Construction of quasi‐cyclic low‐density parity‐check codes with low encoding complexity

Low encoding complexity is very important for quasi‐cyclic low‐density parity‐check (QC‐LDPC) codes used in wireless communication systems. In this paper, a new scheme is presented to construct QC‐LDPC codes with low encoding complexity. This scheme is called two‐stage particle swarm optimization (TS‐PSO) algorithm, in which both the threshold and girth distribution of QC‐LDPC codes are considered. The proposed scheme is composed of two stages. In the first stage, we construct a binary base matrix of QC‐LDPC code with the best threshold. The matrix is constructed by combining a binary PSO algorithm and the protograph extrinsic information transfer (PEXIT) method. In the second stage, we search an exponent matrix of the QC‐LDPC code with the best girth distribution. This exponent matrix is based on the base matrix obtained in the first stage. Consequently, the parity‐check matrix of the QC‐LDPC code with the best threshold and best girth distribution are constructed. Furthermore, bit error rate performances are compared for the QC‐LDPC codes constructed by proposed scheme, the QC‐LDPC code in 802.16e standard, and the QC‐LDPC code in Tam's study. Simulation results show that the QC‐LDPC codes proposed in this study are superior to both the 802.16e code and the Tam code on the additive white Gaussian noise (AWGN) and Rayleigh channels. Moreover, proposed scheme is easily implemented, and is flexible and effective for constructing QC‐LDPC codes with low encoding complexity. Copyright © 2012 John Wiley & Sons, Ltd.     

A ZCZ‐CDMA system with BFSK modulation

A quasi‐timing synchronous code division multiple access (CDMA) system called ZCZ‐CDMA, which uses a set of sequences with a zero‐correlation zone called ZCZ code as a spreading code, is useful for short‐range wireless communications because of its excellent properties such as co‐channel interference‐free performance, simplified hardware design, and low transmit power as well as fast frame synchronization capability. In this paper, a ZCZ‐CDMA system with binary frequency‐shift keying (BFSK) modulation called BFSK‐ZCZ‐CDMA is proposed. This system is characterized by using a pair of balanced ZCZ codes for spreading and transmitting the two spread components over the respective keying carrier frequencies. Its bit error rate performance, compared with those of existing BPSK‐ZCZ‐CDMA, ASK‐ZCZ‐CDMA, and CDMA systems using the other spreading codes, is evaluated in theory and simulation. The bit error rate performance of the three ZCZ‐CDMA systems over additive white Gaussian noise and Rayleigh fading channels are formulated. It is proved that BFSK‐ZCZ‐CDMA is much more robust in anti‐fading performance and low transmit power in such an environment that fading distributions on the keying frequencies are independent mutually. Fading versus frequency characteristics are also investigated. Copyright © 2012 John Wiley & Sons, Ltd.     

LT码和q-LDPC码级联方案在深空通信中的应用

该文针对深空通信对长纠删码的需求,提出了LT (Luby Transform)码和q-LDPC码的级联方案。在综合考虑性能和复杂度的情况下,选取8-LDPC码和8PSK的级联作为等效的删除信道,长度选择灵活、编译码简单的LT码实现纠删功能。文中设计了两种短8-LDPC码,并对整个级联系统的纠错性能进行了仿真。仿真结果表明8-LDPC码的性能优于信源信息速率和码率相同的二进制LDPC码,级联系统在等效包删除概率不超过0.1时,系统误比特率以概率1趋于0。     

A near‐Nyquist rate transmission: A new minimum‐bandwidth direct‐sequence code division multiple access scheme

Bandlimited direct‐sequence code division multiple access (DS‐CDMA) attracts much attention for its compact spectrum and the ability to suppress inter‐symbol interference. Among the various bandlimited DS‐CDMA systems available, minimum‐bandwidth DS‐CDMA (MB‐DS‐CDMA) is the only realizable Nyquist rate transmission system. But, MB‐DS‐CDMA only applies to certain kinds of spreading codes. Accordingly, this study proposes a modified DS‐CDMA structure which extends the application of MB‐DS‐CDMA to all common spreading codes at the expense of a negligible reduction in the transmission rate. Additionally, the bit error rate of the proposed schemes adopting either single‐user or multi‐user detection receiver is analyzed and compared with that of the commonly‐used raised‐cosine‐pulsed DS‐CDMA over multipath fading channels. The numerical results show that given a sufficiently large number of users, the bit error rate performance of modified MB‐DS‐CDMA is comparable to that of the raised‐cosine‐pulsed DS‐CDMA scheme; meanwhile, the realizable modified MB‐DS‐CDMA approaches the ultimate transmission rate.     

Performance of a turbo‐coded CDMA system in a mobile satellite channel

The bit error rate (BER) performance of a turbo‐coded code‐division multiple‐access (CDMA) system operating in a satellite channel is analysed and simulated. The system performance is compared for various constituent decoders, including maximum a posteriori probability (MAP) and Max‐Log‐MAP algorithms, and the soft‐output Viterbi algorithm. The simulation results indicate that the Max‐Log‐MAP algorithm is the most promising among these three algorithms in overall terms of performance and complexity. It is also shown that, for fixed code rate, the BER performance is improved substantially by increasing the number of iterations in the turbo decoder, or by increasing the interleaver length in the turbo encoder. The results in this paper are of interest in CDMA‐based satellite communications applications. Copyright © 2005 John Wiley & Sons, Ltd.     

Performance of low density parity check coded continuous phase frequency shift keying (LDPCC‐CPFSK) over fading channels

In this paper, in order to improve bit error performance, bandwidth efficiency and reduction of complexity compared to related schemes such as turbo codes, we combine low density parity check (LDPC) codes and continuous phase frequency shift keying (CPFSK) modulation and introduce a new scheme, called ‘low density parity check coded‐continuous phase frequency shift keying (LDPCC‐CPFSK)’. Since LDPC codes have very large Euclidean distance and use iterative decoding algorithms, they have high error correcting capacity and have very close performances to Shannon limit. In all communication systems, phase discontinuities of modulated signals result extra bandwidth requirements. Continuous phase modulation (CPM) is a powerful solution for this problem. Beside CPM provides good bandwidth efficiency; it also improves bit error performance with its memory unit. In our proposed scheme, LDPC and CPFSK, which is a special type of CPM, are considered together to improve both error performance and bandwidth efficiencies. We also obtain error performance curves of LDPCC‐CPFSK via computer simulations for both regular and irregular LDPC code. Simulation results are drawn for 4‐ary CPFSK, 8‐ary CPFSK and 16‐ary CPFSK over AWGN, Rician and Rayleigh fading channels for maximum 100 iterations, while the frame size is chosen as 504. Copyright © 2006 John Wiley & Sons, Ltd.     

Design and analysis of simple irregular LDPC codes with finite‐lengths and their application in CDMA systems

In this paper, we design and optimize simple irregular low‐density parity‐check (LDPC) codes for finite‐length applications where the asymptotic noise threshold of the channel cannot play as a dominant optimization factor. Our design procedure is based on some observations resulted from analytical study of these codes. Although we present our design procedure for some specified rates but it can generally be used for any rate. Specifically, we design a simple irregular LDPC code for IS‐95 and compare its performance with the other reported codes 1 - 3 for this application. Our results show a 3.7‐fold increase in the capacity at bit error rate (BER) equal to 10⁻⁵ compared to the low‐rate orthogonal convolutional codes and 1.2 times increase compared to a high performance LDPC code of Reference 3 . Copyright © 2004 John Wiley & Sons, Ltd.     

Efficient LDPC‐Based,Threaded Layered Space‐Time‐Frequency System with Iterative Receiver

We present a low‐density parity‐check (LDPC)‐based, threaded layered space‐time‐frequency system with emphasis on the iterative receiver design. First, the unbiased minimum mean‐squared‐error iterative‐tree‐search (U‐MMSE‐ITS) detector, which is known to be one of the most efficient multi‐input multi‐output (MIMO) detectors available, is improved by augmentation of the partial‐length paths and by the addition of one‐bit complement sequences. Compared with the U‐MMSE‐ITS detector, the improved detector provides better detection performance with lower complexity. Furthermore, the improved detector is robust to arbitrary MIMO channels and to any antenna configurations. Second, based on the structure of the iterative receiver, we present a low‐complexity belief‐propagation (BP) decoding algorithm for LDPC‐codes. This BP decoder not only has low computing complexity but also converges very fast (5 iterations is sufficient). With the efficient receiver employing the improved detector and the low‐complexity BP decoder, the proposed system is a promising solution to high‐data‐rate transmission over selective‐fading channels.     

Quasi‐regular rate‐compatible LDPC codes with a novel diagonal‐tailed encoding on noisy channels

It is well known that conventional rate‐compatible (RC) codes, such as Raptor codes, only perform well at long code lengths. However, we propose a class of RC codes with short code lengths in this paper. Particularly, we develop a computational approach to design online‐generated RC low‐density parity‐check (LDPC) codes available on noisy channels. We first propose a diagonal‐tailed encoding to generate Quasi‐regular low‐density generator matrix codes. Then, an optimal encoding profile for RC codes is achieved with a linear interpolation approach that is based on the fixed‐rate quasi‐regular LDPC codes. Finally, we evaluate the rateless and fixed‐rate performances of the proposed RC codes by extensive simulation results on various code rates with different modulations. Copyright © 2013 John Wiley & Sons, Ltd.     

Spreading‐code‐dependent bit error rate and capacity analysis for finite asynchronous CDMA systems

Most CDMA systems serve only finite number of active users. Therefore, using Gaussian approximation to evaluate its performance is inappropriate. In such finite CDMA systems, the selection of spreading codes is of great importance because its performance is very much spreading‐code‐dependent. In this paper, a new algorithm based on multiple variable Bernoulli process is introduced to evaluate bit error rate due to co‐channel interference and thus the capacity of a CDMA system. The algorithm can also be used for large‐sized CDMA systems. The results show that small Kasami and Gold‐like codes offer higher capacity than the others do. Copyright © 1999 John Wiley & Sons, Ltd.     

Euclidean Geometry LDPC-VBLAST System Design and Performance Evaluation

Among popular multi-transmit and multi-receive antennas techniques, the VBLAST (Vertical Bell Laboratories Layered Space-Time) architecture has been shown to be a good solution for wireless communications applications that require the transmission of data at high rates. Recently, the application of efficient error correction coding schemes such as low density parity-check (LDPC) codes to systems with multi-transmit and multi-receive antennas has shown to significantly improve bit error rate performance. Although irregular LDPC codes with non-structure are quite popular due to the ease of constructing the parity check matrices and their very good error rate performance, the complexity of the encoder is high. Simple implementation of both encoder and decoder can be an asset in wireless communications applications. In this paper, we study the application of Euclidean geometry LDPC codes to the VBLAST system. We assess system performance using different code parameters and different numbers of antennas via Monte-Carlo simulation and show that the combination of Euclidean geometry LDPC codes and VBLAST can significantly improve bit error rate performance. We also show that interleaving data is necessary to improve performance of LDPC codes when a higher number of antennas is, used in order to mitigate the effect of error propagation. The simplicity of the implementation of both encoder and decoder makes Euclidean geometry LDPC codes with VBLAST system attractive and suitable for practical applications.     

Performance of joint multilevel/AES‐LDPCC‐CPFSK schemes over wireless sensor networks

In wireless sensor networks, data encryption and channel coding are considered together for ensuring secure and robust communication. In order to achieve this purpose, we introduce a new joint scheme, namely ‘Multilevel/Advanced Encryption Standard‐Low Density Parity Check Coded‐Continuous Phase Frequency Shift Keying (ML/AES‐LDPCC‐CPFSK)’. AES algorithm is the most powerful and widely used symmetric key cryptography in providing secure data transmission. LDPC codes have very large Euclidean distance and use iterative decoding algorithms. In this study, we have increased error performance employing multilevel structure to AES and LDPC. In all communications systems, phase discontinuities of modulated signals result in extra bandwidth requirements. CPFSK, which is a special type of continuous phase modulation, is a powerful solution for this problem. In this paper, we simulate error performance of ML/AES‐LDPCC‐CPFSK for regular LDPC codes. Simulation results are drawn for 4CPFSK, 8CPFSK and 16CPFSK over wireless cooperative sensor networks. Using this scheme, we are able to improve bit error performance, channel throughput, security level of communication and reduction in complexity compared with related schemes such as various turbo code structures. Copyright © 2009 John Wiley & Sons, Ltd.     

Design of Quasi‐Cyclic Low‐Density Parity Check Codes with Large Girth

In this paper we propose a graph‐theoretic method based on linear congruence for constructing low‐density parity check (LDPC) codes. In this method, we design a connection graph with three kinds of special paths to ensure that the Tanner graph of the parity check matrix mapped from the connection graph is without short cycles. The new construction method results in a class of (3, ρ)‐regular quasi‐cyclic LDPC codes with a girth of 12. Based on the structure of the parity check matrix, the lower bound on the minimum distance of the codes is found. The simulation studies of several proposed LDPC codes demonstrate powerful bit‐error‐rate performance with iterative decoding in additive white Gaussian noise channels.     

Analysis and performance evaluation of new coding options for space telecommand links ‐ Part I: AWGN channels

We investigate and compare, over the additive white Gaussian noise channel, different options for updating the error correcting code currently used in space mission telecommand links. Besides some more consolidated proposals, using low‐density parity‐check codes, we characterize and assess the performance of alternative schemes, based on parallel turbo codes and soft‐decision decoded Bose‐Chaudhuri‐Hocquenghem (BCH) codes. The analysis considers relevant metrics like the codeword error rate, the frame error rate, and the undetected frame error rate. The considered codes include binary and non‐binary low‐density parity‐check codes, parallel turbo codes and extended BCH codes, with different decoding algorithms. The complexity of the various schemes and possible limits for their application are considered and discussed. Several numerical examples are provided. International Journal of Satellite Communications and Networking. Copyright © 2014 John Wiley & Sons, Ltd.     

比特级码率兼容多元LDPC码打孔算法

多元低密度奇偶校验(Non-binary Low-density Parity-check,NB-LDPC)码在中短码情况下性能优于传统二元LDPC码,更接近香农限。针对多元LDPC码码率兼容(Rate-compatible)的问题,提出了一种基于比特级的新型多元打孔算法。首先采用二进制镜像矩阵概念对多元校验矩阵进行映射处理,再根据变量节点的度分布选择合适的打孔节点,从而实现比特级多元LDPC码码率兼容的打孔方案。仿真结果证明与基于符号级的多元打孔算法相比,所提方案的误码率性能在各个码率分别有0.2~0.4 d B的增益。     

Performance of coded DS‐CDMA system using reduced rank MMSE receiver in Rayleigh fading channels

This paper examines the performance of a reduced rank minimum mean square error (MMSE) receiver‐based direct sequence code division multiple access (DS‐CDMA) system. For such system, when a large processing gain is employed, substantial time is consumed in computing the filter tap weights. Many schemes for reducing the complexity of the MMSE have been proposed in recent years. In this paper, computational complexity reduction of the MMSE receiver is achieved by using the K‐mean classification algorithm. The performance of the uncoded and coded systems are investigated for the full rank MMSE receiver and reduced rank MMSE receiver and results are compared in terms of bit error rate at different loading levels in both AWGN and fading channels. A system with the matched filter (MF) receiver is also presented for the purpose of comparison and an analytical pair‐wise error bound for the coded system is derived. In the adaptive implementation of the receivers, results show that good performance is achieved for the reduced rank receiver when compared to the full rank receiver in both coded and uncoded systems, while in the optimum implementation of the tap weights, the reduced dimension receiver performance experiences degradation when compared to the full rank scheme. Over the band‐limited channels considered, results for the reduced rank receiver also reiterate the fact that higher code rates tend to yield lower BER than that of low rate codes. Copyright © 2006 John Wiley & Sons, Ltd.     

一种非规则广义LDPC码的构造方法

广义低密度奇偶校验(Generalized Low睤ensity Parity睠heck,GLDPC)码把低密度奇偶校验(Low睤ensity Parity睠heck,LDPC)码中的单奇偶校验(Single Parity睠heck,SPC)节点替换为校验能力更强的广义约束(Generalized Constraint,GC)节点,使其在中短码和低码率的条件下具有更低的误码率。传统GLDPC码要求基矩阵的行重等于分量码的码长,这限制了GLDPC码构造的灵活性。另外,相比于传统GLDPC码中GC节点位置的随机选取,GC节点的位置选择在GLDPC码的误码率性能上有一定的优化空间。针对以上两点,提出了一种基于渐进边增长(Progressive Edge-rowth,PEG)算法的非规则GLDPC码构造方法和一种基于Tanner图边数的GC节点位置选择算法。使用PEG算法生成的非规则LDPC码作为本地码,根据本地码的校验节点度使用多种分量码,结合GC节点位置选择算法构造非规则GLDPC码。仿真结果表明,与传统方法构造的GLDPC码相比,基于Tanner图边数的GC节点位置选择算法构造的非规则PEG-LDPC码在误码率和译码复杂度上均得到明显改善。     

A fast low‐density parity‐check code simulator based on compressed parity‐check matrices

Low‐density parity‐check (LDPC) codes are very powerful error‐correction codes with capabilities approaching the Shannon's limits. In evaluating the error performance of an LDPC code, the computer simulation time taken becomes a primary concern when tens of millions of noise‐corrupted codewords are to be decoded, particularly for codes with very long lengths. In this paper, we propose modeling the parity‐check matrix of an LDPC code with compressed parity‐check matrices in the check‐node domain (CND) and in the bit‐node domain (BND), respectively. Based on the compressed parity‐check matrices, we created two message matrices, one in the CND and another in the BND, and two domain conversion matrices, one from CND to BND and another from BND to CND. With the proposed message matrices, the data used in the iterative LDPC decoding algorithm can be closely packed and stored within a small memory size. Consequently, such data can be mostly stored in the cache memory, reducing the need for the central processing unit to access the random access memory and hence improving the simulation time significantly. Furthermore, the messages in one domain can be easily converted to another domain with the use of the conversion matrices, facilitating the central processing unit to access and update the messages. Copyright © 2011 John Wiley & Sons, Ltd.     

Pre‐filtering technique for MAI cancellation in MC‐CDMA systems

Multicarrier code division multiple access (MC‐CDMA), is a promising multiplexing technique for future communication systems. In this study, we employ the well‐known Walsh‐Hadamard spreading codes for synchronous downlink transmission of MC‐CDMA systems. The spreading codes allow that the frequency diversity to be efficiently exploited. However, multipath propagation may cause orthogonality among users is distorted, and this distortion produces multiple access interference (MAI). To eliminate this effect, we propose a pre‐filtering‐based MC‐CDMA system which uses a pre‐filtering technique at the transmitter and an equal gain combining (EGC) scheme at the receivers, respectively. Our proposed pre‐filtering technique transforms the transmitted signals so that the MAI can be eliminated, and the EGC scheme weights the signals received from all subcarriers so that channel distortions can be compensated. Furthermore, the proposed technique can calculate the transmitted power over all subcarriers to satisfy the required quality of service of each user and archive MAI‐free. In this paper, performance in terms of bit error rate is analyzed; in comparison with the EGC, orthogonal restoring combining, and maximal ratio combining schemes at receiver, respectively. Copyright © 2011 John Wiley & Sons, Ltd.     

On Combining Chase‐2 and Sum‐Product Algorithms for LDPC Codes

This letter investigates the combination of the Chase‐2 and sum‐product (SP) algorithms for low‐density parity‐check (LDPC) codes. A simple modification of the tanh rule for check node update is given, which incorporates test error patterns (TEPs) used in the Chase algorithm into SP decoding of LDPC codes. Moreover, a simple yet effective approach is proposed to construct TEPs for dealing with decoding failures with low‐weight syndromes. Simulation results show that the proposed algorithm is effective in improving both the waterfall and error floor performance of LDPC codes.