Quasi-cyclic Low Density Parity Research Articles

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.

Huffrith Algorithm with Quasi Cyclic Low Density Parity Check in NOMA Systems

Huffrith Algorithm with Quasi Cyclic Low Density Parity Check in NOMA Systems

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.

A Joint Encryption-Encoding Scheme using QC-LDPC Codes based on Finite Geometry

Joint encryption-encoding schemes have been released to fulfill both reliability and security desires in a single step. Using Low Density Parity Check (LDPC) codes in joint encryption-encoding schemes, as an alternative to classical linear codes, would shorten the key size as well as improving error correction capability. In this article, we present a joint encryption-encoding scheme using Quasi Cyclic-Low Density Parity Check (QC-LDPC) codes based on finite geometry. We observed that our proposed scheme not only outperforms its predecessors in key size and transmission rate, but also remains secure against all known cryptanalyses of code-based secret key cryptosystems. We subsequently show that our scheme benefits from low computational complexity. In our proposed joint encryption-encoding scheme, by taking the advantage of QC-LDPC codes based on finite geometries, the key size decreases to 1/5 of that of the so far best similar system. In addition, using our proposed scheme a wide range of desirable transmission rates are achievable. This variety of codes makes our cryptosystem suitable for a number of different communication and cryptographic standards.

Secrecy Coding Analysis of Short-Packet Full-Duplex Transmissions with Joint Iterative Channel Estimation and Decoding Processes.

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

Joint Iterative Blind Self-Interference Cancellation, Propagation Channel Estimation and Decoding Processes in Full-Duplex Transmissions

The paper proposes a joint blind iterative Self-Interference (SI) cancellation, propagation channel estimation and decoding algorithm in Full-Duplex (FD) transmissions via feedback of channel estimates and decoded messages combined with the process of Digital Self-Interference Cancellation (DSIC). Different from the conventional algorithm, the proposed blind algorithm simultaneously estimates the self-interference and propagation channels and decodes messages in each decoding iteration of 5G Quasi-Cyclic Low Density Parity Check (QC-LDPC) codes. The temporary propagation channel estimate and decoded message are fed back to improve the self-interference cancellation and also the channel estimation as well as decoding in the next iteration. The results show that the proposed algorithm outperforms the conventional algorithm, especially at high signal to noise ratio (SNR) and small number of symbols, and requires much less processing time and computational complexity while achieving the convergence performance. The results also show that the proposed algorithm is less sensitive to SI level than the conventional algorithm. The paper further proposes a partial feedback scheme, which only use few feedback symbols for channel estimation, to significantly reduce the processing time and computational complexity while maintaining the performance. These good properties seem quite suitable for a use of this proposed blind iterative algorithm for short-length packet FD transmissions in Internet-of-Things (IoT) applications and green communications.

Generator Matrices of Quasi-cyclic Codes over Extension Fields Obtained from Gröbner Basis

Quasi-cyclic codes over finite fields are an important class of linear block codes. A fundamental problem in the theory of these codes is to describe their algebraic structure. In this paper it is shown that every quasi-cyclic code is the subfield code and the trace code of a quasi-cyclic code over an extension field. The latter is defined by a parity check matrix obtained from a spectral analysis of a reduced Gröbner basis of the former. Moreover, it is shown that the quasi-cyclic code over the extension field and the one under consideration have the same length, dimension and minimum Hamming distance. Furthermore, we show that under certain conditions it is possible to construct a generator matrix of the quasi-cyclic code over the extension field using similar techniques to construct its parity check matrix. We illustrate that this construction is attainable for some good quasi-cyclic low density parity check codes like the [155, 64, 20] binary Tanner code.

Integer Ring Sieve for Constructing Compact QC-LDPC Codes With Girths 8, 10, and 12

This paper proposes a new method of constructing compact fully-connected Quasi-Cyclic Low Density Parity Check (QC-LDPC) codes with girth <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$g$ </tex-math></inline-formula> = 8, 10, and 12. The originality of the proposed method is to impose constraints on the exponent matrix P to reduce the search space drastically. For a targeted lifting degree of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$N$ </tex-math></inline-formula> , the first step of the method is to sieve the integer ring <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\mathbb {Z}_{N}$ </tex-math></inline-formula> to make a particular sub-group with specific properties to construct the second column of P (the first column being filled with zeros). The remaining columns of P are determined recursively as multiples of the second column by adapting the sequentially multiplied column (SMC) method whereby a controlled greedy search is applied at each step. The codes constructed with the proposed semi-algebraic method show lengths that can be significantly shorter than their best counterparts in the literature.

Performance of Hybrid RF/FSO Cooperative Systems Based on Quasicyclic LDPC Codes and Space-Coupled LDPC Codes

Free space optical (FSO) communication systems provide wireless line of sight connectivity in the unlicensed spectrum, and wireless optical communication achieves higher data rates compared to their radio frequency (RF) counterparts. FSO systems are particularly attractive for last mile access problem by bridging fiber optic backbone connectivity to RF access networks. To cope with this practical deployment scenario, there has been increasing attention to the so-called dual-hop (RF/FSO) systems where RF transmission is used at a hop followed by FSO transmission to another. In this article, we study the performance of cooperative transmission systems using a mixed RF-FSO DF (decode and forward) relay using error-correcting codes including QC-LDPC codes at the relay level. The FSO link is modeled by the gamma-gamma distribution, and the RF link is modeled by the Additive White Gaussian Noise (AWGN) model. Another innovation in this article is the use of cooperative systems using a mixed FSO/RF DF relay using quasicyclic low-density parity check (QC-LDPC) codes at the relay level. We also use the space-coupled low-density parity check (SC-LDPC) codes on the same scheme to show its importance in cooperative optical transmission but also in hybrid RF/FSO transmission. The latter will be compared with QC-LDPC codes. The use of mixed RF/FSO cooperative transmission systems can improve the reliability and transmission of information in networks. The results demonstrate an improvement in the performance of the cooperative RF/FSO DF system based on QC-LDPC and SC-LDPC codes compared to RF/FSO systems without the use of codes, but also to the DF systems proposed in the existing literature.

High-throughput GPU layered decoder of quasi-cyclic multi-edge type low density parity check codes in continuous-variable quantum key distribution systems

The decoding throughput during post-processing is one of the major bottlenecks that occur in a continuous-variable quantum key distribution (CV-QKD) system. In this paper, we propose a layered decoder to decode quasi-cyclic multi-edge type LDPC (QC-MET-LDPC) codes using a graphics processing unit (GPU) in continuous-variable quantum key distribution (CV-QKD) systems. As described herein, we optimize the storage methods related to the parity check matrix, merge the sub-matrices which are unrelated, and decode multiple codewords in parallel on the GPU. Simulation results demonstrate that the average decoding speed of LDPC codes with three typical code rates, i.e., 0.1, 0.05 and 0.02, is up to 64.11 Mbits/s, 48.65 Mbits/s and 39.51 Mbits/s, respectively, when decoding 128 codewords of length {10}^{{6}} simultaneously without early termination.

Flexible High Throughput QC-LDPC Decoder With Perfect Pipeline Conflicts Resolution and Efficient Hardware Utilization

Modern communication standards, such as 5G new radio (5G NR), require a high speed decoder for highly irregular quasi-cyclic low density parity check (QC-LDPC) codes. A widely used approach in QC-LDPC decoders is a layered decoding schedule which processes the parity check matrix in parts, thus providing faster convergence. However, pipelined layered decoding architecture suffers from data hazards that reduce the throughput. This paper presents a novel architecture, which can facilitate any QC-LDPC decoding without stall cycles caused by pipeline hazards. The decoder conveniently incorporates both the layered and the flooding schedules in cases when hazards occur. The paper also presents the genetic algorithm based optimization of the decoding schedule for better signal-to-noise ratio (SNR) performance. The proposed architecture enables insertion of a large number of pipeline stages, thus providing high operating frequency. As a case study, the FPGA implementation for WiMAX, DVB-S2X, and 5G NR provided coded throughput of up to 1.77 Gbps, 4.32 Gbps, and 4.92 Gbps at 10 iterations, respectively. The results show a strong throughput increase of 30%–109% compared with the conventional layered decoder for 5G NR for the same SNR performance. The decoder provides highly efficient utilization of resources when compared with the state-of-the-art solutions.

Low Complexity Rate Compatible Puncturing For Future Communication network

An efficient low complexity puncturing method has studied to achieve rate compatible. The parallel concatenation codes are use mixing of one component of Quasi-Cyclic (QC) low-density parity check codes LDPC codes with two components of (LDPC) in linear coding. The proposed QC-PCGC have lower computation complexity when compared with traditional punctured PCGC. The decreasing in the complexity analysis yields to the reducing in the memory requirement for the encoding/decoding system. It is possible to use the suggested coding system structure in the future communication applications like fifth generation (5G), where it is needed to have coding flexibility, with less complexity in encoding and decoding.

Hybrid forward error correction coding efficiency for MIMO-PLC with symmetric alpha-stable noise

Power line communication (PLC) medium is a very hostile environment, this is due to the fact that severe impairments adhering this means of communication, which cannot be described as a Gaussian noise. In this paper, we propose a powerful scheme to combat the impulsive noise effect and efficiently increase the transmission bit rate. The proposed technique makes use of a new hybrid coding (HC) process and a multiple input multiple output (MIMO) based orthogonal frequency division multiplexing (OFDM), namely, HC-MIMO-OFDM. The HC is mainly constructed based on the combination of convolutional codes (CC) and quasi cyclic-low density parity check codes (QC-LDPC). The HC-MIMO-OFDM stage is then followed by an orthogonal space time block code to provide more robustness under a heavy impulsive noise environment. Furthermore, the symmetric $$\alpha $$-stable model is applied to characterize the realistic PLC noise and consequently avoid the overestimation of the overall performance in such communication systems. The obtained results showed the increase improvement in performance of the bit-error-rate with the raise of the bit rate, when going from single input single output to MIMO. In addition, it has been illustrated that there was a gain when the MIMO was supplemented with only the CC and an additional gain when the HC is considered (i.e., combination of CC plus QC-LDPC coding).

FER Performance Analysis and Optimization of Diagonal Structure Based QC-LDPC Codes with Girth 12 Using LU Decomposition

The manuscript presents the construction of a diagonally structured Parity check matrix using lower and upper (LU) decomposition for regular Quasi Cyclic-Low Density Parity Check Codes (QC-LDPC) with girth 12. This diagonally structured parity check matrix reduces the sparsity characteristics of QC-LDPC codes. The regular Quasi Cyclic-LDPC code has been constructed using circulant shifting and randomization method in which uniform distribution of non-zero elements, XOR operation, and pairing of row and column has been done. A Simplified Log Domain Sum-Product Algorithm (SLDSPA) is used for the decoding of the constructed code. To reduce the CPU run time of the constructed code, a column-wise loop optimization technique is applied. The frame error rate and CPU run time is calculated for different code lengths such as code1 (816, 408), code2 (1008, 504), code3 (1032, 516), code4 (1944, 972), code5 (672, 336) and code6 (504, 252). The construction of regular QC-LDPC codes on half code rate is obtained for the weight of each row is 6 and each column is given by 3. The results showing that the constructed code is better performing in terms of Low FER (10−1 to 10−7), Low SNR (0 to 3.5 dB) and Less CPU run time in milliseconds.

Optimization of QC-LDPC Codes by Edge Exchange Method Based on ACE

Long quasi-cyclic low-density parity check (QC-LDPC) codes have been chosen as one of the forward error correction (FEC) schemes in passive optical network (PON) systems benefiting from the excellent performance. About how to get the appropriate LDPC codes, some traditional methods which focus on obtaining large girth or flat approximated cycle extrinsic message degree (ACE) spectrums are proposed for the design of LDPC codes. These methods which may still make the existence of small stopping sets containing short cycles probably are not so useful for long QC-LDPC codes. Recently, the parallel vector message passing (PMP) algorithm oriented-to decreasing the number of short cycles is proved to be an effective method to optimize LDPC codes. Since ignoring short cycles with poor connectivity which can induce error floor, this method cannot guarantee its effectiveness for long QC-LDPC codes. In this letter, an edge exchange optimization method based on the global properties of ACE and girth called EEA method is proposed, which tries to reduce cycles with low ACE in the order of cycle length. The numerical results prove that our EEA method can bring the improvements of error floor up to two orders of magnitude to long QC-LDPC codes and obviously outperforms PMP algorithm.

A new construction method of QC-LDPC codes with low error floor based on EETS and Zig-Zag

Aiming at the problem that quasi-cyclic low density parity check (QC-LDPC) codes may have the error floor in the high signal to noise ratio (SNR) region, a new construction method of the QC-LDPC codes with the low error floor is proposed. The basic matrix of the method is based on the progressive edge growth (PEG) algorithm and the improved eliminate elementary trapping sets (EETS) algorithm so as to eliminate the elementary trapping sets in the basic matrix, then the Zig-Zag method is used to construct the cyclic shift matrix which is used to extend the basic matrix in order to construct the parity check matrix. The method not only can improve the error floor in the high SNR region, but also can flexibly design the code length and code rate. The simulation results show that at the bit error rate of 10−6, the PEG-trapping-Zig-Zag (PTZZ)-QC-LDPC(3024,1512) codes with the code rate of 0.5, compared with the PEG-Zig-Zag (PZZ)-QC-LDPC(3024,1512) codes and the PEG-QC-LDPC(3024,1512) codes, can respectively improve the net coding gain of 0.1 dB and 0.16 dB. The difference among the bit error rate performance curves will become better with the increase of the SNR. In addition, the PTZZ-QC-LDPC(3024,1512) codes have no error floor above the SNR of 2.2 dB.

Performance Analysis of Practical QC-LDPC Codes: From DVB-S2 to ATSC 3.0

In this paper, a new analysis method is introduced to predict the gap between Shannon limit and successful decoding signal-to-noise ratio threshold (SNR loss) of practical quasi-cyclic low-density parity check (QC-LDPC) codes. The SNR loss of a QC-LDPC code is summed up from three aspects: 1) the base matrix; 2) the number of iterations for decoding; and 3) the finite codeword length. As an example, the SNR loss of DVB-S2 and ATSC 3.0 LDPC codes is analyzed with the proposed method. Results show that a large portion of the SNR loss of DVB-S2 LDPC codes is due to their base matrices, which is significantly improved in latest ATSC 3.0 standard. Furthermore, with the aid of the proposed analysis method, newly designed QC-LDPC codes with raptor-like structure are proposed. Bit-error rate simulations show that the proposed codes are only 0.4 dB away from Shannon limit under binary-input additive white Gaussian noise channel and only 0.65 dB away from Shannon limit under binary-input Rayleigh fading channel, which are comparable with state-of-art design.

Construction of Quasi-Cyclic Low Density Parity Check Codes for Magnetic Induction Communication

The magnetic induction (MI) communication has been proved to be an effective method in the wireless underground sensor networks (WUSN). MI communication system based on quasi-cyclic low density parity check (QC-LDPC) codes is expected to improve the transmission performance in WUSN for its good performance and hardware friendliness. In this paper, we aim to construct an optimized QC-LDPC code with low encoding complexity for MI communication system. Firstly, we present a novel method, magnetic induction - protograph extrinsic information transfer (MI-PEXIT) algorithm, which can evaluate the performance of the QC-LDPC codes and predict the distance threshold for successfully transmission of the direct MI communication. Then, we combine the discrete particle swarm optimization (PSO) algorithm with the MI-PEXIT algorithm, and propose a novel scheme DPMIP method to optimize the QC-LDPC codes for MI communication system. Furthermore, two groups of QC-LDPC codes with low encoding complexity are constructed by the proposed DPMIP algorithm, which have different code parameters and different coil parameters. Simulation results validate the superiority of the proposed QC-LDPC codes for MI communication in WUSN, and the proposed codes also can achieve a good trade-off between the complexity and the performance.

Progressive Matrix Growth Algorithm for Constructing Rate-Compatible Length-Scalable Raptor-Like Quasi-Cyclic LDPC Codes

With the worldwide deployment and rapid development of digital television terrestrial broadcasting (DTTB) systems, the demands of diversified multimedia services from the fixed/mobile receptions increase significantly. To satisfy the various requirements of quality of service, the forward error correction codes with multiple code rates and lengths become a trend for DTTB standards. In this paper, rate-compatible length-scalable raptor-like quasi-cyclic low density parity check (RL-QC-LDPC) codes are proposed for future DTTB systems, where a wide range of code rates and information/parity block lengths can be obtained with low implementation complexity. A low-complexity construction method, called progressive matrix growth (PMG), is also proposed for such kind of RL-QC-LDPC codes. Unlike conventional construction methods, PMG performs 2-D progressive extension of both information variable nodes and check nodes with limited computational complexity and memory resources. Based on the performance prediction provided by the tool of multi-edge type density evolution, several code families are constructed with PMG as examples, and careful discussions on design parameters are given. The numerical results show that the average gaps of SNR threshold to Shannon limit of binary-input additive white Gaussian noise channel are only 0.41~0.44 dB for the code families with information-bit puncturing.

Arithmetic and Huffman Coding using Quasi-Cyclic Low Density Parity Check Techniques with F-OFDMA for 5G System

The rising demand of the future 5th generation (5G) wireless systems has led to the development of wireless communication technologies that can provide higher user capacity. Therefore, filtered orthogonal frequency division multiple access (F-OFDMA) was introduced to accommodate large number of users. F-OFDMA has the advantage over OFDM since it is capable of overcoming the high side lobes and increasing the spectrum utilization by eliminating the out-of-band emission which can degrade the system’s performance. In this paper, a joint method between two block coding techniques (Arithmetic coding (AC) and Huffman Coding (HC)) with an error correcting code (Quasi-Cyclic Low Density Parity Check (QC-LDPC))was proposed. AC-QC-LDPC and HC-QC-LDPC schemes were compared in terms of BER performance. Based on the simulation results, AC-QC-LDPC technique has been proven to give the 44.75% BER improvement to the F-OFDMA system which outperforms the HC-QC-LDPC technique. It is clear from the results that Arithmetic coding always give better BER improvements compared to Huffman coding with QC-LDPC.