A Compact 1.1-Gb/s Encoder and a Memory-Based 600-Mb/s Decoder for LDPC Convolutional Codes

We present a rate-1/2 (128,3,6) LDPC convolutional code encoder and decoder that we implemented in a 90-nm CMOS process. The 1.1-Gb/s encoder is a compact, low-power implementation that includes one-hot encoding for phase generation and built-in termination. The decoder design uses a memory-based interface with a minimum number of memory banks to deliver an information throughput of 1 b per clock cycle. The decoder shares one controller among a pipeline of decoder processors. The decoder dissipates 0.61 nJ of energy per decoded information bit at an SNR of 2 dB and a decoded throughput of 600 Mb/s. On-chip test circuitry permits accurate power measurements to be made at selectable SNR settings.      

Twin-stack decoding of recursive systematic convolutional codes

We present a method for soft-in/soft-out sequential decoding of recursive systematic convolutional codes. The proposed decoder, the twin-stack decoder, is an extension of the well-known ZJ stack decoder, and it uses two stacks. The use of the two stacks lends itself to the generation of soft outputs, and the decoder is easily incorporated into the iterative “turbo” configuration. Under thresholded decoding, it is observed that the decoder is capable of achieving near-maximum a posteriori bit-error rate performance at moderate to high signal-to-noise ratios (SNRs). Also, in the iterative (turbo) configuration, at moderate SNRs (above 2.0 dB), the performance of the proposed decoder is within 1.5 dB of the BCJR algorithm for a 16-state, R=1/3, recursive code, but this difference narrows progressively at higher SNRs. The complexity of the decoder asymptotically decreases (with SNR) as 1/(number of states), providing a good tradeoff between computational burden and performance. The proposed decoder is also within 1.0 dB of other well-known suboptimal soft-out decoding techniques     

基于信噪比分类网络的调制信号分类识别算法

针对传统降噪算法损伤高信噪比(SNR)信号而造成信号识别准确率下降的问题,该文提出基于卷积神经网络的信噪比分类算法,该算法利用卷积神经网络对信号进行特征提取,用固定K均值(FK-means)算法对提取的特征进行聚类处理,准确分类高低信噪比信号。低信噪比信号采用改进的中值滤波算法降噪,改进的中值滤波算法在传统中值滤波的基础上增加了前后采样窗口的关联性机制,来改善传统中值滤波算法处理连续噪声效果不佳的问题。为充分提取信号的空间特征和时间特征,该文提出卷积神经网络和长短时记忆网络并联的卷积长短时(P-CL)网络,利用卷积神经网络和长短时记忆网络分别提取信号的空间特征与时间特征,并进行特征融合与分类。实验表明,该文提出的调制信号分类模型识别准确率为91%,相比于卷积长短时(CNN-LSTM)网络提高了6%。     

Joint Source and Channel Coding using Punctured Ring Convolutional Coded CPM

In this paper, a novel trellis source encoding scheme based on punctured ring convolutional codes is presented. Joint source and channel coding (JSCC) using trellis coded continuous phase modulation (CPM) with punctured convolutional codes over rings is investigated. The channels considered are the additive white gaussian noise (AWGN) channel and the Rayleigh fading channel. Optimal soft decoding for the proposed JSCC scheme is studied. The soft decoder is based on the a posteriori probability (APP) algorithm for trellis coded CPM with punctured ring convolutional codes. It is shown that these systems with soft decoding outperform the same systems with hard decoding especially when the systems operate at low to medium signal-to-noise ratio (SNR). Furthermore, adaptive JSCC approaches based on the proposed source coding scheme are investigated. Compared with JSCC schemes with fixed source coding rates, the proposed adaptive approaches can achieve much better performance in the high SNR region. The novelties of this work are the development of a trellis source encoding method based on punctured ring convolutional codes, the use of a soft decoder, the APP algorithm for the combined systems and the adaptive approaches to the JSCC problem.     

(2,1,7)卷积编码及其维特比译码算法的软件实现

提出了一种（2，1，7）卷积编码及其维特（Viterbi）译码的软件实现方案，在Matlab环境中应用软件技术实现了（2，1，7）卷积码的Viterbi译码器功能。测试证明，该Viterbi译码算法在低信噪比下的误码率仍能达到10^-6。     

TD-SCDMA中(2,1,9)卷积编码及其VITERBI译码算法的SIMULINK S-FUNCTION实现

文章提出了TD-SCDMA系统中一种(2,1,9)卷积编码及其Viterbi译码的软件实现方案,在Matlab/Simulink平台中应用S-Function实现了(2,1,9)卷积码的Viterbi译码器功能.测试证明,该Viterbi译码器输出的信息比特误码率在低信噪比下仍能达到0.0583.     

Code-aided SNR estimation based on expectation maximisation algorithm

A code-aided signal-to-noise ratio (SNR) estimator based on the expectation maximisation algorithm is proposed. The method iteratively uses the soft information from the channel decoder and significantly improves estimation precision in the low SNR regime. It can be extended to higher-order modulation such as MPSK and MQAM directly.     

Fano Decoding with Timeout: Queuing Analysis

In mobile communications, a class of variable‐complexity algorithms for convolutional decoding known as sequential decoding algorithms is of interest since they have a computational time that could vary with changing channel conditions. The Fano algorithm is one well‐known version of a sequential decoding algorithm. Since the decoding time of a Fano decoder follows the Pareto distribution, which is a heavy‐tailed distribution parameterized by the channel signal‐to‐noise ratio (SNR), buffers are required to absorb the variable decoding delays of Fano decoders. Furthermore, since the decoding time drawn by a certain Pareto distribution can become unbounded, a maximum limit is often employed by a practical decoder to limit the worst‐case decoding time. In this paper, we investigate the relations between buffer occupancy, decoding time, and channel conditions in a system where the Fano decoder is not allowed to run with unbounded decoding time. A timeout limit is thus imposed so that the decoding will be terminated if the decoding time reaches the limit. We use discrete‐time semi‐Markov models to describe such a Fano decoding system with timeout limits. Our queuing analysis provides expressions characterizing the average buffer occupancy as a function of channel conditions and timeout limits. Both numerical and simulation results are provided to validate the analytical results.     

Computing upper bounds to error probability of coded modulationschemes

To evaluate an upper bound on error probabilities of signal constellations used for transmission over the additive white Gaussian noise (AWGN) channel, enumeration of all the constellation intradistances is required. These may be infinite in number, for example, when convolutional codes are used and the constellations are lattices. Truncation of the series does not necessarily provide a bound anymore, and must be done with care. Yet the union bound is very simple, as it does not require any further knowledge about the signal constellation than the distance enumerator. In this paper, we describe some methods that can be used to evaluate error probabilities of infinite signal constellations, and that require only a finite number of terms. These methods are applicable, for example, to convolutional codes decoded with a finite-depth Viterbi algorithm and to signal constellations carved from lattices. Coded modulations based on lattices and convolutional or block codes can also be dealt with. As an example of application, we analyze a variable-rate 3-stage coded modulation encoder/decoder, which has been built and is based on a combination of convolutional codes with a single-parity-check block code     

2,1,7卷积码Viterbi译码器的一种设计方案

卷积码在通信系统中得到了极为广泛的应用.其中约束长度K=7,码率为1/2和1/3的Odenwalder卷积码已经成为商业卫星通信系统中的标准编码方法.提出了一种(2,1,7)卷积码Viterbi译码器的设计方案,该译码器采用全并行结构的加/比/选模块和回溯法以提高译码速度,重点介绍了幸存路径存储与交换单元的设计与实现.     

Iterative turbo decoder analysis based on density evolution

We track the density of extrinsic information in iterative turbo decoders by actual density evolution, and also approximate it by symmetric Gaussian density functions. The approximate model is verified by experimental measurements. We view the evolution of these density functions through an iterative decoder as a nonlinear dynamical system with feedback. Iterative decoding of turbo codes and of serially concatenated codes is analyzed by examining whether a signal-to-noise ratio (SNR) for the extrinsic information keeps growing with iterations. We define a “noise figure” for the iterative decoder, such that the turbo decoder will converge to the correct codeword if the noise figure is bounded by a number below zero dB. By decomposing the code's noise figure into individual curves of output SNR versus input SNR corresponding to the individual constituent codes, we gain many new insights into the performance of the iterative decoder for different constituents. Many mysteries of turbo codes are explained based on this analysis. For example, we show why certain codes converge better with iterative decoding than more powerful codes which are only suitable for maximum likelihood decoding. The roles of systematic bits and of recursive convolutional codes as constituents of turbo codes are crystallized. The analysis is generalized to serial concatenations of mixtures of complementary outer and inner constituent codes. Design examples are given to optimize mixture codes to achieve low iterative decoding thresholds on the signal-to-noise ratio of the channel     

Threshold decoder and two feedback checkers for nonsystematic convolutional code (2,1,6)

A threshold decoder of the well known convolutional code (2,1,6) is proposed. Two simple approaches to reduce error propagation are presented. This decoder can be used when the communication channel does not require a more efficient and expensive decoder such as the Viterbi decoder.<>     

Truncation length for Viterbi decoding

A bound is derived and analyzed for the bit error rate (BER) of a Viterbi decoder with survivor truncation. Estimates of the SNR (signal-to-noise ratio) loss on the AWGN (additive white Gaussian noise) channel due to truncation are obtained for convolutional codes. Larger truncation lengths are required than the smallest value that does not effectively decrease the code's free distance, especially at low E _b/N₀     

Iterative threshold decoding without interleaving for convolutional self-doubly orthogonal codes

A novel iterative error control technique based on the threshold decoding algorithm and new convolutional self-doubly orthogonal codes is proposed. It differs from parallel concatenated turbo decoding as it uses a single convolutional encoder, a single decoder and hence no interleaver, neither at encoding nor at decoding. Decoding is performed iteratively using a single threshold decoder at each iteration, thereby providing good tradeoff between complexity, latency and error performance.     

An extensive search for good punctured rate-k/(k+1) recursive convolutional codes for serially concatenated convolutional codes

In many practical applications requiring variable-rate coding and/or high-rate coding for spectral efficiency, there is a need to employ high-rate convolutional codes (CC), either by themselves or in a parallel or serially concatenated scheme. For such applications, in order to keep the trellis complexity of the code constant and to permit the use of a simplified decoder that can accommodate multiple rates, a mother CC is punctured to obtain codes with a variety of rates. This correspondence presents the results of extensive search for optimal puncturing patterns for recursive convolutional codes leading to codes of rate k/(k+1) (k an integer) to be used in serially concatenated convolutional codes (SCCC). The code optimization is in the sense of minimizing the required signal-to-noise ratio (SNR) for two target bit-error rate (BER) and two target frame-error rate (FER) values. We provide extensive sample simulation results for rate-k/(k+1) SCCC codes employing our optimized punctured CC.     

Multistage decoding for internally bandwidth efficient coded Poisson fiber-optic CDMA communication systems

We consider the structure and performance of a multistage decoding scheme for an internally bandwidth efficient convolutionally coded Poisson fiber-optic code division multiple access (CDMA) communication system. The decoder is implemented electronically in several stages in which in each stage, the interfering users' coded bit decisions obtained in the previous stage is applied for computing the likelihood of the coded symbols of the desired user. The first stage is a soft-input Viterbi decoder for the internally coded scheme, in which the soft-input coded symbol likelihood values are computed by considering the multiuser interference as a noise signal. The likelihood of coded symbol computed in each stage is then entered into the convolutional decoder for the next bit decisions. The convolutional codes that are used for demonstrating the performance of the multistage decoder are super orthogonal codes (SOCs). We derive the bit error rates (BERs) of the proposed decoder for internally coded Poisson fiber-optic CDMA systems using optical orthogonal codes (OOCs) along with both ON-OFF keying (OOK) and binary pulse position modulation (BPPM) schemes. Our numerical results indicate that the proposed decoding scheme substantially outperforms the single-stage soft-input Viterbi decoder. We also derive the upper bound on the probability of error of a decoder for the known interference case, which is the ultimate performance of a multiuser decoder, and compare the result with that of the soft-input Viterbi decoder.     

Variable-complexity trellis decoding of binary convolutional codes

Considers trellis decoding of convolutional codes with selectable effort, as measured by decoder complexity. Decoding is described for single parent codes with a variety of complexities, with performance “near” that of the optimal fixed receiver complexity coding system. Effective free distance is examined. Criteria are proposed for ranking parent codes, and some codes found to be best according to the criteria are tabulated, Several codes with effective free distance better than the best code of comparable complexity were found. Asymptotic (high SNR) performance analysis and error propagation are discussed. Simulation results are also provided     

Burst error statistics of simulated Viterbi decoded BPSK on fadingand scintillating channels

The author presents and analyzes burst error statistics of a soft-decision Viterbi decoder when the transmitted signal is encoded with the 313 (3, 1/2) or 31123 (5, 1/2) convolutional codes, modulated via coherent binary phase-shift keying (BPSK) for the additive white Gaussian noise (AWGN) channel, and subjected to slow and nonselective scintillation/fading modeled by the Nakagami-m distribution. These statistics were generated by Monte-Carlo simulations, and presented in terms of burst error length average and quantile (90 and 99%) statistics versus SNR (E_b/N₀) parameterized by the fading intensity parameter m. The results indicate how Viterbi decoder burst error statistics vary with the fading/scintillation intensity m for Nakagami-m channels, and, consequently, provide information important to the design of interleaved or noninterleaved concatenated coding schemes for such channel environments     

Optimum mean-square error use of convolutional codes

Thekinput and output digits of a rate(k/n)linear convolutional code over a finite field GF(q)are related to a finite set of integers by aq-ary expansion. The mean-square error criterion is used to simultaneously select the optimum encoder and decoder rules. This optimization is performed over all one-to-one generalized encoding rules and all decoding functions that map into the real numbers. The optimal design procedure relies upon generalized Fourier transforms, and it is shown that the encoder part of the optimum pair of rules can be taken as a linear function when the input space of symbols is viewed in a natural algebraic setting. The decoder part is a conditional mean estimator coupled with a rounding operation. One method of implementing the decoder uses the nonlinear combination of filter functions defined in the generalized frequency domain.     

几个影响Woven卷积码纠错性能的因素

为了解决性能和设备复杂性的矛盾，普通级联卷积码将两个卷积编码器串联。然而在通信系统的接收端内码解码器会将差错汇集在突发(burst)中使外码解码器不能完全纠正这些错误．Woven卷积码采用特殊的“编织”方式，将内码解码器的错误以某种形式分散开来，这种结构使其获得良好的纠错性能。本文在介绍Woven码的构造和生成矩阵后，对影响Woven码纠错性能的几个因素进行了分析。