ARQ‐based updatable relay selection for distributed EO‐STBC cooperative system

In this work, we investigate the closed loop extended orthogonal‐space time block codes in decode‐ and‐forward cooperative networks and propose an updatable automatic repeat request protocol with relay selection. In the system, the relays decoding correctly are incorporated into a relay set, the optimal relays within this relay set can be selected based on the channel information, and the extended orthogonal‐space time block codes scheme is employed with the help of the feedback in automatic repeat request message. With the consideration of the relay selection, the system performance can be improved. Simulation and analysis results prove the efficiency of the proposed scheme, which achieves better performance than conventional relay schemes. Copyright © 2012 John Wiley & Sons, Ltd.     

Hybrid Iterative Decoding for Low-Density Parity-Check Codes Based on Finite Geometries

In this letter, a two-stage hybrid iterative decoding algorithm which combines two iterative decoding algorithms is proposed to reduce the computational complexity of finite geometry low-density parity-check (FG-LDPC) codes. We introduce a fast weighted bit-flipping (WBF) decoding algorithm for the first stage decoding. If the first stage decoding fails, the decoding is continued by the powerful belief propagation (BP) algorithm. The proposed hybrid decoding algorithm greatly reduces the computational complexity while maintains the same performance compared to that of using the BP algorithm only.     

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.     

有限平面LDPC码的停止集

有限平面LDPC码是一类重要的有结构的LDPC码,在利用和积算法(SPA)等迭代译码方法进行译码时表现出卓越的纠错性能。众所周知,次优的迭代译码不是最大似然译码,因而如何对迭代译码的性能进行理论分析一直是LDPC码的核心问题之一。近几年来,Tanner图上的停止集(stopping set)和停止距离(stopping distance)由于其在迭代译码性能分析中的重要作用而引起人们的重视。该文通过分析有限平面LDPC码的停止集和停止距离,从理论上证明了有限平面LDPC码的最小停止集一定是最小重量码字的支撑,从而对有限平面LDPC码在迭代译码下的良好性能给出了理论解释。     

Hybrid ARQ scheme using interleaved Reed-Solomon codes in apower-controlled DS-CDMA cellular system

A new hybrid automatic repeat request (ARQ) scheme is proposed for data transmission in a power-controlled direct sequence (DS) code division multiple access (CDMA) system cellular system. The data frame is composed of interleaved Reed-Solomon codes. The depth of interleaving is determined by a power-control interval. After decoding each codeword with algebraic decoding, the post-decoding processor decides whether to accept the codeword or to discard it by using channel state information from the power-control processor. The proposed hybrid ARQ scheme significantly reduces the probability of undetected error among accepted codewords without significantly reducing the throughput     

An Efficient Stopping Criterion for Turbo Product Codes

In this letter, a stopping criterion using the error- detecting capability of linear block codes is proposed for the decoding of turbo product codes. The iterative decoding is stopped when the outputs from the Chase decoder are valid codewords for all rows and columns simultaneously. Simulation shows that the proposed method can reduce about one and half iterations compared with an existing stopping method, without noticeable BER performance loss. Some modification has also been discussed which may further reduce the decoding complexity.     

一种简化的LDPC码BP译码算法的研究

低密度奇偶校验码(LDPC码)是一种逼近香农限的线性分组码,译码的复杂度较低;在LDPC码译码算法中性能较好的是置信传播译码(BP)算法,他能够在迭代译码过程中确定码字是否已译出,但是复杂度高,运算量大。采用一种改进的BP译码算法,在迭代译码过程中对校验节点的更新信息进行曲线拟合,以减小译码运算量,有利于硬件的并行实现,减少译码延时。仿真结果表明,改进的BP算法译码性能和原来的BP算法接近,而且复杂度较低。     

Link optimization for energy‐constrained wireless networks with packet retransmissions

With the objective to minimize the energy consumption for packet based communications in energy‐constrained wireless networks, this paper establishes a theoretical model for the joint optimization of the parameters at the physical layer and data link layer. Multilevel quadrature amplitude modulation (MQAM) and automatic repeat request (ARQ) techniques are considered in the system model. The optimization problem is formulated into a three dimensional nonlinear integer programming (NIP) problem with the modulation order, packet size, and retransmission limit as variables. For the retransmission limit, a simple search method is applied to degenerate the three dimensional problem into a two dimensional NIP problem, for which two optimization algorithms are proposed. One is the successive quadratic programming (SQP) algorithm, combining with the continuous relaxation based branch‐and‐bound method, which can obtain the global optimal solution since the continuous relaxation problem is proved to be hidden convex. The other is a low‐complexity sub‐optimal iterative algorithm, combining with the nearest‐neighboring method, which can be implemented with a polynomial complexity. Numerical examples are given to illustrate the optimization solution, which suggests that the joint optimization of the physical/data link layer parameters contributes noticeably to the energy saving in energy‐constrained wireless networks. Copyright © 2010 John Wiley & Sons, Ltd.     

LDPC码加权比特翻转译码算法的低复杂度提前停止准则

近年来,针对LDPC码置信传播(BP)译码算法的提前停止准则的研究已经有了很多,但设计适合加权比特翻转(WBF)译码算法的提前停止准则却研究甚少。依据对WBF算法的全新理解方式,该文提出一种实现简单、适用性强的WBF算法提前停止准则,它能在译码的初始阶段检测绝大多数不可纠错的帧。仿真结果表明,基于提前停止准则的WBF算法在性能损失可以忽略的条件下,极大地降低迭代次数,在实现复杂度和性能之间达到了很好的折中。     

H-ARQ信道上高性能全分集LDPC码的构造与性能分析

为了提高混合自动重传请求(H-ARQ)系统的通信性能,研究了H-ARQ块衰落信道上全分集低密度奇偶校验(LDPC)码的构造与性能.首先分析了H-ARQ块衰落信道的中断概率及其固有分集,然后构造了在H-ARQ块衰落信道上能取得全分集的LDPC码,新构造的码字采用根校验节点把每次传输联系起来,从而获得全分集.在此基础上,分析了全分集LDPC码的结构,提出了通过提高全分集校验比特的比例,改善全分集LDPC码在H-ARQ信道上编码增益的方法.仿真结果表明,所提算法在H-ARQ信道上不仅能取得全分集,而且具有较高的编码增益     

Viterbi decoding algorithm for convolutional codes with repeat request

Using the Viterbi decoding algorithm with repeat request for convolutional codes is proposed, and the resulting performance is analyzed by random coding and generating function arguments and by simulation. It is shown that the reliability function of the proposed decoding algorithm is asymptotically twice that of the Viterbi decoding algorithm without repeat request, and that in certain practical situations the proposed algorithm can save about 50 percent in constraint length over the ordinary Viterbi algorithm for a given performance.     

Results on the Improved Decoding Algorithm for Low-Density Parity-Check Codes Over the Binary Erasure Channel

In this correspondence, we first investigate some analytical aspects of the recently proposed improved decoding algorithm for low-density parity-check (LDPC) codes over the binary erasure channel (BEC). We derive a necessary and sufficient condition for the improved decoding algorithm to successfully complete decoding when the decoder is initialized to guess a predetermined number of guesses after the standard message-passing terminates at a stopping set. Furthermore, we present improved bounds on the number of bits to be guessed for successful completion of the decoding process when a stopping set is encountered. Under suitable conditions, we derive a lower bound on the number of iterations to be performed for complete decoding of the stopping set. We then present a superior, novel improved decoding algorithm for LDPC codes over the binary erasure channel (BEC). The proposed algorithm combines the observation that a considerable fraction of unsatisfied check nodes in the neighborhood of a stopping set are of degree two, and the concept of guessing bits to perform simple and intuitive graph-theoretic manipulations on the Tanner graph. The proposed decoding algorithm has a complexity similar to previous improved decoding algorithms. Finally, we present simulation results of short-length codes over BEC that demonstrate the superiority of our algorithm over previous improved decoding algorithms for a wide range of bit error rates     

Gaussian integers and interleaved rank codes for space–time block codes

This paper presents the design of space–time block codes (STBCs) over maximum rank distance (MRD) codes, energy‐efficient STBCs, STBCs using interleaved‐MRD codes, the use of Gaussian integers for STBCs modulation, and Gabidulin's decoding algorithm for decoding STBCs. The design fundamentals of STBCs using MRD codes are firstly put forward for different number of transmit antennas. Extension finite fields (Galois fields) are used to design these linear block codes. Afterward, a comparative study of MRD‐based STBCs with corresponding orthogonal and quasi‐orthogonal codes is also included in the paper. The simulation results show that rank codes, for any number of transmit antennas, exhibit diversity gain at full rate contrary to orthogonal codes, which give diversity gain at full rate only for two transmit antennas case. Secondly, an energy‐efficient MRD‐STBC is proposed, which outperforms orthogonal STBC at least for 2 × 1 antenna system. Thirdly, interleaved‐MRD codes are used to construct higher‐order transmit antenna systems. Using interleaved‐MRD codes further reduces the complexity (compared with normal MRD codes) of the decoding algorithm. Fourthly, the use of Gaussian integers is utilized in mapping MRD‐based STBCs to complex constellations. Furthermore, it is described how an efficient and computationally less complex Gabidulin's decoding algorithm can be exploited for decoding complex MRD‐STBCs. The decoding results have been compared against hard‐decision maximum likelihood decoding. Under this decoding scheme, MRD‐STBCs have been shown to be potential candidate for higher transmit antenna systems as the decoding complexity of Gabidulin's algorithm is far less, and its performance for decoding MRD‐STBCs is somewhat reasonable. Copyright © 2015 John Wiley & Sons, Ltd.     

基于原型图的低码率LDPC码最小和译码算法改进方案

低密度奇偶校验(LDPC)码的译码硬件实现方案大多采用计算复杂度较低的修正最小和(NMS)算法,然而对于低码率LDPC码,由于校验节点度数低,NMS算法的修正误差较大,导致其译码性能和标准的置信传播(BP)算法相比有较大差异。该文针对基于原图构造的一类低码率LDPC码,提出了在NMS迭代译码中结合震荡抵消(OSC)处理和多系数(MF)修正技术的方案。结合低码率原型图LDPC码行重分布差异较大的特点,MF修正算法可以有效地减少计算误差,从而改善译码性能。另外低码率原型图LDPC码的收敛较慢,而OSC处理则可以较好地抑制正反馈信息,进一步提高NMS算法的性能增益。仿真结果表明,对于此类低码率LDPC码, MF-OSC-NMS算法可以达到接近BP算法的性能。OSC处理和MF修正技术硬件实现简单,与NMS算法相比几乎没有增加计算复杂度,因此MF-OSC-NMS算法是译码算法复杂度和性能之间一个较好的折中处理方案。     

Partial iterative decoding for binary turbo codes via cross-entropy based bit selection

Near-capacity performance of turbo codes is generally achieved with a large number of decoding iterations. Various iteration stopping rules introduced in the literature often induce performance loss. This paper proposes a novel partial decoding iteration scheme using a bit-level convergence test. We first establish decoding optimality of windowed partial iteration for non-converged bits given that convergence has been achieved on window boundaries. We next present two criteria for testing bit convergence based on cross-entropy, and propose a windowed partial iteration algorithm. The overall complexity and memory requirements of the new algorithm are evaluated and compared with known algorithms. Simulations reveal that the proposed scheme suffers essentially no performance loss compared to full iterations, while reducing the decoding complexity. We also briefly discuss possible extensions of the proposed scheme to general iterative receivers.     

An adaptive error control system using hybrid ARQ schemes

A simple and efficient system utilizing the class of Hamming codes in a cascaded manner is proposed to provide high throughput over a wide range of channel bit error probability. Comparisons with other adaptive schemes indicate that the proposed system is superior from the point of view of throughput, while still providing the same order of reliability as an ARQ (automatic repeat request) system. The main feature of this system is that the receiver uses the same decoder for decoding the received information after each transmission while the error-correcting capability of the code increases. As a result, the system is kept to the minimum complexity and the system performance is improved     

浅海水声信道中原模图LDPC码的设计及性能分析

原模图低密度奇偶校验码相较于传统LDPC码,具有结构简单、迭代译码门限低、易于扩展及线性编译码复杂度等优点。针对强多途、长时延、窄带宽的浅海水声信道,该文研究了PG-LDPC码的设计及性能特征,提出一种码型设计方案,并采用基于原模图度分布的外部信息转移图算法,对所设计PG-LDPC码的纠错性能进行分析及预测。仿真与实验结果表明,与(3,6)随机规则LDPC码相比,所提的PG-LDPC码在低、高信噪比区域均有良好的纠错性能。     

Iterative reliability-based decoding of low-density parity checkcodes

In this paper, reliability based decoding is combined with belief propagation (BP) decoding for low-density parity check (LDPC) codes. At each iteration, the soft output values delivered by the BP algorithm are used as reliability values to perform reduced complexity soft decision decoding of the code considered. This approach allows to bridge the error performance gap between belief propagation decoding which remains suboptimum, and maximum likelihood decoding which is too complex to be implemented for the codes considered. Trade-offs between decoding complexity and error performance are also investigated. In particular, a stopping criterion which reduces the average number of iterations at the expense of very little performance degradation is proposed for this combined decoding approach. Simulation results for several Gallager (1963, 1968) LDPC codes and different set cyclic codes of hundreds of information bits are given and elaborated     

基于停止集的喷泉编码有限长性能估计

喷泉编码是一类基于删除信道、面向数据分组的前向纠错编码技术。该文分析了停止集的尺度分布对固定码率喷泉编码解码性能的影响,提出了一种估算低误码条件下喷泉编码有限长性能的方法以及一种低复杂度的停止集尺度分布搜索算法。比较结果表明,该文给出的喷泉码解码性能上下界与实际仿真结果非常接近。     

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.