Design of Protograph LDPC-Coded MIMO-VLC Systems with Generalized Spatial Modulation

This paper investigates the bit-interleaved coded generalized spatial modulation(BICGSM) with iterative decoding(BICGSM-ID) for multiple-input multiple-output(MIMO) visible light communications(VLC). In the BICGSM-ID scheme, the information bits conveyed by the signal-domain(SiD) symbols and the spatial-domain(SpD) light emitting diode(LED)-index patterns are coded by a protograph low-density parity-check(P-LDPC) code. Specifically, we propose a signal-domain symbol expanding and re-allocating(SSER) method for constructing a type of novel generalized spatial modulation(GSM) constellations, referred to as SSERGSM constellations, so as to boost the performance of the BICGSM-ID MIMO-VLC systems.Moreover, by applying a modified PEXIT(MPEXIT) algorithm, we further design a family of rate-compatible P-LDPC codes, referred to as enhanced accumulate-repeat-accumulate(EARA) codes,which possess both excellent decoding thresholds and linear-minimum-distance-growth property. Both analysis and simulation results illustrate that the proposed SSERGSM constellations and P-LDPC codes can remarkably improve the convergence and decoding performance of MIMO-VLC systems. Therefore, the proposed P-LDPC-coded SSERGSM-mapped BICGSMID configuration is envisioned as a promising transmission solution to satisfy the high-throughput requirement of MIMO-VLC applications.

Weighted symbol-flipping decoding algorithm for nonbinary LDPC codes with flipping patterns

A novel low-complexity weighted symbol-flipping algorithm with flipping patterns to decode nonbinary low-density parity-check codes is proposed. The proposed decoding procedure updates the hard-decision received symbol vector iteratively in search of a valid codeword in the symbol vector space. Only one symbol is flipped in each iteration, and symbol flipping function, which is employed as the symbol flipping metric, combines the number of failed checks and the reliabilities of the received bits and calculated symbols. A scheme to avoid infinite loops and select one symbol to flip in high order Galois field search is also proposed. The design of flipping pattern＇s order and depth, which is dependent of the computational requirement and error performance, is also proposed and exemplified. Simulation results show that the algorithm achieves an appealing tradeoff between performance and computational requirement over relatively low Galois field for short to medium code length.

Efficient Helicopter-Satellite Communication Scheme Based on Check-Hybrid LDPC Coding

When implementing helicopter-satellite communications, periodical interruption of the received signal is a challenging problem because the communication antenna is intermittently blocked by the rotating blades of the helicopter. The helicopter-satellite channel model and the Forward Error Control（FEC） coding countermeasure are presented in this paper. On the basis of this model, Check-Hybrid（CH） Low-Density Parity-Check（LDPC）codes are designed to mitigate the periodical blockage over the helicopter-satellite channels. The CH-LDPC code is derived by replacing part of single parity-check code constraints in a Quasi-Cyclic LDPC（QC-LDPC） code by using more powerful linear block code constraints. In particular, a method of optimizing the CH-LDPC code ensemble by searching the best matching component code among a variety of linear block codes using extrinsic information transfer charts is proposed. Simulation results show that, the CH-LDPC coding scheme designed for the helicopter-satellite channels in this paper achieves more than 25% bandwidth efficiency improvement, compared with the FEC scheme that uses QC-LDPC codes.

Joint Iterative Decoding for Network-Coding-Based Multisource LDPC-Coded Cooperative MIMO

A network-coding-based multisource LDPC-coded cooperative MIMO scheme is proposed,where multiple sources transmit their messages to the destination with the assistance from a single relay.The relay cooperates with multiple sources simultaneously via network-coding.It avoids the issues of imperfect frequency/timing synchronization and large transmission delay which may be introduced by frequency-division multiple access(FDMA)/code-division multiple access(CDMA)and time-division multiple access(TDMA)manners.The proposed joint″Min-Sum″iterative decoding is effectively carried out in the destination.Such a decoding algorithm agrees with the introduced equivalent joint Tanner graph which can be used to fully characterize LDPC codes employed by the sources and relay.Theoretical analysis and numerical simulation show that the proposed scheme with joint iterative decoding can achieve significant cooperation diversity gain.Furthermore,for the relay,compared with the cascade scheme,the proposed scheme has much lower complexity of LDPC-encoding and is easier to be implemented in the hardware with similar bit error rate(BER)performance.

LDPC Decoding for Signal Dependent Visible Light Communication Channels

Avalanche photodiodes （APD） are widely employed in visible light communication （VLC） systems. The general signal dependent Gaussian channel is investigated. Experiment results reveal that symbols on different constellation points under official illuminance inevitably suffer from different levels of noise due to the multiplication process of APDs. In such a case, conventional log likely-hood ratio （LLR） calculation for signal independent channels may cause performance loss. The optimal LLR calculation for decoder is then derived because of the existence of non-ignorable APD shot noise. To find the decoding thresholds of the optimal and suboptimal detection schemes, the extrinsic information transfer （EXIT） chat is further analyzed. Finally a modified minimum sum algorithm is suggested with reduced complexity and acceptable performance loss. Numerical simulations show that, with a reg- ular （3, 6） low-density parity check （LDPC） code of block length 20,000, 0.7 dB gain is achieved with our proposed scheme over the LDPC decoder designed for signal independent noise. It is also found that the coding performance is improved for a larger modulation depth.

LDPC Code’s Decoding Algorithms for Wireless Sensor Network:a Brief Review

As an effective error correction technology,the Low Density Parity Check Code(LDPC)has been researched and applied by many scholars.Meanwhile,LDPC codes have some prominent performances,which involves close to the Shannon limit,achieving a higher bit rate and a fast decoding.However,whether these excellent characteristics are suitable for the resource-constrained Wireless Sensor Network(WSN),it seems to be seldom concerned.In this article,we review the LDPC code’s structure brief.ly,and them classify and summarize the LDPC codes’construction and decoding algorithms,finally,analyze the applications of LDPC code for WSN.We believe that our contributions will be able to facilitate the application of LDPC code in WSN.

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.

Doped low-density parity-check codes

In this paper,we propose a doping approach to lower the error floor of Low-Density Parity-Check(LDPC)codes.The doping component is a short block code in which the information bits are selected from the coded bits of the dominant trapping sets of the LDPC code.Accordingly,an algorithm for selecting the information bits of the short code is proposed,and a specific two-stage decoding algorithm is presented.Simulation results demonstrate that the proposed doped LDPC code achieves up to 2.0 dB gain compared with the original LDPC code at a frame error rate of 10^(-6)Furthermore,the proposed design can lower the error floor of original LDPC Codes.

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.

基于相对残余度的LDPC码置信传播译码调度算法(英文)

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.

Joint Source-Channel Coding for 6G Communications

In order to provide ultra low-latency and high energy-efficient communication for intelligences,the sixth generation(6G)wireless communication networks need to break out of the dilemma of the depleting gain of the separated optimization paradigm.In this context,this paper provides a comprehensive tutorial that overview how joint source-channel coding(JSCC)can be employed for improving overall system performance.For the purpose,we first introduce the communication requirements and performance metrics for 6G.Then,we provide an overview of the source-channel separation theorem and why it may not hold in practical applications.In addition,we focus on two new JSCC schemes called the double low-density parity-check(LDPC)codes and the double polar codes,respectively,giving their detailed coding and decoding processes and corresponding performance simulations.In a nutshell,this paper constitutes a tutorial on the JSCC scheme tailored to the needs of future 6G communications.

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.

Accelerating BP-Based Iterative Low-Density Parity-Check Decoding by Modified Vertical and Horizontal Processes

Two modified BP algorithms related to vertical and horizontal processes are proposed to accelerate iterative low-density parity- check （LDPC） decoding over an additive white Gaussian noise （AWGN） channel, where the newly updated extrinsic information is immediately used in the current decoding round. Theoretical analysis and simulation results demonstrate that both the modified approaches provide significant performance improvements over the traditional BP algorithm with almost no additional decoding complexity. The proposed algorithm with modified horizontal process offers even better performance than another algorithm with the modified horizontal process. The two modified BP algorithms are very promising in practical communications since both can achieve an excellent trade-off between the performance and decoding complexity.

Construction of time-frequency codes based on protograph LDPC codes in OFDM communication systems

This paper proposes a scheme to construct time- frequency codes based on protograph low density parity check （LDPC） codes in orthogonal frequency division multiplexing （OFDM） communication systems. This approach synthesizes two techniques： protograph LDPC codes and OFDM. One symbol of encoded information by protograph LDPC codes corresponds to one sub-carrier, namely the length of encoded information equals to the number of sub-carriers. The design of good protograph LDPC codes with short lengths is given, and the proposed proto- graph LDPC codes can be of fast encoding, which can reduce the encoding complexity and simplify encoder hardware implementa- tion. The proposed approach provides a higher coding gain in the Rayleigh fading channel. The simulation results in the Rayleigh fading channel show that the bit error rate （BER） performance of the proposed time-frequency codes is as good as random LDPC- OFDM codes and is better than Tanner LDPC-OFDM codes under the condition of different fading coefficients.

DESIGN OF QUASI-CYCLIC LDPC CODES BASED ON EUCLIDEAN GEOMETRIES

A new method for constructing Quasi-Cyclic (QC) Low-Density Parity-Check (LDPC) codes based on Euclidean Geometry (EG) is presented. The proposed method results in a class of QC-LDPC codes with girth of at least 6 and the designed codes perform very close to the Shannon limit with iterative decoding. Simulations show that the designed QC-LDPC codes have almost the same performance with the existing EG-LDPC codes.

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.

High Robust Broadcasting over DTMB-A with Low-rate LDPC Codes

As the 2nd generation digital terrestrial television broadcasting(DTTB)standard,digital terrestrial/television multimedia broadcasting-advanced(DTMB-A)can provide higher spectrum efficiency and transmission reliability by adopting flexible frame structure and advanced forward error correction coding compared with the 1 st generation DTTB systems.In order to increase the flexibility and robustness of the DTTB network,the frequency reuse scheme of factor one(reuse-1)is proposed,where the same RF channel is used by different stations covering the adjacent service areas.However,it demands a very low carrier-tonoise ratio(C/N)threshold below 0 dB at the DTTB physical layer.In this paper,a robust broadcasting technique is proposed based on DTMB-A with newly designed low-rate low density parity check(LDPC)codes.By adopting quasi-cyclic(QC)Raptor-like structure and progressive lifting method,the high performance low-rate LDPC codes are designed supporting multiple code lengths.Both density-evolution analyses and laboratory measurements demonstrate that DTMB-A with low-rate coding can complete the demodulation reliably with the C/N threshold below0 d B,which is one important necessary condition to support frequency reuse-1 scheme.

Irregular and regular LDPC codes with high spectrum efficiency modulation in image transmission over fading channel

If the degree distribution is chosen carefully, the irregular low-density parity-check (LDPC) codes can outperform the regular ones. An image transmission system is proposed by combining regular and irregular LDPC codes with 16QAM/64QAM modulation to improve both efficiency and reliability. Simulaton results show that LDPC codes are good coding schemes over fading channel in image communication with lower system complexity. More over, irregular codes can obtain a code gain of about 0.7 dB compared with regular ones when BER is 10 -4. So the irregular LDPC codes are more suitable for image transmission than the regular codes.

Ensemble of High Performance Structured Binary Convolutional LDPC Codes with Moderate Rates

An algebraic construction methodology is proposed to design binary time-invariant convolutional low-density parity-check(LDPC)codes.Assisted by a proposed partial search algorithm,the polynomialform parity-check matrix of the time-invariant convolutional LDPC code is derived by combining some special codewords of an(n,2,n−1)code.The achieved convolutional LDPC codes possess the characteristics of comparatively large girth and given syndrome former memory.The objective of our design is to enable the time-invariant convolutional LDPC codes the advantages of excellent error performance and fast encoding.In particular,the error performance of the proposed convolutional LDPC code with small constraint length is superior to most existing convolutional LDPC codes.

Optimized LDPC differential-encoded 16QAM scheme for high-speed transmission systems

The 16-ary quadrature amplitude modulation （16QAM） is a high spectral efficient scheme for high-speed transmission systems. To remove the phase ambiguity in the coherent detection system, differential-encoded 16QAM （DE-16QAM） is usually used, however, it will cause performance degradation about 3 dB as compared to the conventional 16QAM. To overcome the performance loss, a serial concatenated system with outer low density parity check （LDPC） codes and inner DE-16QAM is proposed. At the receiver, joint iterative differential demodulation and decoding （ID） is carried out to approach the maximum likelihood performance. Moreover, a genetic evolution algorithm based on the extrinsic information transfer chart is proposed to optimize the degree distribution of the outer LDPC codes. Both theoretical analyses and simulation results indicate that this algorithm not only compensates the performance loss, but also obtains a significant performance gain, which is up to 1 dB as compared to the conventional non-DE-16QAM.