Quasi-cyclic Low-density Parity-check Research Articles

Efficient Construction of Quasi-Cyclic LDPC Codes With Multiple Lifting Sizes

Efficient Construction of Quasi-Cyclic LDPC Codes With Multiple Lifting Sizes

A Quasi-Cyclic LDPC Based Low Complexity and Area-Efficient Communication System for IEEE 802.11n

Low-density parity-check (LDPC) code, which has an excellent error-correcting performance that is close to the Shannon limit, is the most often used error correction code (ECC) for reliable and effective communication. Despite higher performance and lower decoding complexity, the main disadvantage of LDPC codes is their high encoding complexity. A significant problem is the VLSI implementation of the LDPC encoder and decoder. In this paper, structured LDPC codes—also known as quasi-cyclic low-density parity check codes—have been used since it is good bit error ratio (BER) performance and adaptable hardware execution characteristics. The Complete (Encoder-Channel-Decoder) communication system with a 1/2 code rate, 648 bits codeward length, and sub-block size of z = 27 has been constructed for the IEEE 802.11n wireless standard.

Jointly optimized quasi-cyclic LDPC codes for coded-cooperative wireless networks based on split labeling diversity

Jointly optimized quasi-cyclic LDPC codes for coded-cooperative wireless networks based on split labeling diversity

A cyclic‐shift based method for counting cycles of quasi‐cyclic LDPC codes

AbstractM. Fossorier proposed how to determine the necessary and sufficient conditions for the existence of cycles in the Tanner graph of quasi‐cyclic LDPC (QC‐LDPC) codes, which has been widely investigated in the study of LDPC codes. This paper presents some new necessary and sufficient conditions for the existence of cycles with arbitrary lengths and proposes a simple and novel method for counting cycles of QC‐LDPC codes based on the improved conditions. Numerical results show that, compared with the existing methods, the presented method is effective and feasible and can enumerate cycles of QC‐LDPC codes in a cyclic‐shift way.

Fast computation of cyclic convolutions and their applications in code-based asymmetric encryption schemes

The development of fast algorithms for key generation, encryption and decryption not only increases the efficiency of related operations. Such fast algorithms, for example, for asymmetric cryptosystems on quasi-cyclic codes, make it possible to experimentally study the dependence of decoding failure rate on code parameters for small security levels and to extrapolate these results to large values of security levels. In this article, we explore efficient cyclic convolution algorithms, specifically designed, among other things, for use in encoding and decoding algorithms for quasi-cyclic LDPC and MDPC codes. Corresponding convolutions operate on binary vectors, which can be either sparse or dense. The proposed algorithms achieve high speed by compactly storing sparse vectors, using hardware-supported XOR instructions, and replacing modulo operations with specialized loop transformations. These fast algorithms have potential applications not only in cryptography, but also in other areas where convolutions are used.

Design and Implementation of a Highly Efficient Quasi-Cyclic Low-Density Parity-Check Transceiving System Using an Overlapping Decoder.

The traditional LDPC encoding and decoding system is characterized by low throughput and high resource consumption, making it unsuitable for use in cost-efficient, energy-saving sensor networks. Aiming to optimize coding complexity and throughput, this paper proposes a combined design of a novel LDPC code structure and the corresponding overlapping decoding strategies. With regard to structure of LDPC code, a CCSDS-like quasi-cyclic parity check matrix (PCM) with uniform distribution of submatrices is constructed to maximize overlap depth and adapt the parallel decoding. In terms of reception decoding strategies, we use a modified 2-bit Min-Sum algorithm (MSA) that achieves a coding gain of 5 dB at a bit error rate of 10-6 compared to an uncoded BPSK, further mitigating resource consumption, and which only incurs a slight loss compared to the standard MSA. Moreover, a shift-register-based memory scheduling strategy is presented to fully utilize the quasi-cyclic characteristic and shorten the read/write latency. With proper overlap scheduling, the time consumption can be reduced by one third per iteration compared to the non-overlap algorithm. Simulation and implementation results demonstrate that our decoder can achieve a throughput up to 7.76 Gbps at a frequency of 156.25 MHz operating eight iterations, with a two-thirds resource consumption saving.

Improved underwater wireless optical communication using a passively mode-locked VECSEL

This paper presents improved underwater wireless optical communication (UWOC) based on a 490 nm passively mode-locked vertical-external-cavity surface-emitting laser (VECSEL) with the repetition rate of 1.46 GHz and the pulse width of 2.25 ps. After conducting a comprehensive evaluation of the performance characteristics of quasi-cyclic low-density parity-check (QC-LDPC) coding and pulse-position modulation (PPM) in relation to bit-error-rate (BER) and communication capacity across different signal-to-noise ratios (SNRs), a passively mode-locked VECSEL based UWOC system is designed and experimentally performed. The UWOC system employs the QC-LDPC encoding technique and PPM modulation scheme that are most suitable for the system. Compared with the case without QC-LDPC, the minimum received optical power with coding is improved by 3.5 dBm, and the SNR with coding is improved by 0.4 dB under condition of 256-PPM and forward error correction (FEC) threshold of 3.8×10−3. Meanwhile, compared with the UWOC system using a continuous-wave (CW) VECSEL as the light source, the attenuation coefficient of the UWOC system based on the mode-locked VECSEL is decreased by 0.04 m-1, and the BER of the mode-locked VECSEL based UWOC system is decreased by 0.3 dB.

Optimizing quasi-cyclic spatially coupled LDPC codes by eliminating harmful objects

It is well known that some harmful objects in the Tanner graph of low-density parity-check (LDPC) codes have a negative impact on their error correction performance under iterative message-passing decoding. Depending on the channel and the decoding algorithm, these harmful objects are different in nature and can be stopping sets, trapping sets, absorbing sets, or pseudocodewords. Differently from LDPC block codes, the design of spatially coupled LDPC codes must take into account the semi-infinite nature of the code, while still reducing the number of harmful objects as much as possible. We propose a general procedure, based on edge spreading, enabling the design of good quasi-cyclic spatially coupled LDPC (QC-SC-LDPC) codes. These codes are derived from quasi-cyclic LDPC (QC-LDPC) block codes and contain a considerably reduced number of harmful objects with respect to the original QC-LDPC block codes. We use an efficient way of enumerating harmful objects in QC-SC-LDPCCs to obtain a fast algorithm that spans the search space of potential candidates to select those minimizing the multiplicity of the target harmful objects. We validate the effectiveness of our method via numerical simulations, showing that the newly designed codes achieve better error rate performance than codes presented in previous literature.

Parity-Check Matrix Partitioning for Efficient Layered Decoding of QC-LDPC Codes

In this paper, we consider how to partition the parity-check matrices (PCMs) to reduce the hardware complexity and increase decoding throughput for the row layered decoding of quasi-cyclic low-density parity-check (QC-LDPC) codes. First, we formulate the PCM partitioning as an optimization problem, which targets to minimize the maximum column weight of each layer while maintaining a block cyclic shift property among different layers. As a result, we derive all the feasible solutions for the problem and propose a tight lower bound ω <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><i>LB</i></sub> on the minimum possible maximum column weight to evaluate a solution. Second, we define a metric called layer distance to measure the data dependency between consecutive layers and further illustrate how to identify the solutions with desired layer distance from those achieving the minimum value of ω <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><i>LB</i></sub> = 1, which is preferred to reduce computation delay. Next, we demonstrate that up-to-now, finding an optimal solution for the optimization problem with polynomial time complexity is unachievable. Therefore, both enumerative and greedy partition algorithms are proposed instead. After that, we modify the quasi-cyclic progressive edge-growth (QC-PEG) algorithm to directly construct PCMs that have a straightforward partition scheme to achieve ω <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><i>LB</i></sub> or the desired layer distance. Simulation results showed that the constructed codes have better error correction performance and achieve less average number of iterations than the underlying 5G LDPC codes.

Construction of protograph LDPC codes based on the convolution neural network

This paper presents an intelligent protograph construction algorithm. Protograph LDPC codes have shown excellent error correction performance and play an important role in wireless communications. Random search or manual construction are often used to obtain a good protograph, but the efficiency is not high enough and many experience and skills are needed. In this paper, a fast searching algorithm is proposed using the convolution neural network to predict the iterative decoding thresholds of protograph LDPC codes effectively. A special input data transformation rule is applied to provide stronger generalization ability. The proposed algorithm converges faster than other algorithms. The iterative decoding threshold of the constructed proto-graph surpasses greedy algorithm and random search by about 0.53 dB and 0.93 dB respectively under 100 times of density evolution. Simulation results show that quasi-cyclic LDPC (QC-LDPC) codes constructed from the proposed algorithm have competitive performance compared to other papers.

Deterministic Construction of Compressed Sensing Measurement Matrix with Arbitrary Sizes via QC-LDPC and Arithmetic Sequence Sets

It is of great significance to construct deterministic measurement matrices with good practical characteristics in Compressed Sensing (CS), including good reconstruction performance, low memory cost and low computing resources. Low-density-parity check (LDPC) codes and CS codes can be closely related. This paper presents a method of constructing compressed sensing measurement matrices based on quasi-cyclic (QC) LDPC codes and arithmetic sequence sets. The cyclic shift factor in each submatrix of QC-LDPC is determined by arithmetic sequence sets. Compared with random matrices, the proposed method has great advantages because it is generated based on a cyclic shift matrix, which requires less storage memory and lower computing resources. Because the restricted isometric property (RIP) is difficult to verify, mutual coherence and girth are used as computationally tractable indicators to evaluate the measurement matrix reconstruction performance. Compared with several typical matrices, the proposed measurement matrix has the minimum mutual coherence and superior reconstruction capability of CS signal according to one-dimensional (1D) signals and two-dimensional (2D) image simulation results. When the sampling rate is 0.2, the maximum (minimum) gain of peak signal-to-noise ratio (PSNR) and structural similarity index (SSIM) is up to 2.89 dB (0.33 dB) and 0.031 (0.016) while using 10 test images. Meanwhile, the reconstruction time is reduced by nearly half.

Optimized Design of Distributed Quasi-Cyclic LDPC Coded Spatial Modulation.

We propose a distributed quasi-cyclic low-density parity-check (QC-LDPC) coded spatial modulation (D-QC-LDPCC-SM) scheme with source, relay and destination nodes. At the source and relay, two distinct QC-LDPC codes are used. The relay chooses partial source information bits for further encoding, and a distributed code corresponding to each selection is generated at the destination. To construct the best code, the optimal information bit selection algorithm by exhaustive search in the relay is proposed. However, the exhaustive-based search algorithm has large complexity for QC-LDPC codes with long block length. Then, we develop another low-complexity information bit selection algorithm by partial search. Moreover, the iterative decoding algorithm based on the three-layer Tanner graph is proposed at the destination to carry out joint decoding for the received signal. The recently developed polar-coded cooperative SM (PCC-SM) scheme does not adopt a better encoding method at the relay, which motivates us to compare it with the proposed D-QC-LDPCC-SM scheme. Simulations exhibit that the proposed exhaustive-based and partial-based search algorithms outperform the random selection approach by 1 and 1.2 dB, respectively. Because the proposed D-QC-LDPCC-SM system uses the optimized algorithm to select the information bits for further encoding, it outperforms the PCC-SM scheme by 3.1 dB.

Energy-Efficient Backscatter-Assisted Coded Cooperative NOMA for B5G Wireless Communications

In this manuscript, we propose an alternating optimization framework to maximize the energy efficiency of a backscatter-enabled cooperative Non-orthogonal multiple access (NOMA) system by optimizing the transmit power of the source, power allocation coefficients (PAC), and power of the relay node under imperfect successive interference cancellation (SIC) decoding. A three-stage low-complexity energy-efficient alternating optimization algorithm is introduced which optimizes the transmit power, PAC, and relay power by considering the quality of service (QoS), power budget, and cooperation constraints. Subsequently, a joint channel coding framework is introduced to enhance the performance of far user which has no direct communication link with the base station (BS) and has bad channel conditions. In the destination node, the far user data is jointly decoded using a Sum-product algorithm (SPA) based joint iterative decoder realized by jointly-designed Quasi-cyclic Low-density parity-check (QC-LDPC) codes. Simulation results evince that the proposed backscatter-enabled cooperative NOMA system outperforms its counterpart by providing an efficient performance in terms of energy efficiency. Also, proposed jointly-designed QC-LDPC codes provide an excellent bit-error-rate (BER) performance by jointly decoding the far user data for considered BSC cooperative NOMA system with only a few decoding iterations.

Implementation of encoder and decoder for low-density parity-check codes in continuous-variable quantum key distribution on a field programmable gate array

Quantum key distribution (QKD) can provide an unconditionally secure communication encryption method. Continuous-variable QKD (CVQKD) requires extracting the key from the noisy channel, leading to higher requirements for the error-correcting codes used in multidimensional reconciliation. We extend the quasi-cyclic low-density parity-check of the radio design for the global 5G mobile communication technology standard to achieve error correction under lower signal-to-noise ratio on integrated hardware. A field programmable gate array (FPGA) chip is used to realize the approximate lower triangular matrix encoding algorithm, and the core module only has the circular shift register, which reduces the encoding complexity, improves the encoding efficiency, and reduces the hardware resource consumption. For extended super-long code words, the decoding algorithm requires additional hardware resources to implement, which the previous algorithm cannot meet. Therefore, we present a hardware implementation of offset minimum sum algorithm (OMSA), which can avoid operations of complex mathematical formula. The offset factor of OMSA reduce the error caused by the low accuracy of calculation on the hardware. The update of the decoding information is layered in a partially parallel way in the matrix to achieve the cross processing of node information. It speeds up the transmission of information between different nodes and the convergence of decoding algorithm of low-complexity parallel structure. Simulation results show that the maximum theoretical coordination efficiency is 85% when the code with block length is 69632 at a bit rate of 22/68 and the signal-to-noise ratio asymptotic threshold is 0.7. Using an FPGA, ∼0.1 frame error rate was achieved, but with a zero-bit error rate, the optimal achievable secret key rate is about 200 Kbps at 30-km distance theoretically. For a 200-MHz system clock on the successfully decoded block, 125 Gbps encoding throughput and 472 Kbps decoding throughput was achieved, better than the theoretical key rate of prototype of CVQKD.

Quasi-Cyclic LDPC Codes With Girth at Least Eight Based on Disjoint Difference Sets

A novel relationship between disjoint difference sets (DDS) and QC-LDPC codes without cycles of length up to six is established. Based on DDS with two sets, a class of column-weight-four QC-LDPC codes is constructed with girth at least eight. In the literature there are several explicit or semi-random methods which can yield column-weight-four QC-LDPC codes without 4-cycles and 6-cycles. Compared with these existing methods, the new DDS-based method is able to offer QC-LDPC codes with desirable decoding performance and flexible circulant sizes, and at the same time able to provide a large number of non-equivalent candidate codes. Moreover, by employing DDS with only one set, a class of column-weight-three QC-LDPC codes is constructed with short lengths and with girth at least eight.

Full-Length Row-Multiplier QC-LDPC Codes With Girth Eight and Short Circulant Sizes

As a special case of a quasi-cyclic (QC) low-density parity-check (LDPC) code, a full-length row-multiplier (FLRM) QC-LDPC code is described by a compact exponent matrix based on two sequences of integers. The codes designed by a framework known as greatest-common-divisor (GCD) method, belong to a salient class of FLRM QC-LDPC codes, which can eliminate cycles of length up to six by carefully selecting a special sequence subject to a set of simple inequalities. However, the GCD method ensures the absence of these cycles only if circulant sizes are larger than a certain threshold. By combining the existing GCD method, novel sequences and a new analysis method (based on new lemmas of circulants and integers) for modulo equations, a group of novel FLRM QC-LDPC codes free of 4-cycles and 6-cycles are explicitly proposed for column weights from three to five in this paper, which possess circulant sizes much smaller than the forgoing threshold. Simulations show that the new FLRM QC-LDPC codes with shorter lengths perform almost the same as the existing FLRM QC-LDPC codes with longer lengths, and that the novel FLRM QC-LDPC codes noticeably outperform their counterparts with (nearly) identical lengths.

An Efficient Strategy to Count Cycles in the Tanner Graph of Quasi-Cyclic LDPC Codes

An Efficient Strategy to Count Cycles in the Tanner Graph of Quasi-Cyclic LDPC Codes

Multi-Layer Progressive Tree-Structured Edge Growth Algorithm for Nested Lifting Design of 5G-NR-Like LDPC Codes

We proposed an algorithm called multi-layer progressive tree-structured edge growth, to design rate-compatible length-scalable raptor-like quasi-cyclic LDPC codes with nested base matrices and nested lifting, like 5G new radio (NR) LDPC codes. The nested lifting design is mainly investigated in this letter. To deal with the complicated dependency of the performance for nested base matrices and lifting sizes simply and effectively, the design of nested lifting is decomposed into the lifting design of each lifting size, which is called a layer. In each layer, the lifting of nested base matrices is designed via progressive tree-structured edge growth algorithm, where tree structure is employed to reserve diversified intermediate results and achieve better trade-off of error floor performance among nested base matrices. The criterion composed of improved cycle classification, minimum distance test and performance evaluation is employed for tree pruning, which could better optimize the error floor performance under acceptable complexity. The effectiveness of the proposed algorithm is demonstrated via construction and simulation.

REDUCTION OF PAPR USING ASYMMETRIC NUMERAL SYSTEM QC-LDPC WITH HUFFMAN AND ARITHMETIC CODING FOR F-OFDMA SYSTEM

As modern wireless communication systems move towards 5G implementation, the system must provide sophisticated and ubiquitous service and flexibility. Therefore, Filtered Orthogonal Frequency Division Multiple Access (F-OFDMA) is one of the most suitable modulation techniques used in 5G systems to achieve efficient and reliable wireless communication. Other than that, F-OFDMA also has good quality rather than OFDM since it provides a better result of high side lobes and enlarges the scale of the spectrum analyzer. However, one of the significant problems in the F-OFDMA system is the high peak-to-average power ratio (PAPR), affecting the system's overall performance and causing high transmit power at the transmitter. In this paper, combination of Arithmetic Coding (AC) and Huffman coding (HC) with Asymmetric Numeral Systems (ANS) provide better performance for PAPR as well as bit error rate (BER) in F-OFDMA. Both AC and HC are proposed to combine with ANS and Quasi-Cyclic Low-Density Parity Check (QC-LDPC) since it provides a good result to defeat the high PAPR. BER and PAPR performance were compared for the AC and HC with ANS QC-LDPC. Based on the results, ANS-AC-QCLDPC proved as the best joint method has 35.25% improvement for PAPR while BER has 89.87%. This research also justified that ANS with Arithmetic-QCLDPC and Huffman-QCLDPC give better BER results as well.

Performance analysis and design of quasi-cyclic LDPC codes for underwater magnetic induction communications

Magnetic induction (MI) communication is an effective scheme for underwater wireless communication. In this paper, we aim to design an underwater MI communication system based on Quasi-cyclic LDPC (QC-LDPC) codes. Firstly, for a given QC-LDPC code used in underwater MI communication, we propose a novel algorithm to evaluate its performance, which is named as underwater magnetic induction protograph (UWMIP) extrinsic information transfer algorithm. Furthermore, we present a differential evolution UWMIP (DE-UWMIP) algorithm, which incorporates the differential evolution method and the UWMIP algorithm. By this algorithm, we search the optimized QC-LDPC codes with best distance threshold. Simulation results show that the proposed algorithm is effective and provide a good guidance to design the underwater MI communication system.