phase-shift keying modulation scheme and transmitted through a vehicular channel model. Finally, the best performance ratio against complexity algorithm was chosen to be implemented on a Xilinx FPGA platform. [ABSTRACT FROM AUTHOR]

Multilevel coding (MLC) provides a low-complexity encoding scheme for lattices obtained via construction D. On the other hand, multistage decoding is also a practical decoding scheme for MLC provided that the underlying error correcting codes are capacity achieving, which requires using a powerful soft decoder for each code. Proposed is an approximation of the log-likelihood ratio (LLR) which used for the soft decoding of the different error correcting codes employed in the lattice construction. This approximation is based on the von Mises distribution and achieves, with lower complexity, the same error rate performance obtained with the exact LLR calculation. [ABSTRACT FROM AUTHOR]

The article presents an interview with professor Xiao Ma. Topics mentioned include the study on the transmission mechanics for the Internet of Vehicles (IoV), the relation of IoV to Internet of Things (IoT), and the importance of decoding algorithms. Also mentioned are the development of fifth generation (5G) transmission system and the development in cellular communications.

In this reported work, a modified decoding and detection scheme with dispersion compensation is investigated for spectral-amplitude-coding optical code division multiple access (SAC-OCDMA) systems. For simultaneously decoding and compensating the chromatic dispersion of signals in the 40 km-long standard single-mode fibre transmission, based on reconstruction equivalent-chirp method the array configuration of fibre Bragg grating (FBG) segments can be controlled with a quadratic dispersion of -680 ps/nm for an extra time delay. The traditional triple-branch signal detection (TBSD) scheme is then modified and the principle of multiuser interference elimination is theoretically analysed. The simulated results show that, without adding a dispersion compensation device, the modified TBSD scheme adopting the FBG decoder can realise the decoding and detection function in SACOCDMA. [ABSTRACT FROM AUTHOR]

A new architecture for a polar decoder using a reduced complexity successive-cancellation (SC) decoding algorithm is presented. This novel fully unrolled, deeply pipelined architecture is capable of achieving a coded throughput of over 237 Gbit/s for a (1024, 512) polar code implemented using a field-programmable gate array. This decoder is two orders of magnitude faster than state-of-the-art polar decoders. [ABSTRACT FROM AUTHOR]

The three-dimensional (3D) extension of the high-efficiency video coding (3D-HEVC) standard adopts new depth-modelling modes (DMMs) to provide an alternative prediction scheme for depth-map intra-coding. In 3D-HEVC, although edges in depth maps can be accurately estimated by utilising the DMMs, testing the DMMs in the mode decision introduces a huge computational load to the encoder. A fast mode decision algorithm is proposed that can significantly reduce the computational overhead incurred by the DMMs. Experimental results indicate that the proposed algorithm reduces the encoding complexity by 33.89% on average without any penalty in coding efficiency. [ABSTRACT FROM AUTHOR]

A network polar coded-cooperative (NPCC) scheme with joint successive cancellation (SC) decoding at the destination is proposed. Plotkin's construction is employed to build polar codes; however, the proposed construction is opposite to the conventional method where two short codes jointly construct a longer length code. In the proposed construction the two short codes (subcodes) are derived from the longer length code. The proposed construction is then employed to achieve coded cooperation between two users, and also offers a network coding, which not only improves the data rate of the coded cooperative system but also improves the overall bit error rate performance which is shown with the help of numerical simulations. [ABSTRACT FROM AUTHOR]

A random code is a rateless erasure code with a generator matrix of randomly distributed binary values. It encodes a message of k symbols into a potentially infinite number of coded symbols. For asymptotically large k, the tail bound in Kolchin's theorem asserts that the high probability of complete decoding (PCD) is attained almost surely with k + 10 coded symbols. However, for small values of k (short messages) it is unclear if such asymptotics are useful. That the random codes achieve a high PCD with k + 10 coded symbols for small k is demonstrated. In particular, a set of lemmas is established and show that the PCD converges to five decimal digits after k = 30. A theorem extending Kolchin's work is formulated and the theorem is used to explain the complete decoding probabilities of random codes in short messages. [ABSTRACT FROM AUTHOR]

The two-dimensional parity check is the optimum single-error-correction code in terms of speed. In this reported work it is employed to develop two sliding schemes for through-silicon-via cluster error correction in three-dimensional ICs. For k bits of source data, the onedimensional sliding scheme can correct a single cluster error up to about √k bits and more extra discrete errors can be corrected by the two-dimensional sliding scheme. Experiments show that for several hundreds of through-silicon vias (TSVs), two trees of 3-level 2-input exclusive-OR (XOR) gates are almost optimised to encode and decode each interconnect, and the time penalty can be controlled within about 1 ns. [ABSTRACT FROM AUTHOR]

The generation of intrinsic LLR messages in non-binary (NB) coded schemes associated with quadrature amplitude modulation (QAM) is considered. It is shown that the intrinsic LLR message generation corresponds to the same kind of computation as the one performed at the elementary check nodes in extended min-sum NB-LDPC decoders, i.e. finding a given number of minimum values in a structured set. It is proposed to use the bubble-check algorithm for the LLR calculation to benefit from two advantages: low-complexity hardware architecture and sharing the same hardware at the demapping and the decoding steps. [ABSTRACT FROM AUTHOR]

The computation of the entropy of a high-speed data stream in a one-pass fashion is crucial to many network security applications. Motivated by the work of Lall et al., this study examines the design trade-off of processing speed and accuracy for estimating the entropy norm. The proposed scheme leverages the Count Sketch with constant memory access on counter update and point query operations. With a bounded relative error and a constant memory access cycle, the design can process incoming traffic with a throughput of 30 Gbit/s. [ABSTRACT FROM AUTHOR]

A very fast decoding algorithm using matrix dimensionality reduction for RaptorQ codes is proposed. The algorithm exploits a pre-calculated inverse matrix to achieve dimensionality reduction for the received code constraint matrix. As a result, the decoding complexity is decreased significantly, whereas the failure-overhead curve is still identical to that of conventional approaches. Simulations show that the decoding speed of the proposed algorithm can be as fast as 17.5 times the state-of-the-art algorithm when the erasure probability is relatively low. [ABSTRACT FROM AUTHOR]

A method for correcting both errors and erasures of Reed-Solomon (RS) codes using error-only and erasure-only decoding algorithms is proposed. First, the method removes the effect of erasures from syndromes, then it uses error-only and erasure-only correcting processes to correct errors and erasures, respectively; thus, the overall decoding complexity can be reduced substantially. Furthermore, with hardware implementation, the most time-consuming operations in these two processes can be calculated concurrently to obtain a significant reduction of decoding latency. [ABSTRACT FROM AUTHOR]

A method for correcting both errors and erasures of Reed‐Solomon (RS) codes using error‐only and erasure‐only decoding algorithms is proposed. First, the method removes the effect of erasures from syndromes, then it uses error‐only and erasure‐only correcting processes to correct errors and erasures, respectively; thus, the overall decoding complexity can be reduced substantially. Furthermore, with hardware implementation, the most time‐consuming operations in these two processes can be calculated concurrently to obtain a significant reduction of decoding latency. [ABSTRACT FROM AUTHOR]

A polar coding method to construct a distributed source coding scheme which can achieve any point on the dominant face of the Slepian-Wolf rate region for sources with uniform marginals is proposed. Source encoding and decoding operations are performed using efficient algorithms which makes practical implementation feasible. Simulation results are given to exhibit the performance of the presented method. [ABSTRACT FROM AUTHOR]