Blind Recognition of Non-Binary LDPC Codes Based on Ant Colony Optimization

This paper introduces a novel blind recognition of non-binary low-density parity-check(LDPC)codes without a candidate set,using ant colony optimization(ACO)algorithm over additive white Gaussian noise(AWGN)channels.Specifically,the scheme that effectively combines the ACO algorithm and the non-binary elements over finite fields is proposed.Furthermore,an improved,simplified elitist ACO algorithm based on soft decision reliability is introduced to recognize the parity-check matrix over noisy channels.Simulation results show that the recognition rate continuously increases with an increased signalto-noise ratio(SNR)over the AWGN channel.

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 protograph 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.

Efficient construction and encoding of QC-LDPC codes by cyclic lifting of protographs

Quasi-cyclic low-density parity-check （QC-LDPC） codes can be constructed conveniently by cyclic lifting of protographs. For the purpose of eliminating short cycles in the Tanner graph to guarantee performance, first an algorithm to enumerate the harmful short cycles in the protograph is designed, and then a greedy algorithm is proposed to assign proper permutation shifts to the circulant permutation submatrices in the parity check matrix after lifting. Compared with the existing deterministic edge swapping （DES） algorithms, the proposed greedy algorithm adds more constraints in the assignment of permutation shifts to improve performance. Simulation results verify that it outperforms DES in reducing short cycles. In addition, it is proved that the parity check matrices of the cyclic lifted QC-LDPC codes can be transformed into block lower triangular ones when the lifting factor is a power of 2. Utilizing this property, the QC- LDPC codes can be encoded by preprocessing the base matrices, which reduces the encoding complexity to a large extent.

PERFORMANCE OF SIMPLE-ENCODING IRREGULAR LDPC CODES BASED ON SPARSE GENERATOR MATRIX

A new method for the construction of the high performance systematic irregular low-density paritycheck （LDPC） codes based on the sparse generator matrix （G-LDPC） is introduced. The code can greatly reduce the encoding complexity while maintaining the same decoding complexity as traditional regular LDPC （H-LDPC） codes defined by the sparse parity check matrix. Simulation results show that the performance of the proposed irregular LDPC codes can offer significant gains over traditional LDPC codes in low SNRs with a few decoding iterations over an additive white Gaussian noise （AWGN） channel.

Design of Raptor Design of Raptor-Like Rate Compatible SC Like Rate Compatible SC-LDPC Codes

This paper proposes a family of raptor-like rate-compatible spatially coupled low-density parity-check(RL-RC-SC-LDPC)codes from RL-RC-LDPC block codes.There are two important keys.One is the performance of the base matrix.RL-LDPC codes have been adopted in the technical specification of 5G new radio(5G-NR).We use the 5G NR LDPC code as the base matrix.The other is the edge coupling design.In this regard,we have designed a rate-compatible coupling algorithm,which can improve performance under multiple code rates.The constructed RL-RC-SC-LDPC code property requires a large coupling length L and thus we improved the reciprocal channel approximation(RCA)algorithm and proposed a sliding window RCA algorithm.It can provide lower com-plexity and latency than RCA algorithm.The code family shows improved thresholds close to the Shannon limit and finite-length performance compared with 5G NR LDPC codes for the additive white Gaussian noise(AWGN)channel.

Construction of LDPC Codes for the Layered Decoding Algorithm

Abstract： The layered decoding algorithm has been widely used in the implementation of Low Density Parity Check （LDPC） decoders, due to its high convergence speed. However, the pipeline operation of the layered decoder may introduce memory access conflicts, which heavily deteriorates the decoder throughput. To essentially deal with the issue of memory access conflicts,

Relative-Residual-Based Dynamic Schedule for Belief Propagation Decoding of LDPC Codes

Two Relative-Residual-based Dynamic Schedules(RRDS) for Belief Propagation(BP) decoding of Low-Density Parity-Check(LDPC) codes are proposed,in which the Variable code-RRDS(VN-RRDS) is a greediness-reduced version of the Check code-RRDS(CN-RRDS).The RRDS only processes the variable(or check) node,which has the maximum relative residual among all the variable(or check) nodes in each decoding iteration,thus keeping less greediness and decreased complexity in comparison with the edge-based Variable-to-Check Residual Belief Propagation(VC-RBP) algorithm.Moreover,VN-RRDS propagates first the message which has the largest residual based on all check equations.For different types of LDPC codes,simulation results show that the convergence rate of RRDS is higher than that of VC-RBP while keeping very low computational complexity.Furthermore,VN-RRDS achieves faster convergence as well as better performance than CN-RRDS.

A Decode-and-Forward Scheme for LDPC Coded Three-Way Relay Fading Channels

In this paper a low-density pairwise check(LDPC) coded three-way relay system is considered, where three user nodes desire to exchange messages with the help of one relay node. Since physical-layer network coding is applied, two time slots are sufficient for one round information exchange. In this paper, we present a decode-and-forward(DF) scheme based on joint LDPC decoding for three-way relay channels, where relay decoder partially decodes the network code rather than fully decodes all the user messages. Simulation results show that the new DF scheme considerably outperforms other common schemes in three-way relay fading channels.

NEW CONSTRUCTIONS OF LDPC CODES BASED ON CIRCULANT PERMUTATION MATRICES FOR AWGN CHANNEL

Two new design approaches for constructing Low-Density Parity-Check(LDPC) codes are proposed.One is used to design regular Quasi-Cyclic LDPC(QC-LDPC) codes with girth at least 8.The other is used to design irregular LDPC codes.Both of their parity-check matrices are composed of Circulant Permutation Matrices(CPMs).When iteratively decoded with the Sum-Product Algorithm(SPA),these proposed codes exhibit good performances over the AWGN channel.

Lowering the Error Floor of ADMM Penalized Decoder for LDPC Codes

Decoding by alternating direction method of multipliers(ADMM) is a promising linear programming decoder for low-density parity-check(LDPC) codes. In this paper, we propose a two-step scheme to lower the error floor of LDPC codes with ADMM penalized decoder.For the undetected errors that cannot be avoided at the decoder side, we modify the code structure slightly to eliminate low-weight code words. For the detected errors induced by small error-prone structures, we propose a post-processing method for the ADMM penalized decoder. Simulation results show that the error floor can be reduced significantly over three illustrated LDPC codes by the proposed two-step scheme.

Bilayer expurgated LDPC codes with uncoded relaying

Bilayer low-density parity-check （LDPC） codes are an effective coding technique for decode-and-forward relaying, where the relay forwards extra parity bits to help the destination to decode the source bits correctly. In the existing bilayer coding scheme, these parity bits are protected by an error correcting code and assumed reliably available at the receiver. We propose an uneoded relaying scheme, where the extra parity bits are forwarded to the destination without any protection. Through density evolution analysis and simulation results, we show that our proposed scheme achieves better performance in terms of bit erasure probability than the existing relaying scheme. In addition, our proposed scheme results in lower complexity at the relay.

Algebraic-Based Nonbinary LDPC Codes with Flexible Field Orders and Code Rates

In this paper, we study the rank of matrices over GF(2~p),and propose two construction methods for algebraic-based nonbinary LDPC codes from an existing LDPC code, referred to as the original code. By multiplying all elements of each column of the binary parity-check matrix H corresponding to the original code with the same nonzero element of any field, the first class of nonbinary LDPC codes with flexible field order is proposed. The second method is to replace the nonzero elements of some columns in H with different nonzero field elements in a given field, and then another class of nonbinary LDPC codes with various rates is obtained. Simulation results show that the proposed nonbinary LDPC codes perform well over the AWGN channel with the iterative decoding algorithms.

Performance of LDPC Coded OTFS Systems over High Mobility Channels

The upcoming 6G wireless networks have to provide reliable communications in high-mobility scenarios at high carrier frequencies.However,high-mobility or high carrier frequencies will bring severe inter-carrier interference(ICI)to conventional orthogonal fre⁃quency-division multiplexing(OFDM)modulation.Orthogonal time frequency space(OTFS)modulation is a recently developing multi-carrier transmission scheme for wireless commu⁃nications in high-mobility environments.This paper evaluates the performance of coded OT⁃FS systems.In particular,we consider 5G low density parity check(LDPC)codes for OTFS systems based on 5G OFDM frame structures over high mobility channels.We show the per⁃formance of the OTFS systems with 5G LDPC codes when sum-product detection algorithm and iterative detection and decoding are employed.We also illustrate the effect of channel estimation error on the performance of the LDPC coded OTFS systems.

Construction of Short-Block Nonbinary LDPC Codes Based on Cyclic Codes

In this paper, we focus on shortblock nonbinary LDPC(NB-LDPC) codes based on cyclic codes. Based on Tanner graphs' isomorphism, we present an efficient search algorithm for finding non-isomorphic binary cyclic LDPC codes. Notice that the parity-check matrix H of the resulting code is square and not of full rank, and its row weight and column weight are the same. By replacing the ones in the same column of H with a nonzero element of fi nite fi elds GF(q), a class of NB-LDPC codes over GF(q) is obtained. Numerical results show that the constructed codes perform well over the AWGN channel and have fast decoding convergence. Therefore, the proposed NB-LDPC codes provide a promising coding scheme for low-latency and high-reliability communications.

HIGH-PERFORMANCE SIMPLE-ENCODING GENERATOR-BASED SYSTEMATIC IRREGULAR LDPC CODES AND RESULTED PRODUCT CODES

Low-Density Parity-Check (LDPC) code is one of the most exciting topics among the coding theory community.It is of great importance in both theory and practical communications over noisy channels.The most advantage of LDPC codes is their relatively lower decoding complexity compared with turbo codes,while the disadvantage is its higher encoding complexity.In this paper,a new ap- proach is first proposed to construct high performance irregular systematic LDPC codes based on sparse generator matrix,which can significantly reduce the encoding complexity under the same de- coding complexity as that of regular or irregular LDPC codes defined by traditional sparse parity-check matrix.Then,the proposed generator-based systematic irregular LDPC codes are adopted as con- stituent block codes in rows and columns to design a new kind of product codes family,which also can be interpreted as irregular LDPC codes characterized by graph and thus decoded iteratively.Finally, the performance of the generator-based LDPC codes and the resultant product codes is investigated over an Additive White Gaussian Noise (AWGN) and also compared with the conventional LDPC codes under the same conditions of decoding complexity and channel noise.

Design of bilayer lengthened LDPC codes over expanded graph for relay channels

This paper presents a low complexity optimized algorithm for design of bilayer lengthened LDPC(BL-LDPC) code for decode-and-forward relay system.The design is performed over the expanded graph of the BL-LDPC code,which consists of the original bilayer graph and the extra added relaygenerated parity check bits.To build up our proposed optimized algorithm,we present a modified Gaussian approximation algorithm for the expanded structure of the BL-LDPC code.Then using the proposed optimized algorithm,we find the optimum overall expanded graph of the BL-LDPC code.Simulation results show that the BL-LDPC codes obtained by our proposed optimized algorithm have excellent bit-error-rate performances and small gaps between the convergence thresholds and the theoretical limits when transmitted over the additive white Gaussian noise channels.

Construction of protograph LDPC codes with circular generator matrices

The application of protograph low density parity check （LDPC） codes involves the encoding complexity problem. Since the generator matrices are dense, and if the positions of ＂1＂ s are irregularity, the encoder needs to store every ＂1＂ of the generator matrices by using huge chip area. In order to solve this problem, we need to design the protograph LDPC codes with circular generator matrices. A theorem concerning the circulating property of generator matrices of nonsingular protograph LDPC codes is proposed. The circulating property of generator matrix of nonsingular protograph LDPC codes can be obtained from the corresponding quasi-cyclic parity check matrix. This paper gives a scheme of constructing protograph LDPC codes with circulating generator matrices, and it reveals that the fast encoding algorithm of protograph LDPC codes has lower encoding complexity under the condition of the proposed theorem. Simulation results in ad- ditive white Gaussian noise （AWGN） channels show that the bit error rate （BER） performance of the designed codes based on the proposed theorem is much better than that of GB20600 LDPC codes and Tanner LDPC codes.

Design of Irregular QC-LDPC Code Based Multi-Level Coded Modulation Scheme for High Speed Optical Communication Systems

In this paper, we focus on the design of irregular QC-LDPC code based multi-level coded modulation(MLCM) scheme by jointly optimizing the component code rate and the degree distribution of the irregular QC-LDPC component code. Firstly, the sub-channel capacities of MLCM systems is analyzed and discussed, based on which the optimal component code rate can be obtained. Secondly, an extrinsic information transfer chart based two-stage searching algorithm is proposed to find the good irregular QC-LDPC code ensembles with optimal component code rates for their corresponding sub-channels. Finally, by constructing the irregular QC-LDPC component codes from the designed ensembles with the aim of possibly enlarging the girth and reducing the number of the shortest cycles, the designed irregular QC-LDPC code based 16QAM and 64QAM MLCM systems can achieve 0.4 dB and 1.2 dB net coding gain, respectively, compared with the recently proposed regular QC-LDPC code based 16QAM and 64QAM MLCM systems.

QIM digital watermarkingbased on LDPC code and messagepassingunder scalingattacks

Watermarking system based on quantization index modulation （QIM） is increasingly popular in high payload applications,but it is inherently fragile against amplitude scaling attacks.In order to resist desynchronization attacks of QIM digital watermarking,a low density parity check （LDPC） code-aided QIM watermarking algorithm is proposed,and the performance of QIM watermarking system can be improved by incorporating LDPC code with message passing estimation/detection framework.Using the theory of iterative estimation and decoding,the watermark signal is decoded by the proposed algorithm through iterative estimation of amplitude scaling parameters and decoding of watermark.The performance of the proposed algorithm is closer to the dirty paper Shannon limit than that of repetition code aided algorithm when the algorithm is attacked by the additive white Gaussian noise.For constant amplitude scaling attacks,the proposed algorithm can obtain the accurate estimation of amplitude scaling parameters.The simulation result shows that the algorithm can obtain similar performance compared to the algorithm without desynchronization.

Design of good QC-LDPC codes without small girth in the p-plane

A construction method based on the p-plane to design high-girth quasi-cyclic low-density parity-check （QC-LDPC） codes is proposed. Firstly the good points in every line of the p-plane can be ascertained through filtering the bad points, because the designed parity-check matrixes using these points have the short cycles in Tanner graph of codes. Then one of the best points from the residual good points of every line in the p-plane will be found, respectively. The optimal point is also singled out according to the bit error rate （BER） performance of the QC-LDPC codes at last. Explicit necessary and sufficient conditions for the QC-LDPC codes to have no short cycles are presented which are in favor of removing the bad points in the p-plane. Since preventing the short cycles also prevents the small stopping sets, the proposed construction method also leads to QC-LDPC codes with a higher stopping distance.