SCLDGM coded modulation for MIMO systems with spatial multiplexing and space‐time block codes

We analyze Multiple‐Input Multiple‐Output (MIMO) coded modulation systems where either Bit‐Interleaved Coded Modulation (BICM) with spatial multiplexing or concatenation of channel coding and Space‐Time Block Codes (STBCs) is used at transmission, assuming iterative Turbo‐like decoding at reception. We optimize Serially‐Concatenated Low‐Density Generator Matrix (SCLDGM) codes (a subclass of LDPC codes) for each system configuration, with the goal of assessing its ability to approach the capacity limits in either ergodic or quasi‐static channels. Our focus is on three relevant STBCs: the Orthogonal Space‐Time Block Codes (OSTBCs) for two transmit antennas (i.e., the Alamouti code), which enables optimum detection with low complexity; the Golden code, which provides a capacity increase with respect to the input constellation; and Linear Dispersion (LD) codes, which enable practical detection in asymmetrical antenna configurations (i.e., more transmit than receive antennas) for cases in which optimum detection is infeasible. We conclude that BICM without concatenation with STBCs is in general the best option, except for Alamouti‐coded 2×1 and Golden‐coded 2×2 MIMO systems. Copyright © 2009 John Wiley & Sons, Ltd.     

MB iterative decoding algorithm on systematic LDGM codes: Performance evaluation

We investigate the performance of regular systematic low-density generator matrix (LDGM) codes under the majority rule based (MB) iterative decoding algorithm. We derive a recursive form which can be used to extract the error performance of the code. Based on the recursive expression, we derive a tight non-recursive lower bound. These results can serve as efficient tools to evaluate the performance of the code for different degrees.     

一种基于LDGM码的有损信息压缩方法

利用多边缘二分图代替传统的三分图,实现对低密度生成矩阵码（Low density generator matrix codes,LDGM码）的描述。基于多边缘二分图,提出多边缘置信度传播算法和滤波衰减消解方法,实现基于LDGM码的二进制信息压缩编码。仿真结果表明,该算法具有近香农限的压缩性能,并具有较低的复杂度。     

Lossy Source Compression of Non‐Uniform Binary Source via Reinforced Belief Propagation over GQ‐LDGM Codes

In this letter, we consider the lossy coding of a non‐uniform binary source based on GF(q)‐quantized low‐density generator matrix (LDGM) codes with check degree d_c=2. By quantizing the GF(q) LDGM codeword, a non‐uniform binary codeword can be obtained, which is suitable for direct quantization of the non‐uniform binary source. Encoding is performed by reinforced belief propagation, a variant of belief propagation. Simulation results show that the performance of our method is quite close to the theoretic rate‐distortion bounds. For example, when the GF(16)‐LDGM code with a rate of 0.4 and block‐length of 1,500 is used to compress the non‐uniform binary source with probability of 1 being 0.23, the distortion is 0.091, which is very close to the optimal theoretical value of 0.074.     

A low‐complexity single‐carrier frequency‐division multiple access transmitter

A framework for a computationally efficient single‐carrier frequency‐division multiple access (SC‐FDMA) transmitter is proposed in this paper. Compared with a wide system bandwidth, the uplink allocation for each user is supposed to be relatively small because of multiple user access, which makes each user's signal vector to be sparse. When the localized subcarrier allocation is used for SC‐FDMA, the inverse fast fourier transform can take advantage of the sparse user input vector to reduce its complexity. The analytical and simulation results show that the proposed framework can provide a significant complexity reduction compared with the conventional SC‐FDMA transmitter. Copyright © 2011 John Wiley & Sons, Ltd.     

Low rate convolutional and turbo codes based on non‐linear cyclic codes

Low rate convolutional and turbo codes that output non‐linear cyclic (NLC) codewords of length n = 2^m, m being a positive integer, are described. These codes have a very low coding rate, which makes them especially suitable for spread spectrum systems where they can be used for simultaneously achieving error correction and bandwidth expansion. Due to the cyclic properties and codeword length of the component codes, branch metrics can be efficiently computed using the fast Fourier transform (FFT), enabling simple implementation of the encoder and decoder. Among the possible NLC base codes, special attention is given to the Tomlinson, Cercas, Hughes (TCH) codes family due to their good autocorrelation properties. It is shown by simulation that the turbo codes schemes studied usually perform better than traditional turbo codes (in this paper the universal mobile telecommunications system (UMTS), rate 1/3 turbo code was used as a reference). This improvement is accomplished at the cost of bandwidth expansion. One of the advantages of the presented solutions over other low rate codes is their ability to improve the synchronization process at the receiver due to the good autocorrelation properties of the available NLC codes (especially TCH codes). A comparison of performance between the UMTS uplink connection and an equivalent system using the proposed codes for a multiuser scenario in a multipath fading channel is presented showing the possibility of capacity increase when using these codes. Copyright © 2006 John Wiley & Sons, Ltd.     

Design and comparison of turbo codes under frame‐length and code‐rate constraints

When the performances of error‐correcting codes for space communications are investigated, with the aim to translate them into practical recommendations, comparison among different schemes is usually a very difficult task. As a matter of fact, these comparisons rarely yield general conclusions. On the other hand, most practical space applications impose strong constraints on the code parameters, which have important effects on code selection. In this paper, we show a methodology and several examples of design and comparison, derived under fixed constraints imposed by the system application on the frame‐length and the code‐rate. CCSDS Earth observation missions requiring both large coding gains and high spectral efficiency are considered as a case study. Though referred to this specific space mission framework, the presented study is quite general and applies to many other digital communication systems; e.g. for wireless or wired applications where similar constraints exist but are often not taken in due consideration by the designer of the error‐correcting schemes. Copyright © 2006 John Wiley & Sons, Ltd.     

Non‐binary protograph low‐density parity‐check codes for space communications

Protograph‐based non‐binary low‐density parity‐check (LDPC) codes with ultra‐sparse parity‐check matrices are compared with binary LDPC and turbo codes (TCs) from space communication standards. It is shown that larger coding gains are achieved, outperforming the binary competitors by more than 0.3 dB on the additive white Gaussian noise channel (AWGN). In the short block length regime, the designed codes gain more than 1 dB with respect to the binary protograph LDPC codes recently proposed for the next generation up‐link standard of the Consultative Committee for Space Data Systems. Copyright © 2012 John Wiley & Sons, Ltd.     

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 new decoder of synchronous optical code division multiple access systems using segmented correlation

A new segmented correlating decoder of synchronous optical CDMA using modified prime sequence codes is proposed. The performance of the proposed system is analyzed under the assumption of Poisson shot noise model for the receiver photodetector. The decoder technique is shown to be more effective to improve the bit error probability performance than the method using an optical hard-limiter.     

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.     

二维光正交码OCDMA系统编解码器的设计

文章提出了二维光正交码的概念并对其性有进行了分析，重点介绍了二维光正交码光纤延迟线编解码器的设计，并且给出了二维光正交码光纤光栅编码原理。     

Bit error rate performance of Haar wavelet based scale‐code division multiple access (HW/S‐CDMA) over the asynchronous AWGN channel

In this paper, we study a recently proposed multirate system, called wavelet based scale‐code division multiple access (W/S‐CDMA). W/S‐CDMA depends on the code, time and scale orthogonality introduced by pseudo‐noise (PN) sequences, and wavelets. In this system, the channel is partitioned into different scales, and each scale into time slots. In addition, the PN sequences are used in each scale to identify multiple users. In W/S‐CDMA, each user is assigned a specific scale and PN sequence, and transmits its successive information symbols with its PN sequence and the wavelets in that scale. More symbols are transmitted in finer scales. We analyse the bit error rate performance of Haar wavelet based S‐CDMA (HW/S‐CDMA) over an asynchronous additive white Gaussian noise (AWGN) channel by using a conventional detector for deterministic PN sequences. The performance of the system is compared to that of an equivalent multirate CDMA (MR‐CDMA) system for Gold and Kasami PN sequences. Results show that HW/S‐CDMA outperforms MR‐CDMA. In addition, because of its suitable format HW/S‐CDMA is also capable of employing the optimal PN sequence families with limited number of sequences such as Kasami, Bent, etc. repeatedly in different scales. Copyright © 2006 John Wiley & Sons, Ltd.     

Quasi-cyclic LDPC codes using overlapping matrices and their layered decoders

Quasi-cyclic (QC) low-density parity-check (LDPC) codes have the parity-check matrices consisting of circulant matrices. Since QC LDPC codes whose parity-check matrices consist of only circulant permutation matrices are difficult to support layered decoding and, at the same time, have a good degree distribution with respect to error correcting performance, adopting multi-weight circulant matrices to parity-check matrices is useful but it has not been much researched. In this paper, we propose a new code structure for QC LDPC codes with multi-weight circulant matrices by introducing overlapping matrices. This structure enables a system to operate on dual mode in an efficient manner, that is, a standard QC LDPC code is used when the channel is relatively good and an enhanced QC LDPC code adopting an overlapping matrix is used otherwise. We also propose a new dual mode parallel decoder which supports the layered decoding both for the standard QC LDPC codes and the enhanced QC LDPC codes. Simulation results show that QC LDPC codes with the proposed structure have considerably improved error correcting performance and decoding throughput.     

Asymptotic performance comparison of concatenated (turbo) codes over GF(4)

In this paper, we investigate and compare the asymptotic performance of concatenated convolutional coding schemes over GF(4) over additive white Gaussian noise (AWGN) channels. Both parallel concatenated codes (PCC) and serial concatenated codes (SCC) are considered. We construct such codes using optimal non‐binary convolutional codes where optimality is in the sense of achieving the largest minimum distance for a fixed number of encoder states. Code rates of the form k₀/(k₀ + 1) for k₀=1, 8, and 64 are considered, which suite a wide spectrum of communications applications. For all of these code rates, we find the minimum distance and the corresponding multiplicity for both concatenated code systems. This is accomplished by feeding the encoder with all possible weight‐two and weight‐three input information patterns and monitoring, at the output of the encoder, the weight of the corresponding codewords and their multiplicity. Our analytical results indicate that the SCC codes considerably outperform their counterpart PCC codes at a much lower complexity. Inspired by the superiority of SCC codes, we also discuss a mathematical approach for analysing such codes, leading to a more comprehensive analysis and allowing for further improvement in performance by giving insights on designing a proper interleaver that is capable of eliminating the dominant error patterns. Copyright © 2004 John Wiley & Sons, Ltd.     

Blind array channel division multiple access (AChDMA) for mobilecommunications

The paper introduces array channel division multiple access (AChDMA), which is a new blind algorithm for advanced SDMA in mobile communications systems. As an SDMA technique, AChDMA increases the system capacity by improving its time and frequency reuse. Being a blind algorithm, it requires no training sequences, previously known directions of arrival, or user codes, AChDMA separates the moving sources by tracking their multipath configuration and resolving their distinct generalized steering vectors. It maximizes a finite mixture log-likelihood function, combining an efficient initialization procedure with an EM-based algorithm that provides fast convergence to the global maximum. AChDMA reconstructs the mobile data sequences using only internal variables of the EM algorithm. These characteristics and its parallel structure make AChDMA suitable for real-time mobile communications. We test AChDMA with synthetic data in a number of different scenarios, illustrating the ability of the blind algorithm to separate and track in time the moving sources, and showing its good performance in a variety of practical situations     

Co-channel interference in cellular radio systems using frequency hopping code division multiple access (FH-CDMA)

The expected interference power in a digital cellular radio system using frequency hopping code division multiple access is investigated. The up-link only is considered. Using both analytical and numerical methods, a probability density function for this power is derived. This function is used to predict the hop erasure probability of a system, as a function of the tolerable signal to interference ratio and of the system load.Mr. Al-Etaibi is sponsored by Saudi Telecom     

Concatenation of polar codes with three‐dimensional parity check (3D‐PC) codes to improve error performance over fading channels

In this paper, we concatenated of three‐dimensional parity check (3D‐PC) block and polar codes for improving error correction performance and bit error rate (BER). Three different sizes of 3D parity check blocks (4 × 4 × 4, 8 × 8 × 8, and 16 × 16 × 16) are used for polar code concatenation. The 4 × 4 × 4 block returns the best performance, but higher complexity of decoder is needed unlikely. The 8 × 8 × 8 has returned acceptable complexity and good performacne. The complexity of decoder is less in the case of 16 × 16 × 16 with slight performance. The performance of the 3D‐PC is reduced when the codewords length is increased. The experiment considered the presence of additive white Gaussian noise (AWGN) with Rayleigh and Rician fading environments. 3D‐PC and polar code concatenation is more precise with codewords of short length, whereas there is insufficient concatenation accuracy with longer codewords. The outcomes of this study contain comparison between AWGN, Rayleigh, and Rician environments. The AWGN is noticed to have a lesser negative impact on the performance of code. Furthermore, increasing the code length may slightly fill the gap of performance between the concatenated and none concatenated polar codes due to the impact of code length on parity check code performance. Simulation results showed the coding performance in case of the polar code with concatenation and without concatenation for different code lengths. Generally, the 3D‐PC polar code concatenation is drawn the optimal result in AWGN environments.     

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.     

Rate adaptive resource allocation in orthogonal frequency division multiple access system using multi‐objective immune algorithm

Rate adaptive downlink resource allocation in orthogonal frequency division multiple access system is a constraint optimization problem, which is to maximize the minimum data rate of the user subject to constraint that total power cannot exceed a given value. How to handle the constraint is a key issue for constrained optimization problem. Different with the available schemes on constraint handling, the proposed algorithm converts the constraint into an objective. Then, the resource allocation is combined into a multi‐objective optimization problem. An improved multi‐objective optimization algorithm based on artificial immune system is proposed to solve it. The simulation results show that, compared with previous schemes, the proposed algorithm performs remarkable improvement in sum capacity. Copyright © 2013 John Wiley & Sons, Ltd.