Analytical Settling Noise Models of Single-Loop Sigma–Delta ADCs

Switched-capacitor integrators are the basic building components for sigma-delta (SigmaDelta) modulators, and their incomplete charge transfer (settling problem) constitutes one of the dominant error sources in SigmaDelta modulators. Due to the complexity of the settling problem, analytic models for related noises are nonexistent. In this brief, closed forms of settling error models are obtained and represented as functions of SigmaDelta modulator system parameters. Both behavioral simulations and transistor-level circuit simulations are employed to verify these analytical models, and the results show that our analytical models are sufficiently accurate.     

Efficient algorithms for burst error recovery using FFT and othertransform kernels

We show that the problem of signal reconstruction from missing samples can be handled by using reconstruction algorithms similar to the Reed-Solomon (RS) decoding techniques. Usually, the RS algorithm is used for error detection and correction of samples in finite fields. For the case of missing samples of a speech signal, we work with samples in the field of real or complex numbers, and we can use FFT or some new transforms in the reconstruction algorithm. DSP implementation and simulation results show that the proposed methods are better than the ones previously published in terms of the quality of recovered speech signal for a given complexity. The burst error recovery method using the FFT kernel is sensitive to quantization and additive noise like the other techniques. However, other proposed transform kernels are very robust in correcting bursts of errors with the presence of quantization and additive noise     

On decoding unequal error protection product codes

The decoding of unequal error protection product codes, which are a combination of linear unequal error protection (UEP) codes and product codes, is addressed. A nonconstructive proof of the existence of a good error-erasure-decoding algorithm is presented; however, obtaining the decoding procedure is still an open research problem. A particular subclass of UEP product codes is considered, including a decoding algorithm that is an extension of the Blokh-Zyablov decoding algorithm for product codes. For this particular subclass the decoding problem is solved     

基于分布式奇偶校验码的低复杂度极化码SCLF译码算法

针对极化码串行抵消列表比特翻转(Successive Cancellation List Bit-Flip, SCLF)译码算法复杂度较高的问题,提出一种基于分布式奇偶校验码的低复杂度极化码SCLF译码(SCLF Decoding Algorithm for Low-Complexity Polar Codes Based on Distributed Parity Check Codes, DPC-SCLF)算法。与仅采用循环冗余校验(Cyclic Redundancy Check, CRC)码校验的SCLF译码算法不同,该算法首先利用极化信道偏序关系构造关键集,然后采用分布式奇偶校验(Parity Check, PC)码与CRC码结合的方式对错误比特进行检验、识别和翻转,提高了翻转精度,减少了重译码次数。此外,在译码时利用路径剪枝操作,提高了正确路径的竞争力,改善了误码性能,且利用提前终止译码进程操作,减少了译码比特数。仿真结果表明,与D-Post-SCLF译码算法和RCS-SCLF译码算法相比,所提出算法具有更低的译码复杂度且在中高信噪比下具有更好的误码性能。     

基于红外编码结构光的深度测量方法

视觉深度测量是计算机视觉领域的重要问题。提出了一种基于红外编码结构光的深度测量方法。首先,设计一种新的网格图案并提出一种顺序编解码算法,准确计算参考图像与目标图像之间对应点的偏移;然后,提出一种成像系统参数线性拟合算法,建立目标深度与光斑像素偏移之间的线性关系,并修正镜头畸变;最后,基于线性关系实现深度测量,并基于Delaunay三角剖分算法实现三维重建。在实验过程中,通过多组数据进行误差评估与校正,提高测量精度,降低系统误差。多组实验数据表明,该深度测量方法准确性较高,并具有较好的实用性与鲁棒性。     

Spectral Shaping of Dithered Quantization Errors in Sigma–Delta Modulators

A well-known problem in sigma-delta (SigmaDelta) modulators is limit cycle oscillations, which can cause unwanted tones of significant power to appear in the quantization error. This problem becomes more severe as the amplitude of an input signal is small. The unwanted tones can be eliminated from the quantization error by employing a properly chosen random sequence to break up the limit cycle oscillations. However, the injected random sequence inevitably raises the noise floor in the signal band of interest, and thus degrades the signal-to-quantization-noise ratio (SQNR). This paper first presents a spectrally shaped noise generator and the theoretical basis for the behavior of the proposed generator is explained. Then we introduce a class of pseudorandom noise sequences with least significant bit dithering. The effectiveness of this class of dither sequences is demonstrated through a SigmaDelta modulator. Simulation results show that the proposed dither sequences improve the SQNR by more than 10 dB compared to the case wherein a white pseudorandom binary sequence is applied. Meanwhile, it is shown that the proposed sequences successfully break up the limit cycle oscillations for small input signals     

Error-propagation properties of uniform codes

The problem of error propagation in uniform codes is investigated using the concept of parity-parallelogram submatrices and the threshold-decoding algorithm. A set of optimum orthogonalization rules is presented and it is shown that if these rules are incorporated into the decoder, then sufficient conditions can be found for the return of the decoder to correct operation following a decoding error. These conditions are considerably less stringent than the requirement that the channel be completely free of errors following a decoding error. However, this is not the case if the prescribed orthogonalization rules are not followed, as is demonstrated with a simple example. It is also shown that the syndrome memory required with Massey's orthogonalization procedure for definite decoding of uniform codes is the lowest possible. The results of simulation of the ratefrac{1}{4}andfrac{1}{8}uniform codes are presented, and these codes are seen to make fewer decoding errors with feedback decoding than with definite decoding. Comparison of the performance of an ordinary feedback decoder with a genie-aided feedback decoder, which never propagates errors, indicates that error propagation with uniform codes is a minor problem if the optimum orthogonalization rules are used, but that the situation is somewhat worse with nonoptimum orthogonalization.     

On acceptance criterion for efficient successiveerrors-and-erasures decoding of Reed-Solomon and BCH codes

We describe an efficient algorithm for successive errors-and-erasures decoding of BCH codes. The decoding algorithm consists of finding all necessary error locator polynomials and errata evaluator polynomials, choosing the most appropriate error locator polynomial and errata evaluator polynomial, using these two polynomials to compute a candidate codeword for the decoder output, and testing the candidate for optimality via an originally developed acceptance criterion. Even in the most stringent case possible, the acceptance criterion is only a little more stringent than Forney's (1966) criterion for generalised minimum distance (GMD) decoding. We present simulation results on the error performance of our decoding algorithm for binary antipodal signals over an AWGN channel and a Rayleigh fading channel. The number of calculations of elements in a finite field that are required by our algorithm is only slightly greater than that required by hard-decision decoding, while the error performance is almost as good as that achieved with GMD decoding. The presented algorithm is also applicable to efficient decoding of product RS codes     

大气弱湍流信道下松弛极化码译码方法

针对自由空间光通信中存在的大气湍流降低通信系统误码性能的问题,提出了基于松弛极化码的分段式极化码-循环冗余校验-串行抵消列表(PC-CRC-SCL)译码方法,并将其用于自由空间光通信系统中,在大气弱湍流强度下进行了仿真分析.仿真结果表明:与完全极化码的分段式CRC-SCL译码方法相比,在误码率为10-4时,基于松弛极化...     

A bidirectional multiple stack algorithm

Bidirectional sequential decoding (BSD) substantially reduces the computational variability of conventional sequential decoding without compromising the error performance. However, BSD does not completely eliminate the erasure problem. We propose an erasure-free decoding algorithm which combines the idea of BSD in conjunction with that of the multiple stack algorithm (MSA). It is found that the new bidirectional multiple stack algorithm (BMSA) offers substantial advantages over the MSA in terms of computational effort, memory requirements, and error performance. The BMSA appears as an attractive alternative to the Viterbi algorithm (VA) where low error probabilities and high decoding speeds are required     

改进Min-sum的LDPC译码算法研究

为了弥补Min-Sum译码算法相对于LLR-BP算法的性能缺陷,降低LLR-BP算法的实现复杂度,提出一种改进型Min-Sum译码算法,将Normalized BP-Based和Offset BP-Based 2种算法有效地结合,在计算校验节点消息时,同时引进校正因子和偏移因子,并通过最小均方差准则来选择参数。仿真结果表明,在误码率相同的条件下,改进型Min-Sum译码算法比Min-Sum算法、Normalized BP-Based算法和Offset BP-Based算法具有更好的译码性能,译码性能逼近于LLR-BP译码算法。     

Pattern-Flipping Chase-Type Decoders with Error Pattern Extracting Viterbi Algorithm over Partial Response Channels

Towards the goal of achieving better error correction performance in data storage systems, iterative soft decoding of low density parity check (LDPC) codes and soft-decision decoding of Reed-Solomon (RS) codes have started receiving increasing research attention. However, even with increased computing power, complexities of soft-decision decoding algorithms are still too high for real products which require high throughput and small hardware area. Another problem is that the performance gains of those approaches are smaller for magnetic recording channels than they are for memoryless additive white Gaussian noise (AWGN) channels. We propose a new soft-decision decoding algorithm (based on the Chase algorithm), which takes advantage of pattern reliability instead of symbol reliability or bit reliability. We also present a modified Viterbi algorithm that provides probable error patterns with corresponding reliabilities. Simulation results of the proposed algorithms over the partial response (PR) channel show attractive performance gains. The proposed algorithm dramatically reduces the number of iterations compared to the conventional Chase2 algorithm over the PR channel.     

An efficient hybrid decoding algorithm for Reed-Solomon codes based on bit reliability

The paper presents a computationally efficient hybrid reliability-based decoding algorithm for Reed-Solomon (RS) codes. This hybrid decoding algorithm consists of two major components, a re-encoding process and a successive erasure-and-error decoding process for both bit and symbol levels. The re-encoding process is to generate a sequence of candidate codewords based on the information provided by the codeword decoded by an algebraic decoder and a set of test error patterns. Two criteria are used for testing in the decoding process to reduce the decoding computational complexity. The first criterion is devised to reduce the number of re-encoding operations by eliminating the unlikely error patterns. The second criterion is to test the optimality of a generated candidate codeword. Numerical results show that the proposed decoding algorithm can achieve either a near-optimum error performance or an asymptotically optimum error performance.     

北斗导航信号BCH译码器中校正子辅助的列表译码算法

针对北斗卫星导航系统B1I信号中的BCH译码问题,该文提出一种校正子辅助的列表译码算法。首先,以校正子和汉明重量为准则构造若干错误模式列表;然后根据接收数据硬判决的校正子选择对应的错误模式列表;最后按照相关函数差测度搜索最优错误模式并译码。仿真结果表明,校正子辅助的列表译码算法在误码率10-5时,与最大似然译码算法的信噪比仅差0.08 dB,说明该方法是北斗B1I信号BCH码的一种近优译码方法;另外,该方法具有线性复杂度和可并行实现的特点。     

基于RADIX-4的Turbo码全并行译码算法

针对Turbo码全并行译码算法译码迭代次数多、硬件消耗大的问题,提出了一种基于RADIX-4的改进译码算法.将译码算法中状态转移图的相邻两步状态合并为一步计算,译码时以"比特对"的形式操作进行迭代.在保留译码最大并行度同时,译码计算单元使用量减少一半,显著降低了Turbo码全并行译码算法的运算复杂度和存储开销.仿真结果...     

SDH网中低频抖动测量的数字化方法

ＳＤＨ传输网对常规的ＰＤＨ业务将引入低频抖动。这一抖动的测量对于网络维护和运行有重要意义。传统的抖动测试方法对低频抖动无法精确测试。本文利用数字化方法提出了一种新的测试方法ＳＤＪＭ,采用Ｓｉｇｍａ－Ｄｅｌｔａ技术,用调整间隔表示抖动,从而便于数字化处理,可以对低频抖动进行有效的测试。模拟结果表明测量误差一般均在５％以下。     

列表译码在密码中的应用综述

列表译码自上世纪50年代提出以来,不仅在通信与编码等方面得到了广泛应用,也在计算复杂性理论和密码学领域有着广泛的应用。近年来,随着量子计算的发展,基于整数分解等传统困难问题设计的密码方案受到了巨大的威胁。由于编码理论中一些计算问题的NP困难性被广泛认为是量子概率多项式时间不可攻克的,建立在其上的基于纠错码的密码体制得到了越来越多的重视,列表译码也越来越引起人们的关注。该文系统梳理了列表译码在密码学中的应用,包括早期在证明任何单向函数都存在硬核谓词、设计叛徒追踪方案、以多项式重建作为密码原语设计公钥方案、改进传统基于纠错码的密码方案和求解离散对数问题(DLP)等方面的应用,以及近期,列表译码在设计安全通信协议、求解椭圆曲线离散对数问题、设计新的基于纠错码的密码方案等方面的应用。该文对列表译码的算法改进及其在密码协议设计和密码分析中的应用、新应用场景探索等方面的发展趋势进行了探讨。     

An improved AS-SCLF decoding algorithm of polar codes based on the assigned set

An improved successive cancellation list bit-flip based on assigned set (AS-SCLF) decoding algorithm is proposed to solve the problems that the successive decoding of the successive cancellation (SC) decoder has error propagation and the path extension of the successive cancellation list (SCL) decoder has the decision errors in the traditional cyclic redundancy check aided successive cancellation list (CA-SCL) decoding algorithm. The proposed algorithm constructs the AS firstly. The construction criterion is to use the Gaussian approximation principle to estimate the reliabilities of the polar subchannel and the error probabilities of the bits under SC decoding, and the normalized beliefs of the bits in actual decoding are obtained through the path metric under CA-SCL decoding, thus the error bits containing the SC state are identified and sorted in ascending order of the reliability. Then the SCLF decoding is performed. When the CA-SCL decoding fails for the first time, the decision results on the path of the SC state in the AS are exchanged. The simulation results show that compared with the CA-SCL decoding algorithm, the SCLF decoding algorithm based on the critical set and the decision post-processing decoding algorithm, the improved AS-SCLF decoding algorithm can improve the gain of about 0.29 dB, 0.22 dB and 0.1 dB respectively at the block error rate (BLER) of 10-4 and reduce the number of decoding at the low signal-to-noise ratio (SNR), thus the computational complexity is also reduced.     

一种基于奇偶校验码级联极化码的低复杂度译码算法

极化码作为一种纠错码,具有较好的编译码性能,已成为 5G 短码控制信道的标准编码方案。但在码长较短时,其性能不够优异。作为一种新型级联极化码,奇偶校验码与极化码的级联方案提高了有限码长的性能,但是其译码算法有着较高的复杂度。该文针对这一问题,提出一种基于奇偶校验码级联极化码的串行抵消局部列表译码(PC-PSCL)算法,该算法在编码前进行外码构造,通过高斯近似(GA)得到的子信道错误概率选取较不可靠的信息位,对选取的较不可靠的信息位进行串行抵消列表(SCL)译码和奇偶校验,其余信息比特仅进行串行抵消(SC)译码。仿真结果表明,在高斯信道下,当码长为512,码率为1/2,误帧率为10^–3,最大列表长度为8时,该文提出的低复杂度译码算法比SCL译码算法获得了0.5 dB的增益;与基于奇偶校验的SCL译码算法性能相近,但是空间复杂度和时间复杂度分别降低了38.09%, 15.63%。