基于Galois域Reed-Solomon码的数据包层FEC编码软件实现

本文提出一种基于Galois域Reed-Solomon码的数据包层FEC编码软件实现方法。文中利用Galois域的运算封闭性和Reed-Solomon码的变换特笥解决了FEC编码等字长变换问题；通过查找表实现多项式运算，有效降低多项式运算的复杂度，提高了软件FEC编码的效率；文中还介绍了查找表的生成方法。实验表明，基于本文所提出的方法，能够用软件实现高效的数据包层FEC编/解码。     

基于基矩阵排列优化算法的非规则准循环低密度奇偶校验码构造

为了提升非规则准循环低密度奇偶校验(QC-LDPC)码的误码率性能、降低构造算法的复杂度,该文提出一种基于基矩阵排列优化算法的非规则QC-LDPC码构造方法。首先,利用基于外部信息传递(EXIT)图的阈值分析算法得到满足码率和列重要求的非规则QC-LDPC码的最优度分布,然后将围长和短环数量作为新的约束条件对具有最优度分布的码集进行分析,得到具有最优度分布和最少短环数量的最优基矩阵排列结构,最后,根据得到的基矩阵对规则指数矩阵进行置零操作得到目标非规则QC-LDPC码。该构造方法相对于随机构造方法具有更低的实现复杂度,同时可以通过改变算法的参数值实现码长和码率的灵活设计。仿真结果表明,与现有的一些构造方法相比,所提方法构造的非规则QC-LDPC码在加性高斯白噪声(AWGN)信道上具有更好的误码率性能。     

Progressive transmission of images over memoryless noisy channels

An embedded source code allows the decoder to reconstruct the source progressively from the prefixes of a single bit stream. It is desirable to design joint source-channel coding schemes which retain the capability of progressive reconstruction in the presence of channel noise or packet loss. Here, we address the problem of joint source-channel coding of images for progressive transmission over memoryless bit error or packet erasure channels. We develop a framework for encoding based on embedded source codes and embedded error correcting and error detecting channel codes. For a target transmission rate, we provide solutions and an algorithm for the design of optimal unequal error/erasure protection. Three performance measures are considered: the average distortion, the average peak signal-to-noise ratio, and the average useful source coding rate. Under the assumption of rate compatibility of the underlying channel codes, we provide necessary conditions for progressive transmission of joint source-channel codes. We also show that the unequal error/erasure protection policies that maximize the average useful source coding rate allow progressive transmission with optimal unequal protection at a number of intermediate rates     

Performance of zero cross correlation resultant weight spectral amplitude codes in lower Earth orbit‐based optical wireless channel system

A consolidated performance investigation and design of newly constructed zero cross correlation resultant weight (ZCCRW) code is presented without mapping over optical wireless channel (OWC) in lower Earth orbit (LEO). Multiple access interference (MAI) is suppressed by incorporating proposed 1‐D code at 10 Gbps with an algorithm. A further state of the art comparison of diverse optical code division multiple access (OCDMA) codes such as multi diagonal codes and diagonal double weight codes is accomplished with proposed code in terms of root mean square (RMS) jitter, extinction ratio, MAI, quality factor (QF), and bit error rate (BER) at different linewidths, chip sizes, link lengths, and active users. It is perceived that for ZCCRW code, QF obtained is 16.5 for chip size (0.1 ns), and at 4000 km, BER 10^‐9 is achieved using the forward error correction (FEC) technique. OWC system in LEO with lasers in spectral amplitude code (SAC) OCDMA is proposed for the first time as per the author's best knowledge.     

Performance of transmitted reference pulse cluster ultra‐wideband systems with forward error correction

Recently, an improved transmitted reference (TR) signaling scheme, referred to as transmitted reference pulse cluster (TRPC), was proposed for low‐rate ultra‐wideband (UWB) communications. Compared with conventional TR, TRPC has a more compact and uniform spacing for the reference and data pulses and therefore addresses the implementation problems posed by the long delay line requirement, as well as provides better bit error rate (BER) performance. In this paper, a TRPC‐UWB system, which includes practical forward error correction (FEC) coding such as that specified in the IEEE 802.15.4a standard, as well as more powerful convolutional codes, is developed. A performance analysis, which highlights the importance of selecting appropriate FEC codes, is presented. Results show that with a suitable FEC code, the TRPC‐UWB system is a promising candidate for low‐rate wireless personal area networks. Copyright © 2012 John Wiley & Sons, Ltd.     

一种基于分类搜索的Gold误码修正算法

扩频系统侦察对抗时,在低信噪比下估计得到的扩频码存在严重误码,会影响信号解扩解调质量.通过Gold码与其对应m序列优选对的基本特性结合互相关函数特征,提出了一种严格的Gold码分类,并得出一种基于分类搜索的误码修正算法,通过比较待测Gold码与各类样本Gold码互相关函数的三值分布特性,可以快速搜索准确定位到正确的Gold码,实现误码完全修正.当Gold码的误码率不高于11%时,算法可实现对误码的完全修正,能有效降低扩频信号盲处理的信噪比门限.     

Performance Analysis of Wireless Multimedia DS/CDMA Communications with Power Control and Hybrid ARQ

In this paper, we present aperformance analysis of a wireless multimedia direct-sequence code-divisionmultiple-access(DS/CDMA) system based on different error control schemes and an optimal power control algorithm over multipath Rayleigh fading channels.The error control schemes consist of Forward Error Correction (FEC), diversity, and Automatic Repeat reQuest (ARQ). The concatenated codes with a Reed–Solomon outer code andconvolutional inner code are used as FEC. Since a multimedia system is required to support services with different rates and Quality of Services (QoS), different error control schemes are used to satisfy the requirements of different media. In particular, a power control algorithm which can optimize the capacityperformance of the integrated system is presented. Numerical results will show that power optimization can increase the capacity and decrease the total transmission power. By incorporating diversity and hybrid ARQ along with appropriate code ratesin the optimal power controlled system, dramatic increase in system capacitycan also be achieved.     

Rate-compatible punctured convolutional codes (RCPC codes) andtheir applications

The concept of punctured convolutional codes is extended by punctuating a low-rate 1/N code periodically with period P to obtain a family of codes with rate P/(P+l), where l can be varied between 1 and (N-1)P. A rate-compatibility restriction on the puncturing tables ensures that all code bits of high rate codes are used by the lower-rate codes. This allows transmission of incremental redundancy in ARQ/FEC (automatic repeat request/forward error correction) schemes and continuous rate variation to change from low to high error protection within a data frame. Families of RCPC codes with rates between 8/9 and 1/4 are given for memories M from 3 to 6 (8 to 64 trellis states) together with the relevant distance spectra. These codes are almost as good as the best known general convolutional codes of the respective rates. It is shown that the same Viterbi decoder can be used for all RCPC codes of the same M. the application of RCPC codes to hybrid ARQ/FEC schemes is discussed for Gaussian and Rayleigh fading channels using channel-state information to optimise throughput     

Improved FEC Code Based on Concatenated Code for Optical Transmission Systems

The improved three novel schemes of the super forward error correction(super-FEC) concatenated codes are proposed after the development trend of long-haul optical transmission systems and the defects of the existing FEC codes have been analyzed. The performance simulation of the Reed-Solomon(RS)+Bose-Chaudhuri-Hocguenghem(BCH) inner-outer serial concatenated code is implemented and the conceptions of encoding/decoding the parallel-concatenated code are presented. Furthermore, the simulation results for the RS(255,239)+RS(255,239) code and the RS(255,239)+RS(255,223) code show that the two consecutive concatenated codes are a superior coding scheme with such advantages as the better error correction, moderate redundancy and easy realization compared to the classic RS(255,239) code and other codes, and their signal to noise ratio gains are respectively 2～3dB more than that of the RS(255,239)code at the bit error rate of 1×10 -13 . Finally, the frame structure of the novel consecutive concatenated code is arranged to lay a firm foundation in designing its hardware.     

On CS Image Reconstruction Using LDPC Code Over Radio Mobile Channel

In this work, the effect of additive white Gaussian noise and fading channel on the compressed sensing or compressive sampling (CS) image reconstruction process are demonstrated. First, the work suggests encoding of the sensed samples by low density parity check code (LDPC) before transmission. It is well known that longer is the length of the LDPC codes better (lower) is the bit error rate (BER) performance. Thus to improve CS reconstruction a method to construct a larger length but 4 cycle free irregular LDPC code structure is also proposed. The code construction is based on the LDPC code in IEEE WiMAX standard. The proposed CS-LDPC structure is then extended for \(4^n\)-QAM to find an optimal set of thresholds by minimizing BER (equivalently symbol error rate) using differential evolution (DE). The algorithm works on the log likelihood ratio values obtained by LDPC decoding. Extensive simulation results show the efficacy of the use of LDPC codes and the trade-off in code rate and measurements on reconstruction quality. Improved performance with the proposed DE based demodulation is also demonstrated.     

Improving energy efficiency using a link adaptation algorithm dedicated for 100 Gbps wireless communication

This paper presents a link adaptation algorithm dedicated for 100 Gbps wireless transmission. Interleaved Reed-Solomon codes are selected as forward error correction (FEC) algorithms. The redundancy of the codes is selected according to the channel bit error rate (BER). The uncomplicated FEC scheme allows implementing a complete data link layer processor in an FPGA (field programmable gate array). In our case, we use the Virtex7 FPGA to validate the functionality of our implementation. The proposed FPGA-processor achieves 169 Gbps throughput. Moreover, the implementation is synthesized into 40 nm CMOS technology and the described link adaptation algorithm allows reducing consumed energy per bit to values below 1 pJ/bit at BER <1e−4. With higher BER, the energy increases up to ∼13 pJ/bit.     

Space-time block codes based on coordinate symmetric orthogonal designs

Space-time block codes based on coordinate symmetric orthogonal designs are proposed. Compared with space-time block codes from complex orthogonal design when the code rate is the same and the transmission rate is fixed, space-time block codes from coordinate symmetric orthogonal design with more transmit antennas can reduce the bit error rate and symbol error rate. Also these new codes have the same low decoding complexity as space-time block codes from complex orthogonal designs.     

Policy allocation for transmission of embedded bit streams over noisy channels with feedback - [Transactions letters]

An efficient policy allocation algorithm for the transmission of embedded bit streams over noisy channels with feedback is proposed. The transmission is based on the type- II hybrid ARQ/FEC protocol and uses a nested sequence C of channel codes to protect the packets. There are also constraints on the total bit budget and on the allowed number of retransmissions per packet. The allocation algorithm assigns different protection policies, each policy being a subset of C, to different packets to maximize the average number of correctly received source bits. We study the performance and the complexity of the proposed scheme through the transmission of images encoded by JPEG2000 over mobile channels with correlated Rayleigh fading. We demonstrate by simulations that the proposed multiplepolicy scheme provides significant improvements over a purely FEC scheme with no feedback and also the existing fixed-policy schemes. Our results show that feedback is particularly helpful for poor channel conditions and that the proposed scheme is very robust against changes in the channel signal-to-noise ratio (SNR) and the mobile speed.     

Label Stacking in Photonic Packet-Switched Networks With Spectral Amplitude Code Labels

Label stacking is used for hierarchical addressing to reduce the size of lookup tables and to increase the speed of the routing process. We propose an optical label stacking using spectral-amplitude codes (SAC) as labels to accomplish ultrafast packet forwarding. We discuss the advantages of this label architecture compared to other proposals in the literature and present experimental results. We experimentally examine two types of optical packets, one with separable SAC labels and the other one with SAC-encoded payloads. In the first case, the SAC label is a collection of spectral tones modulated at the packet rate (low rate), and the payload is on a separate wavelength modulated at the data rate (fast rate). In the second case, the payload data modulates the collection of wavelengths that constitute the code. We implement a network with two forwarding nodes, and we transmit the packets with two labels in the label stack over 80 km of fiber and measure the bit error rate (BER) after two hops. We achieve error-free transmission (BER<10 ^-9) for the packets with SAC labels and SAC-encoded payload at payload bit rates of 10 and 2.5 Gb/s, respectively. This is the first experimental demonstration of optical label stacking to our knowledge     

纠错编码对OCDMA系统性能的影响

提出了基于RS码(Reed-Solomon Code)的光码分多址(OCDMA)系统的前向纠错编码方案,仿真分析了该方案对一维、二维OCDMA系统的纠错能力.研究结果表明:对于相同码长、相同码重光地址码的OCDMA系统,采用前向纠错(FEC)技术能够有效降低系统误码率,提高系统客量,改善系统性能.对于来自同一码族的OCDMA系统,随码重增加,系统性能改善越好.

Abstract：

A novel forward error-correct (FEC) scheme based on Reed-Solomon code (RS code) is proposed for optical code division multiple access (OCDMA) systems.The error-correcting ability of the presented FEC scheme for one-dimension and two-dimension OCDMA systems are simulated and analyzed.Researched results show that the bit error rate (BER) of OCDMA system using FEC technology is better than that withoutwit using FEC technology at the condition of same code length and code weight.And the capacity is also largely enhanced due to the application of FEC technology.Moreover,for the address code of OCDMA system coming from the same code family,the BER is improved with the increase of the code weight.     

Medical data transmission using the product of TLDPC and BCH error control coding systems with two interleavers

Medical data are very precious since it has the most sensitive data of patient which can save them. If it is handled wrongly or it is manipulated, then it could result in permanent problems or even it can result in fatal. So medical data widely used in a digital format with error detection and correction codes (EDC) in its transmission and storage process. EDC is a method of adding redundant bits to the static message bits to enhance the reliability of binary digital data broadcast while the medical data communication medium adds the errors in the course of transmission. In the proposed method, we use Bose–Chaudhuri–Hocquenghem codes (BCH) as an outline algorithm and trellis Low‐Density Parity Check code (TLDPC) as an inner algorithm along with two interleavers. Product of BCH code and TLDPC code with interleavers can control more errors as compared with its plain code and product of RS‐Hamming code. MATLAB used as a simulation tool. Plain BCH code is simulated first, and then plain LDPC code is simulated for the same information. Finally, the product of BCH and TLDPC with two interleavers is imposed on the same information. The result of our research work shows enhancement in bit error rate (BER) compared to other plain and product codes from 10^?2 to 10^?3. Also, frame error rate (FER) is improved in 0.5 scaling factors when compared with other trellis decoders. Hence, this proposed system can be utilized in an application where less error rate and high accuracy of information transmission between medical data processing systems are required.     

Application layer forward error correction for multicast streaming over LTE networks

The next step beyond third generation mobile networks is the Third Generation Partnership Project standard, named Long Term Evolution. A key feature of Long Term Evolution is the enhancement of multimedia broadcast and multicast services (MBMS), where the same content is transmitted to multiple users located in a specific service area. To support efficient download and streaming delivery, the Third Generation Partnership Project included an application layer forward error correction (AL‐FEC) technique based on the systematic fountain Raptor code, in the MBMS standard. To achieve protection against packet losses, Raptor codes introduce redundant packets to the transmission, that is, the forward error correction overhead. In this work, we investigate the application of AL‐FEC over MBMS streaming services. We consider the benefits of AL‐FEC for a continuous multimedia stream transmission to multiple users and we examine how the amount of forward error correction redundancy can be adjusted under different packet loss conditions. For this purpose, we present a variety of realistic simulation scenarios for the application of AL‐FEC and furthermore we provide an in‐depth analysis of Raptor codes performance introducing valuable suggestions to achieve efficient use of Raptor codes. Copyright © 2012 John Wiley & Sons, Ltd.     

中短码长的率匹配多进制LDPC码研究设计

该课题研究构造了纠错能力强、编译码复杂度低的中短码长的率匹配多进制LDPC码。提出了一种校验位高效编码删余算法,以得到高性能的多进制RC-LDPC码。该删余算法以设计的高性能中短码长、中等码率(1/2码率)的多进制LDPC母码为基础,采用高效的结构化编码删余算法,实现比较宽的速率范围(例如1/10到9/10)内设计高性能的纠错码。仿真结果表明,此算法性能优于传统的随机删余和节点分组与排序删余算法。     

A new probability decoding scheme based on genetic algorithm for FEC codes in optical transmission systems

Based on the genetic algorithm(GA),a new genetic probability decoding(GPD) scheme for forward error correction(FEC) codes in optical transmission systems is proposed.The GPD scheme can further offset the quantification error of the hard decision by making use of the channel interference probability and statistics information to restore the maximal likelihood transmission code word.The theoretical performance analysis and the simulation result show that the proposed GPD scheme has the advantages of lower decoding complexity,faster decoding speed and better decoding correction-error performance.Therefore,the proposed GPD algorithm is a better practical decoding algorithm.     

Estimation of the error performance objectives for satellite communication systems

We consider the physical layer error performance parameters and design criteria for digital satellite systems established by ITU‐R Recommendation S.1062, where the performance objectives are given in terms of the bit error rate (BER) divided by the average number of errors within a cluster. It is well known that errors on satellite links employing forward error correction (FEC) schemes tend to occur in clusters. The resulting block error rate is the same as if it was caused by randomly occurring bit errors with an error‐event ratio of BER/α, where α is the average number of errors within a cluster. The factor, α, accounts for the burstiness of the errors and also represents the ratio between the BER and the error‐event ratio. This paper proposes theoretical methods to estimate the factor, α. Using the weight distributions of the FEC codes, we derive a set of expressions for the factor, α, as well as their compact lower bounds. We present lower bounds for various FEC schemes including binary BCH codes, block turbo codes, convolutional codes, and turbo codes. The simulation results show that the proposed lower bounds are good estimates in the high signal‐to‐noise ratio region. Copyright © 2008 John Wiley & Sons, Ltd.