Journal articles on the topic 'Ordered Statistic Decoding'

In this contribution, KNIH algorithm and Ordered Statistic Decoding (OSD) algorithm are investigated, based on which, a novel KNIH-OSD parallel decoding scheme for LDPC codes is proposed. KNIH decoding algorithm processes certain LRPs of a received sequence, while OSD algorithm processes certain MRIPs of a received sequence. If there are too many errors in MRIPs, the OSD algorithm will fail, on the contrary, if there are too many errors in LRPs, the KNIH algorithm will fail. This contribution proposes a parallel decoding scheme based on the complementary characteristic of these two algorithms. Simulation results show that the proposed scheme is feasible and effective. Compared with OSD and KNIH algorithm, the decoding performance is improved.

Due to the design principle of parallel processing, belief propagation (BP) decoding is attractive, and it provides good error-correction performance compared with successive cancellation (SC) decoding. However, its error-correction performance is still inferior to that of successive cancellation list (SCL) decoding. Consequently, this paper proposes a novel flip-list- (FL)-enabled belief propagation (BP) method to improve the error-correction performance of BP decoding for polar codes with low computational complexity. The proposed technique identifies the vulnerable channel log-likelihood ratio (LLR) that deteriorates the BP decoding result. The FL is utilized to efficiently identify the erroneous channel LLRs and correct them for the next BP decoding attempt. The preprocessed channel LLR through FL improves the error-correction performance with minimal flipping attempts and reduces the computational complexity. The proposed technique was compared with the state-of-the-art BP, i.e., BP bit-flip (BP-BF), generalized BP-flip (GBPF), cyclic redundancy check (CRC)-aided (CA-SCL) decoding, and ordered statistic decoding (OSD), algorithms. Simulation results showed that the FL-BP had an excellent block error rate (BLER) performance gain up to 0.7 dB compared with BP, BP-BF, and GBPF decoder. Besides, the computational complexity was reduced considerably in the high signal-to-noise ratio (SNR) regime compared with the BP-BF and GBPF decoding methods.

In this paper, we propose a low-complexity ordered statistics decoding (OSD) algorithm called threshold-based OSD (TH-OSD) that uses a threshold on the discrepancy of the candidate codewords to speed up the decoding of short polar codes. To determine the threshold, we use the probability distribution of the discrepancy value of the maximal likelihood codeword with a predefined parameter controlling the trade-off between the error correction performance and the decoding complexity. We also derive an upper-bound of the word error rate (WER) for the proposed algorithm. The complexity analysis shows that our algorithm is faster than the conventional successive cancellation (SC) decoding algorithm in mid-to-high signal-to-noise ratio (SNR) situations and much faster than the SC list (SCL) decoding algorithm. Our addition of a list approach to our proposed algorithm further narrows the error correction performance gap between our TH-OSD and OSD. Our simulation results show that, with appropriate thresholds, our proposed algorithm achieves performance close to OSD’s while testing significantly fewer codewords than OSD, especially with low SNR values. Even a small list is sufficient for TH-OSD to match OSD’s error rate in short-code scenarios. The algorithm can be easily extended to longer code lengths.

<span lang="EN-US">In the context of decoding binary linear block codes by polar code decoding techniques, we propose in this paper a new optimization of the serial nature of decoding the polar codes equivalent to binary linear block codes. In addition to the special nodes proposed by the simplified successive-cancellation list technique, we propose a new special node allowing to estimate in parallel the bits of its sub-code. The simulation is done in an additive white gaussian noise channel (AWGN) channel for several linear block codes, namely bose–chaudhuri–hocquenghem codes (BCH) codes, quadratic-residue (QR) codes, and linear block codes recently designed in the literature. The performance of the proposed technique offers the same performance in terms of frame error rate (FER) as the ordered statistics decoding (OSD) algorithm, which achieves that of maximum likelihood decoder (MLD), but with high memory requirements and computational complexity.</span>

We study the decoding transition for quantum error correcting codes with the help of a mapping to random-bond Wegner spin models. Families of quantum low density parity-check (LDPC) codes with a finite decoding threshold lead to both known models (e.g., random bond Ising and random plaquette $\Z2$ gauge models) as well as unexplored earlier generally non-local disordered spin models with non-trivial phase diagrams. The decoding transition corresponds to a transition from the ordered phase by proliferation of ``post-topological'' extended defects which generalize the notion of domain walls to non-local spin models. In recently discovered quantum LDPC code families with finite rates the number of distinct classes of such extended defects is exponentially large, corresponding to extensive ground state entropy of these codes. Here, the transition can be driven by the entropy of the extended defects, a mechanism distinct from that in the local spin models where the number of defect types (domain walls) is always finite.

Relevance. This paper presents relevant topic of the use of unmanned aerial vehicles (UAV) in the agroindustrial complex (AIC) to obtain timely reliable information about the state of agricultural land for the entire period. In modern infocommunication technologies and communication systems, high requirements are placed on the reliability of information transmission. In mobile data exchange systems, compositions of noise-resistant codes are used in the form of cascade designs or turbo codes, and in order to increase their efficiency, it is necessary to make the fullest use of the redundancy introduced at each stage of data processing. To solve such a problem, it is advisable to apply a decoding method based on the ordering of the character confidence indices (CCI) of the code combination.Methods. When determining the encoding-decoding systems, the Mathcad application software was used. Mathematical studies have shown that binary block codes for reaching the specified boundary can be decoded not only on the basis of ordered statistics, but also using the method of dividing the space of allowed code combinations into clusters. Based on this method, a block diagram of the algorithm of the simulation model of the operation of the block code decoder based on cluster calculation is compiled.Results. The application of the proposed method of soft decoding of systematic block codes reduces the processing time of code combinations in the decoder by reducing the dimension of the square matrix to determine the nonlinearity property of the rows of the rearranged generating matrix after ordering the columns of the original generating matrix.

We propose a simplified version of the Kitaev's surface code in which error correction requires only three-qubit parity measurements for Pauli operators XXX and ZZZ. The new code belongs to the class of subsystem stabilizer codes. It inherits many favorable properties of the standard surface code such as encoding of multiple logical qubits on a planar lattice with punctured holes, efficient decoding by either minimum-weight matching or renormalization group methods, and high error threshold. The new subsystem surface code (SSC) gives rise to an exactly solvable Hamiltonian with 3-qubit interactions, topologically ordered ground state, and a constant energy gap. We construct a local unitary transformation mapping the SSC Hamiltonian to the one of the ordinary surface code thus showing that the two Hamiltonians belong to the same topological class. We describe error correction protocols for the SSC and determine its error thresholds under several natural error models. In particular, we show that the SSC has error threshold approximately $0.6\%$ for the standard circuit-based error model studied in the literature. We also consider a model in which three-qubit parity operators can be measured directly. We show that the SSC has error threshold approximately 0.97% in this setting.

PurposeA recent innovative technology used in wireless communication is recognized as multiple input multiple output (MIMO) communication system and became popular for quicker data transmission speed. This technology is being examined and implemented for the latest broadband wireless connectivity networks. Though high-capacity wireless channel is identified, there is still requirement of better techniques to get increased data transmission speed with acceptable reliability. There are two types of systems comprising of multi-antennas placed at transmitting and receiving sides, of which first is diversity technique and another is spatial multiplexing method. By making use of these diversity techniques, the reliability of transmitting signal can be improved. The fundamental method of the diversity is to transform wireless channel such as Rayleigh fading into steady additive white Gaussian noise (AWGN) channel which is devoid of any disastrous fading of the signal. The maximum transmission speed that can be achieved by spatial multiplexing methods is nearly equal to channel capacity of MIMO. Conversely, for diversity methods, the maximum speed of broadcasting is much lower than channel capacity of MIMO. With the advent of space–time block coding (STBC) antenna diversity technique, higher-speed data transmission is achievable for spatially multiplexed multiple input multiple output (SM-MIMO) system. At the receiving end, detection of the signal is a complex task for system which exhibits SM-MIMO. Additionally, a link modification method is implemented to decide appropriate coding and modulation scheme such as space diversity technique STBC to use two-way radio resources efficiently. The proposed work attempts to improve detection of signal at receiving end by employing STBC diversity technique for linear detection methods such as zero forcing (ZF), minimum mean square error (MMSE), ordered successive interference cancellation (OSIC) and maximum likelihood detection (MLD). The performance of MLD has been found to be better than other detection techniques.Design/methodology/approachAlamouti's STBC uses two transmit antennas regardless of the number of receiver antennas. The encoding and decoding operation of STBC is shown in the earlier cited diagram. In the following matrix, the rows of each coding scheme represent a different time instant, while the columns represent the transmitted symbols through each different antenna. In this case, the first and second rows represent the transmission at the first and second time instant, respectively. At a time t, the symbol s1 and symbol s2 are transmitted from antenna 1 and antenna 2, respectively. Assuming that each symbol has duration T, then at time t + T, the symbols –s2* and s1*, where (.)* denotes the complex conjugate, are transmitted from antenna 1 and antenna 2, respectively. Case of one receiver antenna: The reception and decoding of the signal depend on the number of receiver antennas available. For the case of one receiver antenna, the received signals are received at antenna 1 , hij is the channel transfer function from the jth transmit antenna and the ith receiver antenna, n1 is a complex random variable representing noise at antenna 1 and x (k) denotes x at time instant k ( at time t + (k – 1)T.FindingsThe results obtained for maximal ratio combining (MRC) with 1 × 4 scheme show that the BER curve drops to 10–4 for signal-to-noise (SNR) ratio of 10 dB, whereas for MRC 1 × 2 scheme, the BER drops down to 10–5 for SNR of 20 dB. Results obtained in Table 1 show that when STBC is employed for MRC with 1 × 2 scheme (one antenna at transmitter node and two antennas at receiver node), BER curve comes down to 0.0076 for Eb/N0 of 12. Similarly, when MRC with 1 × 4 antenna scheme is implemented, BER drops down to 0 for Eb/N0 of 12. Thus, it can be concluded from the obtained graph that the performance of MRC with STBC gives improved results. When STBC technique is used with 3 × 4 scheme, at SNR of 10 dB, BER comes nearer to 10–6 (figure 7.3). It can be concluded from the analytics observed between AWGN and Rayleigh fading channel that for AWGN channel, BER is found to be equal to 0 for SNR value of 13.5 dB, whereas for Rayleigh fading channel, BER is observed nearer to 10–3 for Eb/N0 = 15. Simulation results (in figure 7.2) from the analytics show BER drops to 0 for SNR value of 12 dB.Research limitations/implicationsOptimal design and successful deployment of high-performance wireless networks present a number of technical challenges. These include regulatory limits on useable radio-frequency spectrum and a complex time-varying propagation environment affected by fading and multipath. The effect of multipath fading in wireless systems can be reduced by using antenna diversity. Previous studies show the performance of transmit diversity with narrowband signals using linear equalization, decision feedback equalization, maximum likelihood sequence estimation (MLSE) and spread spectrum signals using a RAKE receiver. The available IC techniques compatible with STBC schemes at transmission require multiple antennas at the receiver. However, if this not a strong constraint at the base station level, it remains a challenge at the handset level due to cost and size limitation. For this reason, SAIC technique, alternative to complex ML multiuser demodulation technique, is still of interest for 4G wireless networks using the MIMO technology and STBC in particular. In a system with characteristics similar to the North American Digital mobile radio standard IS-54 (24.3 K symbols per sec. with an 81 Hz fading rate), adaptive retransmission with time deviation is not practical.Practical implicationsThe evaluation of performance in terms of bit error rate and convergence time which estimates that MLD technique outperforms in terms of received SNR and low decoding complexity. MLD technique performs well but when higher number of antennas are used, it requires more computational time and thereby resulting in increased hardware complexity. When MRC scheme is implemented for singe input single output (SISO) system, BER drops down to 10–2 for SNR of 20 dB. Therefore, when MIMO systems are employed for MRC scheme, improved results based on BER versus SNR are obtained and are used for detecting the signal; comparative study based on different techniques is done. Initially ZF detection method is utilized which was then modified to ZF with successive interference cancellation (ZFSIC). When successive interference cancellation scheme is employed for ZFSIC, better performance is observed as compared to the estimation of ML and MMSE. For 2 × 2 scheme with QPSK modulation method, ZFSIC requires more computational time as compared to ZF, MMSE and ML technique. From the obtained results, the conclusion is that ZFSIC gives the improved results as compared to ZF in terms of BER ratio. ZF-based decision statistics can be produced by the detection algorithm for a desired sub-stream from the received vector whichs consist of an interference which occurred from previous transmitted sub-streams. Consequently, a decision on the secondary stream is made and contribution of the noise is regenerated and subtracted from the vector received. With no involvement of interference cancellation, system performance gets reduced but computational cost is saved. While using cancellation, as H is deflated, coefficients of MMSE are recalculated at each iteration. When cancellation is not involved, the computation of MMSE coefficients is done only once, because of H remaining unchanged. For MMSE 4 × 4 BPSK scheme, bit error rate of 10–2 at 30 dB is observed. In general, the most thorough procedure of the detection algorithm is the computation of the MMSE coefficients. Complexity arises in the calculation of the MMSE coefficients, when the antennas at the transmitting side are increased. However, while implementing adaptive MMSE receivers on slow channel fading, it is probable to recover the signal with the complications being linear in the antennas of transmitter node. The performance of MMSE and successive interference cancellation of MMSE are observed for 2 × 2 and 4 × 4 BPSK and QPSK modulation schemes. The drawback of MMSE SIC scheme is that the first detected signal observes the noise interference from (NT-1) signals, while signals processed from every antenna later observe less noisy interference as the process of cancellation progresses. This difficulty could be overcome by using OSIC detection method which uses successive ordering of the processed layers in the decreasing power of the signal or by power allocation to the signal transmitted depending on the order of the processing. By using successive scheme, a computation of NT delay stages is desired to bring out the abandoned process. The work also includes comparison of BER with various modulation schemes and number of antennas involved while evaluating the performance. MLD determines the Euclidean distance among the vector signal received and result of all probable transmitted vector signals with the specified channel H and finds the one with the minimum distance. Estimated results show that higher order of the diversity is observed by employing more antennas at both the receiving and transmitting ends. MLD with 8 × 8 binary phase shift keying (BPSK) scheme offers bit error rate near to 10–4 for SNR (16 dB). By using Altamonti space ti.Social implicationsIt should come as no surprise that companies everywhere are pushing to get products to market faster. Missing a market window or a design cycle can be a major setback in a competitive environment. It should be equally clear that this pressure is coming at the same time that companies are pushing towards “leaner” organizations that can do more with less. The trends mentioned earlier are not well supported by current test and measurement equipment, given this increasingly high-pressure design environment: in order to measure signals across multiple domains, multiple pieces of measurement equipment are needed, increasing capital or rental expenses. The methods available for making cross-domain, time-correlated measurements are inefficient, reducing engineering efficiency. When only used on occasion, the learning curve to understand how to use equipment for logic analysis, time domain and RF spectrum measurements often requires an operator to re-learn each piece of separate equipment. The equipment needed to measure wide bandwidth, time-varying spectral signals is expensive, again increasing capital or rental expenses. What is needed is a measurement instrument with a common user interface that integrates multiple measurement capabilities into a single cost-effective tool that can efficiently measure signals in the current wide-bandwidth, time-correlated, cross-domain environments. The market of wireless communication using STBCs has large scope of expansion in India. Therefore, the proposed work has techno-commercial potential and the product can be patented. This project shall in turn be helpful for remote areas of the nearby region particularly in Gadchiroli district and Melghat Tiger reserve project of Amravati district, Nagjira and so on where electricity is not available and there is an all the time problem of coverage in getting the network. In some regions where electricity is available, the shortage is such that they cannot use it for peak hours. In such cases, stand-alone space diversity technique, STBC shall help them to meet their requirements in making connection during coverage problem, thereby giving higher data transmission rates with better QOS (quality of service) with least dropped connections. This trend towards wireless everywhere is causing a profound change in the responsibilities of embedded designers as they struggle to incorporate unfamiliar RF technology into their designs. Embedded designers frequently find themselves needing to solve problems without the proper equipment needed to perform the tasks.Originality/valueWork is original.

AbstractMedium-length LDPC codes are in demand in certain areas such as mobile environment (Wi-Fi and Mobile WiMAX) and in telecommand links from the ground to space because of their lower latency properties. However, because of the length of these codes is rather short, decoding error rates are worse than those of long-length codes. In this paper, we show that the combination of shortened LDPC codes, whose shortened positions are properly selected, and ordered statistic decoding (OSD) significantly improves the decoding error. For the best choice of shortening positions, we used the integer programming approach. In particular, we utilized Feldman–Wainwright–Karger code polytope for this purpose. Some studies have independently reported the efficiency of shortened LDPC codes and OSD methods. This paper emphasizes that their combination results in multiplicative effectiveness.

Quantum key distribution (QKD) is a cryptographic communication protocol that utilizes quantum mechanical properties for provable absolute security against an eavesdropper. The communication is carried between two terminals using random photon polarization states represented through quantum states. Both these terminals are interconnected through disjoint quantum and classical channels. Information reconciliation using delay controlled joint decoding is performed at the receiving terminal. Its performance is characterized using data and error rates. Achieving low error rates is particularly challenging for schemes based on error correcting codes with short code lengths. This article addresses the decoding process using ordered statistics decoding for information reconciliation of both short and medium length Bose–Chaudhuri–Hocquenghem codes over a QKD link. The link’s quantum channel is modeled as a binary symmetric quantum depolarization channel, whereas the classical channel is configured with additive white Gaussian noise. Our results demonstrate the achievement of low bit error rates, and reduced decoding complexity when compared to other capacity achieving codes of similar length and configuration.

The encoding of a message is the creation of the message. The decoding of a message is how people can comprehend, and decipher the message. It is a procedure of understanding and interpretation of coded data into a comprehensible form. In this paper, a self-created explicitly defined function for encoding numerical digits into graphical representation is proposed. The proposed system integrates deep learning methods to get the probabilities of digit occurrence and Edge detection techniques for decoding the graphically encoded numerical digits to numerical digits as text. The proposed system’s major objective is to take in an Image with digits encoded in graphical format and give the decoded stream of digits corresponding to the graph. This system also employs relevant pre-processing techniques to convert RGB to text and image to Canny image. Techniques such as Multi-Label Classification of images and Segmentation are used for getting the probability of occurrence. The dataset is created, on our own, that consists of 1000 images. The dataset has the training data and testing data in the proportion of 9 : 1. The proposed system was trained on 900 images and the testing was performed on 100 images which were ordered in 10 classes. The model has created a precision of 89% for probability prediction.