PERFORMANCE EVALUATION OF LOW DENSITY PARITY CHECK CODES FOR DIGITAL RADIO MONDIALE (DRM) SYSTEM

In Digital Radio Mondiale (DRM) system, achieving good audio quality becomes a challenge due to its limited band-width of 9 or 10kHz and the very bad fading channels. Therefore, DRM needs highly efficient channel coding schemes. This paper, proposes the schemes which use the Low-Density Parity-Check (LDPC) coded Bit-Interleaved Coded Modulation (BICM) schemes for the implementation of DRM systems. Simulation results show that the proposed system is more efficient than the Rate Compatible Punctured Con volutional (RCPC) coded DRM system on various broadcast channels, and may be recommended as a coding technology for Digital Amplitude Modulation Broadcasting (DAMB) systems of China.

REGULAR LOW-DENSITY PARITY-CHECK CODES BASED ON SHIFTED IDENTITY MATRICES

This paper extends the class of Low-Density Parity-Check (LDPC) codes that can be constructed from shifted identity matrices. To construct regular LDPC codes, a new method is proposed. Two simple inequations are adopted to avoid the short cycles in Tanner graph, which makes the girth of Tanner graphs at least 8. Because their parity-check matrices are made up of circulant matrices, the new codes are quasi-cyclic codes. They perform well with iterative decoding.

CONSTRUCTION OF NONSYSTEMATIC LOW-DENSITY PARITY-CHECK CODES BASED ON SYMMETRIC BALANCED INCOMPLETE BLOCK DESIGN

This paper studies the nonsystematic Low-Density Parity-Check(LDPC)codes based onSymmetric Balanced Incomplete Block Design(SBIBD).First,it is concluded that the performancedegradation of nonsystematic linear block codes is bounded by the average row weight of generalizedinverses of their generator matrices and code rate.Then a class of nonsystematic LDPC codes con-structed based on SBIBD is presented.Their characteristics include:both generator matrices andparity-check matrices are sparse and cyclic,which are simple to encode and decode;and almost arbi-trary rate codes can be easily constructed,so they are rate-compatible codes.Because there aresparse generalized inverses of generator matrices,the performance of the proposed codes is only0.15dB away from that of the traditional systematic LDPC codes.

Low-Complexity Optimization Algorithm for Irregular Low-Density Parity-Check Codes

A low-complexity algorithm is proposed in this paper in order to optimize irregular low-density parity-check(LDPC)codes.The algorithm proposed can calculate the noise threshold by means of a one-dimensional density evolution and search the optimal degree profiles with fast-convergence differential evolution,so that it has a lower complexity and a faster convergence speed.Simulation results show that the irregular LDPC codes optimized by the presented algorithm can also perform better than Turbo codes at moderate block length even with less computation cost.

DESIGN OF LOW-DENSITY PARITY CHECK CODES FOR MIMO SYSTEMS WITH DOUBLY-ITERATIVE RECEIVERS

In this paper, the Multiple Input Multiple Output (MIMO) doubly-iterative receiver which consists of the Probabilistic Data Association detector (PDA) and Low-Density Parity-Check Code (LDPC) decoder is developed. The receiver performs two iterative decoding loops. In the outer loop, the soft information is exchanged between the PDA detector and the LDPC decoder. In the inner loop, it is exchanged between variable node and check node decoders inside the LDPC decoder. On the light of the Extrinsic Information Transfer (EXIT) chart technique, an LDPC code degree profile optimization algorithm is developed for the doubly-iterative receiver. Simulation results show the doubly-receiver with optimized irregular LDPC code can have a better performance than the one with the regular one.

Low-Density Parity-Check Codes: Research Status and Development Direction

In this paper, we conclude five kinds of methods for construction of the regular low-density parity matrix H and three kinds of methods for the construction of irregular low-density parity-check matrix H. Through the analysis of the code rate and parameters of these eight kinds of structures, we find that the construction of low-density parity-check matrix tends to be more flexible and the parameter variability is enhanced. We propose that the current development cost should be lower with the progress of electronic technology and we need research on more practical Low-Density Parity-Check Codes (LDPC). Combined with the application of the quantum distribution key, we urgently need to explore the research direction of relevant theories and technologies of LDPC codes in other fields of quantum information in the future.

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.

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.

基于可靠度差值特征的自适应判决多元LDPC译码算法

利用变量节点符号可靠度在迭代过程中的分布特征,提出了一种基于可靠度差值特征的自适应判决多元低密度奇偶校验(Low Density Parity Check, LDPC)译码算法。整个迭代过程划分为两个阶段,针对不同阶段节点可靠度的差值特征分别采用不同的判决策略:前期阶段,采用传统的基于最大可靠度的判决策略;后期阶段,根据最大、次大可靠度之间的差值特征,设计自适应的码元符号判决策略。仿真结果表明,所提算法在相当的译码复杂度前提下,能获得0.15~0.4 dB的性能增益。同时,对于列重较小的LDPC码,具有更低的译码错误平层。

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.

一种引入积分修正的二维信息大数逻辑LDPC译码算法

为了解决基于可靠度的迭代大数逻辑译码(Modified Reliability-based Iterative Majority Logic Decoding,MRBI-MLGD)算法的错误平层问题,提出了一种基于大数逻辑的低密度奇偶校验(Low Density Parity Check,LDPC)译码算法。所提算法在译码函数中引入积分修正项,实现了基于二维信息修正的译码策略,可有效降低错误平层。此外,与基于二元译码信息的的迭代大数逻辑译码(Binary Message Majority Logic Decoding,BM-MLGD)算法不一样,所提算法可适用于不同列重的LDPC码。仿真结果表明,所提译码算法在整个工作信噪比区间内都具有稳定的译码性能,表现出更好的普适性和鲁棒性。

基于原模图的8环QC-LDPC码构造方法

针对当前准循环低密度奇偶校验(Quasi-Cyclic Low-Density Parity-Check,QC-LDPC)码存在短环及纠错性能不够好的问题,基于原模图提出一种新颖的QC-LDPC码构造方法。该方法选择码长码率可灵活调整的原模图作为基矩阵,再结合具有特殊性质的卢卡斯数列和等差数列,通过原模图的低译码门限和数列的特殊性质,构造校验矩阵环长至少为8,且所需存储空间少,易于硬件实现。仿真结果表明:该方法构造的PLA-QC-LDPC(2400,1200)码与同等码长码率中基于卢卡斯数列和最大公约数序列的可快速编码的非规则LG-QC-LDPC码、基于素数和乘法表构造的PM-QC-LDPC码以及基于原模图和消除基本陷阱集的非规则PL-QC-LDPC码相比,净编码增益均有一定程度的提高。

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.

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.

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.

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.

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.

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.

Construction of Rate-Compatible(RC) Low-Density Parity-Check(LDPC) Convolutional Codes Based on RC-LDPC Block Codes

In this paper,a family of rate-compatible(RC) low-density parity-check(LDPC) convolutional codes can be obtained from RC-LDPC block codes by graph extension method.The resulted RC-LDPC convolutional codes,which are derived by permuting the matrices of the corresponding RC-LDPC block codes,are systematic and have maximum encoding memory.Simulation results show that the proposed RC-LDPC convolutional codes with belief propagation(BP) decoding collectively offer a steady improvement on performance compared with the block counterparts over the binary-input additive white Gaussian noise channels(BI-AWGNCs).

JOINT SOURCE-CHANNEL DECODING OF HUFFMAN CODES WITH LDPC CODES

In this paper, we present a Joint Source-Channel Decoding algorithm (JSCD) for Low-Density Parity Check (LDPC) codes by modifying the Sum-Product Algorithm (SPA) to account for the source redun-dancy, which results from the neighbouring Huffman coded bits. Simulations demonstrate that in the presence of source redundancy, the proposed algorithm gives better performance than the Separate Source and Channel Decoding algorithm (SSCD).