Concatenation Scheme Research Articles

An LDPC-RS Concatenation and Decoding Scheme to Lower the Error Floor for FTN Signaling

Faster-than-Nyquist (FTN) signaling has attracted increasing interest in the past two decades. However, when the fifth-generation (5G) communication low-density parity check (LDPC) code is applied to FTN signaling with low Bahl–Cock–Jelinek–Raviv (BCJR) states of detection and few turbo equalization iterations, an error floor near 10−5 is found, which does not exist in the original LDPC used for orthogonal signaling. This can be eliminated through many detection and decoding iterations, but this is unacceptable considering the increase in latency and storage. To solve this problem, we propose an LDPC and Reed–Solomon (RS) concatenation code, shortening, and perturbation scheme to lower the error floor. We propose a parallel encoder architecture for RS component code and a concise algorithm to calculate its constant multiplier coefficients, leveraging a traditional serial encoder, which can also be used for other parallelisms, rates, and lengths. The simulation results show that the proposed concatenation and shortening scheme can lower the error floor to about 10−7. The proposed scheme has an error correction capability for coded FTN signaling and successfully lowers the error floor with the limitation of few turbo iterations and few BCJR states.

Qubit-Oscillator Concatenated Codes: Decoding Formalism and Code Comparison

Concatenating bosonic error-correcting codes with qubit codes can substantially boost the error-correcting power of the original qubit codes. It is not clear how to concatenate optimally, given there are several bosonic codes and concatenation schemes to choose from, including the recently discovered GKP-stabilizer codes [Phys. Rev. Lett. 125, 080503 (2020)}] that allow protection of a logical bosonic mode from fluctuations of the mode's conjugate variables. We develop efficient maximum-likelihood decoders for and analyze the performance of three different concatenations of codes taken from the following set: qubit stabilizer codes, analog/Gaussian stabilizer codes, GKP codes, and GKP-stabilizer codes. We benchmark decoder performance against additive Gaussian white noise, corroborating our numerics with analytical calculations. We observe that the concatenation involving GKP-stabilizer codes outperforms the more conventional concatenation of a qubit stabilizer code with a GKP code in some cases. We also propose a GKP-stabilizer code that suppresses fluctuations in both conjugate variables without extra quadrature squeezing, and formulate qudit versions of GKP-stabilizer codes.

Deep Attention-based Classification of Plant Images with Hierarchical Similarity and Imbalanced Distribution

—Standard datasets in deep learning-basedimage classification usually provide two favorable conditions for design: preservation of visual homogeneity of each category and uniform distribution of sample images. These conditions are not assured in a dataset of plant images. Two different species of plants under the same genus look very similar and the number of collectible images has a large variation over species.Visual similarity, however, can be turned into advantage in hierarchical approach, by assigning two-fold labels of species and genus, in two phases ofrough classification of genera and fine classification of species. We propose a hierarchical classification in which the concatenation scheme is augmented with a channel attention which focuses on the sibling relation of species. We compared our method with flat classification and conventional hierarchical classification. The test was on a PlantNet-300K dataset 300k images, composed of 303 genera and 1081 species. In experimental results, the channel attention layers lead to stable discerningof the minute difference among visually similar species. The proposed hierarchical classification method outperforms both the flat classification and the conventional hierarchical classification.

Partially Concatenated Calderbank-Shor-Steane Codes Achieving the Quantum Gilbert-Varshamov Bound Asymptotically

In this paper, we utilize a concatenation scheme to construct new families of quantum error correction codes achieving the quantum Gilbert-Varshamov (GV) bound asymptotically. We concatenate alternant codes with any linear code achieving the classical GV bound to construct Calderbank-Shor-Steane (CSS) codes. We show that the concatenated code can achieve the quantum GV bound asymptotically and can approach the Hashing bound for asymmetric Pauli channels. By combing Steane's enlargement construction of CSS codes, we derive a family of enlarged stabilizer codes achieving the quantum GV bound for enlarged CSS codes asymptotically. As applications, we derive two families of fast encodable and decodable CSS codes with parameters $\mathscr{Q}_1=[[N,\Omega(\sqrt{N}),\Omega( \sqrt{N})]],$ and $\mathscr{Q}_2=[[N,\Omega(N/\log N),\Omega(N/\log N)/\Omega(\log N)]].$ We show that $\mathscr{Q}_1$ can be encoded very efficiently by circuits of size $O(N)$ and depth $O(\sqrt{N})$. For an input error syndrome, $\mathscr{Q}_1$ can correct any adversarial error of weight up to half the minimum distance bound in $O(N)$ time. $\mathscr{Q}_1$ can also be decoded in parallel in $O(\sqrt{N})$ time by using $O(\sqrt{N})$ classical processors. For an input error syndrome, we proved that $\mathscr{Q}_2$ can correct a linear number of ${X}$-errors with high probability and an almost linear number of ${Z}$-errors in $O(N )$ time. Moreover, $\mathscr{Q}_2$ can be decoded in parallel in $O(\log(N))$ time by using $O(N)$ classical processors.

The Design of Digital System with CSA

In this paper, we present a carry skip adder (CSKA) structure that has a higher speed yet lower energy consumption compared with the conventional one. The speed enhancement is achieved by applying concatenation and incrementation schemes to improve the efficiency of the conventional CSKA (Conv-CSKA) structure. In addition, instead of utilizing multiplexer logic, the proposed structure makes use of AND-OR-Invert (AOI) and ORAND-Invert (OAI) compound gates for the skip logic. The structure may be realized with both fixed stage size and variable stage size styles, wherein the latter further improves the speed and energy parameters of the adder. Finally, a hybrid variable latency extension of the proposed structure, which lowers the power consumption without considerably impacting the speed, is presented. This extension utilizes a modified parallel structure for increasing the slack time, and hence, enabling further voltage reduction. The proposed structures are assessed by comparing their speed, power, and energy parameters with those of other adders using a 45-nm static CMOS technology for a wide range of supply voltages. The results that are obtained using HSPICE simulations reveal, on average, 44% and 38% improvements in the delay and energy, respectively, compared with those of the Conv-CSKA. In addition, the power–delay product was the lowest among the structures considered in this paper, while its energy–delay product was almost the same as that of the Kogge–Stone parallel prefix adder with considerably smaller area and power consumption. Simulations on the proposed hybrid variable latency CSKA reveal reduction in the power consumption compared with the latest works in this field while having a reasonably high speed.

Periocular Data Fusion for Age and Gender Classification.

In recent years, the study of soft biometrics has gained increasing interest in the security and business sectors. These characteristics provide limited biometric information about the individual; hence, it is possible to increase performance by combining numerous data sources to overcome the accuracy limitations of a single trait. In this research, we provide a study on the fusion of periocular features taken from pupils, fixations, and blinks to achieve a demographic classification, i.e., by age and gender. A data fusion approach is implemented for this purpose. To build a trust evaluation of the selected biometric traits, we first employ a concatenation scheme for fusion at the feature level and, at the score level, transformation and classifier-based score fusion approaches (e.g., weighted sum, weighted product, Bayesian rule, etc.). Data fusion enables improved performance and the synthesis of acquired information, as well as its secure storage and protection of the multi-biometric system's original biometric models. The combination of these soft biometrics characteristics combines flawlessly the need to protect individual privacy and to have a strong discriminatory element. The results are quite encouraging, with an age classification accuracy of 84.45% and a gender classification accuracy of 84.62%, respectively. The results obtained encourage the studies on periocular area to detect soft biometrics to be applied when the lower part of the face is not visible.

Finite Rate QLDPC-GKP Coding Scheme that Surpasses the CSS Hamming Bound

Quantum error correction has recently been shown to benefit greatly from specific physical encodings of the code qubits. In particular, several researchers have considered the individual code qubits being encoded with the continuous variable GottesmanKitaev-Preskill (GKP) code, and then imposed an outer discrete-variable code such as the surface code on these GKP qubits. Under such a concatenation scheme, the analog information from the inner GKP error correction improves the noise threshold of the outer code. However, the surface code has vanishing rate and demands a lot of resources with growing distance. In this work, we concatenate the GKP code with generic quantum low-density parity-check (QLDPC) codes and demonstrate a natural way to exploit the GKP analog information in iterative decoding algorithms. We first show the noise thresholds for two lifted product QLDPC code families, and then show the improvements of noise thresholds when the iterative decoder – a hardware-friendly min-sum algorithm (MSA) – utilizes the GKP analog information. We also show that, when the GKP analog information is combined with a sequential update schedule for MSA, the scheme surpasses the well-known CSS Hamming bound for these code families. Furthermore, we observe that the GKP analog information helps the iterative decoder in escaping harmful trapping sets in the Tanner graph of the QLDPC code, thereby eliminating or significantly lowering the error floor of the logical error rate curves. Finally, we discuss new fundamental and practical questions that arise from this work on channel capacity under GKP analog information, and on improving decoder design and analysis.

Enhancing distributed sensing with imperfect error correction

Entanglement has shown promise in enhancing information processing tasks in a sensor network, via distributed quantum sensing protocols. As noise is ubiquitous in sensor networks, error correction schemes based on Gottesman, Kitaev and Preskill (GKP) states are required to enhance the performance, as shown in [New J. Phys. 22, 022001 (2020)] assuming homogeneous noise among sensors and perfect GKP states. Here, we extend the analyses of performance enhancement to finite squeezed GKP states in a heterogeneous noise model. To begin with, we study different concatenation schemes of GKP-two-mode-squeezing codes. While traditional sequential concatenation schemes in previous works do improve the suppression of noise, we propose a balanced concatenation scheme that outperforms the sequential scheme in presence of finite GKP squeezing. We then apply these results to two specific tasks in distributed quantum sensing -- parameter estimation and hypothesis testing -- to understand the trade-off between imperfect squeezing and performance. For the former task, we consider an energy-constrained scenario and provide an optimal way to distribute the energy of the finite squeezed GKP states among the sensors. For the latter task, we show that the error probability can still be drastically lowered via concatenation of realistic finite squeezed GKP codes.

NEW CONCATENATION SCHEMES BASED ON THE MULTITHRESHOLD DECODERS OF CONVOLUTIONAL SELF-ORTHOGONAL CODES FOR GAUSSIAN CHANNELS

New serial concatenation schemes based on the multithreshold decoders and di- vergent principle for the convolutional self-orthogonal codes under Gaussian channels are proposed. Using both binary and symbolic decoders on the second decoding stage of the convolutional codes are considered. Simulation results are indicated the higher performance characteristics of the proposed cascade schemes on majority decoders in comparison with clas- sical schemes based on the Viterbi algorithm and Reed-Solomon codes. A moderate increase in decoding delay during concatenation is revealed. It is determined by the absence of the need to use traditional two-dimensional concatenated structures.

A correlation-breaking interleaving of polar codes in concatenated systems

It is known that the bit errors of polar codes with successive cancellation (SC) decoding are coupled. However, existing concatenation schemes of polar codes with other error correction codes rarely take this coupling effect into consideration. To achieve a better error performance of concatenated systems with polar codes as inner codes, one can divide all bits in an outer block into different polar blocks to completely de-correlate the possible coupled errors in the transmitter side. We call this interleaving a blind interleaving (BI) which serves as a benchmark. Two BI schemes, termed BI-DP and BI-CDP, are proposed in the paper. To better balance performance, memory size, and the decoding delay from the de-interleaving, a novel interleaving scheme, named the correlation-breaking interleaving (CBI), is proposed. The CBI breaks the correlated information bits based on the error correlation pattern proposed and proven in this paper. The proposed CBI scheme is general in the sense that any error correction code can serve as the outer code. In this paper, Low-Density Parity-Check (LDPC) codes and BCH codes are used as two examples of the outer codes of the interleaving scheme. The CBI scheme 1) can keep the simple SC polar decoding while achieving a better error performance than the state-of-the-art (SOA) direct concatenation of polar codes with LDPC codes and BCH codes; 2) achieves a comparable error performance as the BI-DP scheme with a smaller memory size and a shorter decoding delay. Numerical results are provided to verify the performance of the BI schemes and the CBI scheme.

Degenerate asymmetric quantum concatenated codes for correcting biased quantum errors* *Project supported by the National Natural Science Foundation of China (Grant Nos. 61802175, 61871120, 61872184, and 62071240) and the Fundamental Research Funds for the Central Universities, China (Grant No. NZ2020021).

In most practical quantum mechanical systems, quantum noise due to decoherence is highly biased towards dephasing. The quantum state suffers from phase flip noise much more seriously than from the bit flip noise. In this work, we construct new families of asymmetric quantum concatenated codes (AQCCs) to deal with such biased quantum noise. Our construction is based on a novel concatenation scheme for constructing AQCCs with large asymmetries, in which classical tensor product codes and concatenated codes are utilized to correct phase flip noise and bit flip noise, respectively. We generalize the original concatenation scheme to a more general case for better correcting degenerate errors. Moreover, we focus on constructing nonbinary AQCCs that are highly degenerate. Compared to previous literatures, AQCCs constructed in this paper show much better parameter performance than existed ones. Furthermore, we design the specific encoding circuit of the AQCCs. It is shown that our codes can be encoded more efficiently than standard quantum codes.

Asymmetric Quantum Concatenated and Tensor Product Codes With Large Z-Distances

In this paper, we present a new construction of asymmetric quantum codes (AQCs) by combining classical concatenated codes (CCs) with tensor product codes (TPCs), called asymmetric quantum concatenated and tensor product codes (AQCTPCs) which have the following three advantages. First, only the outer codes in AQCTPCs need to satisfy the orthogonal constraint in quantum codes, and any classical linear code can be used for the inner, which makes AQCTPCs very easy to construct. Second, most AQCTPCs are highly degenerate, which means they can correct many more errors than their classical TPC counterparts. Consequently, we construct several families of AQCs with better parameters than known results in the literature. Third, AQCTPCs can be efficiently decoded although they are degenerate, provided that the inner and outer codes are efficiently decodable. In particular, we significantly reduce the inner decoding complexity of TPCs from $\Omega(n_2a^{n_1})(a>1)$ to $O(n_2)$ by considering error degeneracy, where $n_1$ and $n_2$ are the block length of the inner code and the outer code, respectively. Furthermore, we generalize our concatenation scheme by using the generalized CCs and TPCs correspondingly.

A Novel Concatenation Scheme of Protograph-Based LDPC Codes and Markers for Recovering Synchronous Errors

A Novel Concatenation Scheme of Protograph-Based LDPC Codes and Markers for Recovering Synchronous Errors

A Performance Analysis of Quantum Low-Density Parity-Check Codes for Correcting Correlated Errors

In this paper we analyse the performance of quantum low-density parity-check (LDPC) codes over quantum memory channels for correcting correlated errors, where the quantum LDPC codes we use are the hypergraph product quantum LDPC codes. We generalize the classical Gilbert-Elliot markovian memory channel to the quantum Gilbert-Elliot channel and use it to model the memory effect in quantum memory channels. The simulation results show the memory effects in quantum GE channels has a bad effect to the performance of hypergraph product quantum LDPC codes. Then we propose a concatenation scheme by serially concatenating two hypergraph product quantum LDPC codes and it is shown that the serial concatenation scheme can improve the performance of hypergraph product quantum LDPC codes and lower down the error floor over quantum GE channels.

Serially concatenated scheme of polar codes and the improved belief propagation decoding algorithm

In this study, a serially concatenated scheme of polar codes with convolutional codes is proposed to improve the error correction performance. The novel belief propagation (BP) decoding algorithm addresses two issues that are present in the currently available BP decoding algorithms. The first issue is the poor performance of the BP decoding algorithms, in particular the introduction of an error floor. The second is the component codes can only use systematic codes in the traditional concatenated scheme of polar codes with convolutional codes, which inhibits the effective update of the prior information of the redundant check bits. The proposed BP decoding algorithm is based on right-directed message processing, which effectively improves the decoding performance. In addition, the proposed concatenated scheme extends the selection of component codes from the systematic polar codes to the non-systematic polar codes. Hence, the areas of applications and the prior information of information bits for polar codes are expanded and more effectively updated, respectively. The simulation results show that the proposed scheme is much better than the traditional concatenated scheme, and the error floor is no longer introduced in terms of the block error rate, while the storage and computational complexities have not increased obviously.

How to apply polar codes in high throughput space communications

This paper describes how to apply polar codes in high-throughput space communications. The high throughput space communications can enable terabit data rate capacity wideband wireless transmissions, and offer service availability of anywhere and anytime. The paper investigates the channel characteristics in space communications. The channels are lossy, time-varying, intermittent, long-latency, and with imperfect channel state information (CSI). In order to make the polar codes suitable for the space channel, some improvements and designs on the polar codes are provided in this paper. The encoding and decoding methods of polar codes are discussed, which are the key to determine the performance. We describe some rateless polar coding schemes that can guide the construction of suitable codes for time-varying channels with no-CSI in long-haul transmissions. Then, a high-rate parallel concatenation scheme of polar codes is introduced, which can improve the anti-interrupt ability of polar codes. Moreover, in order to support the massive connectivity requirements of future space communication networks, polar-coded sparse-code-multiple-access (SCMA) schemes are investigated.

Optimization Design of Polar-LDPC Concatenated Scheme Based on Deep Learning

In 5G communication system, because of incomplete polarization of the polar codes, the performance of the polar codes is poor at low and medium SNR. Concatenating the polar codes and low-density parity-check codes (LDPC), the Polar-LDPC concatenated scheme improves decoding performance. Although the decoding performance of the Polar-LDPC concatenated scheme is improved, the decoding delay is increased compared with the non-concatenated scheme. In order to solve this problem, we propose a Polar-LDPC concatenated scheme based on deep learning by paralleling multiple neural networks. The decoding delay of the polar codes assisted by the neural network is reduced in the proposed Polar-LDPC concatenated scheme. The experiment results show that the proposed concatenated scheme can reduce time complexity compared with the non-concatenated scheme under the same code length.

On Error Performance and Concatenated Coding of Polar Codes in AWGN Channels

In additive white Gaussian noise (AWGN) channels, construction of polar codes is needed for every operating signal-to-noise ratio (SNR). Recently, the proposal of the design-SNR reduces the computation effort in constructing polar codes. In this paper, we prove that although the BER performance of the design-SNR construction is not affected, the packet-error-rate (PER) performance is degraded compared with the point-by-point construction. Therefore, a concatenation scheme is proposed to improve the degraded PER performance. Results show the validity of the proposed concatenation scheme when employing the design-SNR construction.

Improved Decoding of Linear Block Codes by Concatenated Decoders

The use of decoding algorithms allows us to retrieve information after transmitting it over a noisy communication channel. Soft decision decoding is powerful in concatenation schemes that use two or more levels of decoding. In our case, we make a concatenation between the Hartmann & Rudolph (HR) algorithm as symbol-by-symbol decoder and the chase-2 algorithm that is word-to-word decoding algorithm. In this paper, we propose to combine two decoding algorithms for constructing a new one with more efficiency and less complexity. This work consists firstly to use the HR with a reduced number of codewords of the dual code then the Chase-2 algorithm which exploits the output of PHR. The simulations results and the comparisons made show that the proposed decoding scheme guarantees very good performance with reduced temporal complexity.

Multilevel High-Rate Coding With Twofold Concatenation for IoTs in Wireless Mesh Networks

Recent studies have shown that wireless mesh networks (WMNs) can be cheap, reliable, and efficient solutions for Internet of Things (IoTs) applications and connected devices. However, the increase in the size of the WMNs could lead to a degradation in performance. This makes the network vulnerable to high error rates over noisy and fading channels. This has increased the demand for more efficient channel coding schemes that can provide reliability, high data rate, high coding gain, energy efficiency, and minimum decoding complexity especially for low-cost and special purpose WMNs. In this research, an original multilevel coding with twofold concatenation scheme is designed based on high-rate space-time block codes (HRSTBCs) to cope with this increasing demand, particularly in MIMO-based WMNs. First, a multilevel coding scheme is implemented by correlating HRSTBCs with the uniquely constructed set-partitioning of the transmission matrix, based on the coding gain distance (CGD) criterion. This generates a new scheme, namely multilevel high-rate space-time block code (MHRSTBC), to provide a high transmission rate. Second, a twofold concatenation coding scheme is introduced by concatenating Reed-Solomon (RS) code, has been used for its energy efficiency and optimality in the mobile environment, with the inner code of the associated MHRSTBC. This has formed a new scheme that reaches the maximum coding gains, called the Reed-Solomon multilevel high-rate space-time block code (RS-MHRSTBC). The efficiency of the RS-MHRSTBC is verified by a computer simulation over a Rayleigh flat-fading and additive white Gaussian noise (AWGN) channel. The RS-MHRSTBC is compared with the classical schemes of Alamouti STBC and Multilevel STBC over uncoded QPSK, and the RS-MHRSTBC shows significant high coding gains reached of 47.79 dB, while Alamouti STBC and Multilevel STBC reached 38.12 dB and 44.30 dB at a BER of 10−6 respectively. RS-MHRSTBC also shows a reasonable decoding complexity while maintaining full transmission diversity at spectral efficiency of 2 bits/s/Hz.