Optimization of Two-Dimensional Signal Constellations in the Presence of Gaussian Noise

A considerable amount of literature exists on the problem of selecting an efficient set ofNdigital signals with in-phase and quadrature components for use in a suppressed carrier data transmission system. However, the signal constellation which minimizes the probability of error in Gaussian noise, under an average power constraint, has not been determined when the number of signals is greater than two. In this paper an asymptotic (large signal-to-noise ratio) expression, of the minimum distance type, is derived for the error rate. Using this expression, a gradient-search procedure, which is initiated from several randomly chosenN-point arrays, converges in each case to a locally optimum constellation. The algorithm incorporates a radial contraction technique to meet the average signal power constraint. The best solutions are described for several values ofNand compared with well-known signal formats. As an example, the best locally optimum 16-point constellation shows an advantage of about 0.5 dB in signal-signal-to-noise ratio over quadrature amplitude modulation. The locally optimum constellations are the vertices of a trellis of (almost) equilateral triangles. AsN rightarrow infty, it is rigorously proved in the Appendix that the optimum constellations tend toward an equilateral structure, and become uniformly distributed in a circle.     

广义高斯信源的自适应编码研究

首先介绍了当前最新的几种视频编码标准并且进行了比较,熵编码是每一个视频编码标准必须认真研究的课题,为了减少由于失配所带来的效率损失,本文提出了一种自适应编码技术:自适应指数哥伦布码,并与自适应算术编码进行了比较.分析和仿真都表明即使信源特性在大范围内发生变化,自适应指数哥伦布码对于保持高的编码效率是足够稳健的(90%以上的情况),同时保持了指数哥伦布码和哥伦布-莱期码的简洁性.     

Coding of Multilevel Graphics

In this paper we consider the digitization and coding of graphics, specifically typewritten letters, and make two contributions. The first contribution concerns the tradeoff between resolution and number of gray levels. We carried out subjective tests which showed that, in order to get better image quality at a given bit rate, for good-quality originals, one should use only two levels/sample and higher resolution; while for poor-quality originals, one should use more levels/sample. Second, we estimated the bit rates achievable when bit-plane run length coding is applied to the multilevel images.     

Spectral-Efficient Differential Space–Time Coding Using Non-Full-Diverse Constellations

In this paper, a method is proposed to construct spectral-efficient unitary space–time codes for high-rate differential communications over multiple-antenna channels. Unlike most of the known methods, which are designed to maximize the diversity product (the minimum determinant distance), our objective is to increase the spectral efficiency. The simulation results indicate that for high spectral efficiency and for more than one receive antenna, the new method significantly outperforms the existing alternatives. In the special case of two transmit antennas, which is the main focus of this paper, the relation between the proposed code and the Alamouti scheme helps us to provide an efficient maximum-likelihood decoding algorithm. Also, we demonstrate that similar ideas can be applied for designing codes for more than two transmit antennas. As an example, we present a construction for a 4$times$4 unitary constellations which has a good performance, as compared with the other known codes.     

A Computationally Efficient Multilevel Coding Scheme for ISI Channels

This paper proposes a multilevel coding scheme with linear mapping for intersymbol interference (ISI) channels and derives a low-complexity receiver structure that can achieve the ISI channel capacity. The transmitter superimposes many layers of independent binary antipodal streams to generate a quadrature amplitude modulation (QAM) or Gaussian-like channel input. The receiver performs multistage decoding with decision feedback and interference cancellation. Within each stage is a linear minimum mean-square-error (MMSE) equalizer followed by an error-correcting decoder. The complexity scales linearly with the channel length and the number of layers, and the process is shown to be asymptotically information lossless if a fixed input power is properly distributed over a sufficiently large number of layers. This framework is then extended to achieve the capacity of the ISI channel using a transmitter-side spectral shaping filter that converts a Gaussian input sequence with a white spectrum to one with a water-filling spectrum.      

基于DSP的实时高斯白噪声产生方案

基于浮点型DSP的结构特点,提出了一种实时高斯白噪声产生方案。核心算法采用Wichman.B.A、Hill.I.D提出的组合线性同余法,先生成均匀分布随机数再利用函数变换最终得到高斯白噪声,并对该算法进行理论分析,从假设检验和物理测量的角度同其他方案对比,结果表明该算法性能良好。实现时采用2套种子数的方案进一步提高精度,通过优化DSP代码达到实时要求。应用时通过输入不同的方差值,可获得不同信噪比的数据流。     

Spectrally Efficient Differential Space–Time Coding Using Non-Full-Diverse Constellations

In this paper, a method is proposed to construct spectrally efficient unitary space–time codes for high-rate differential communications over multiple-antenna channels. Unlike most of the known methods which are designed to maximize the diversity product (the minimum determinant distance), our objective is to increase the spectral efficiency. The simulation results indicate that for high spectral efficiency and for more than one receive antenna, the new method significantly outperforms the existing alternatives. In the special case of two transmit antennas, which is the main focus of this paper, the relation between the proposed code and the Alamouti scheme helps us to provide an efficient maximum-likelihood (ML) decoding algorithm. Also, we demonstrate that similar ideas can be applied to designing codes for more than two transmit antennas. As an example, we present a construction for 4-by-4 unitary constellations which has a good performance, compared with the other known codes.     

Successively Structured Gaussian Two-terminal Source Coding

Multiterminal source coding refers to separate encoding and joint decoding of multiple correlated sources. Joint decoding requires all the messages to be decoded simultaneously which is exponentially more complex than a sequence of single-message decodings. Inspired by previous work on successive coding, we apply the successive Wyner-Ziv coding, which is inherently a low complexity approach of obtaining a prescribed distortion, to the two-terminal source coding scheme. First, we consider 1-helper problem where one source provides partial side information to the decoder to help the reconstruction of the main source. Our results show that the successive coding strategy is an optimal strategy in the sense of achieving the rate-distortion function. By developing connections between source encoding and data fusion steps, it is shown that the whole rate-distortion region for the 2-terminal source coding problem is achievable using the successive coding strategy. Comparing the performance of the sequential coding with the performance of the successive coding, we show that there is no sum-rate loss when the side information is not available at the encoder. This result is of special interest in some applications such as video coding where there are processing and storage constraints at the encoder. Finally, we provide an achievable rate-distortion region for the m-terminal source coding.

Differential Coding for Non-Orthogonal Space-Time Block Codes with Non-Unitary Constellations over Arbitrarily Correlated Rayleigh Channels

In this paper, we propose a maximum likelihood (ML) decoder for differentially encoded full-rank square nonorthogonal space-time block codes (STBCs) using unitary or non-unitary signal constellations, which is also applicable to fullranked orthogonal STBC (OSTBC). As the receiver is jointly optimized with respect to the channel and the unknown data, it does not require any knowledge of channel power, signal power, or noise power to decode the signal, and the decision is purely based on two consecutively received data blocks. We analyze the effect of channel correlation on the performance of the proposed system in Rayleigh fading channels. Assuming a general correlation model, an upper bound of the pair-wise error probability (PEP) of the differential OSTBCs is derived. An approximate bound of the PEP for the differential nonorthogonal STBCs is also derived. We propose a precoder designing criterion for differential STBC over arbitrarily correlated Rayleigh channels. Precoding improves the system performance over the correlated Rayleigh MIMO channels. Our precoded differential codes differ from the previously proposed precoder designs for differential OSTBC in the following ways: 1) We propose a precoder design for arbitrarily correlated Rayleigh channels, whereas the previous work considers only for transmit correlation. 2) The previous work is only applicable to the OSTBCs with PSK constellations, whereas our precoder is applicable to any type of full-rank square STBCs with unitary and non-unitary signal constellations.     

高斯尺度混合大气噪声模型的参数估计

非高斯大气噪声的参数估计对甚低频、超低频信号的最佳接收有重要意义。对大气噪声采用基于逆高斯分布的高斯尺度混合分布模型建模,研究了基于逆高斯分布的高斯尺度混合分布模型参数的性质,设计了高斯尺度混合大气噪声模型参数的马尔可夫链蒙特卡罗（ MCMC）算法。算法在贝叶斯层次模型下,采用Gibbs抽样和M-H抽样更新参数。仿真结果表明,该模型对大气噪声有很好的适用性,MCMC算法迭代效率和精度高,具有实际的应用价值。     

Colorization for Gray Scale Facial Image by Locality-Constrained Linear Coding

Colorization for gray scale facial image is an important technique in various practical applications. However, the methods that have been proposed are essentially semi-automatic. In this paper, we present a new probabilistic framework based on Maximum A Posteriori (MAP) estimation to automatically transform the given gray scale facial image to corresponding color one. Firstly, the input image is divided into several patches and non-parametric Markov random field (MRF) is employed to formulate the global energy. Secondly, Locality-constrained Linear Coding (LLC) is employed to learn the color distribution for each patch. At the same time, the simulated annealing algorithm is employed to iteratively update the patches chosen by LLC to optimize the MRF by decreasing global energy cost. The experimental results demonstrate that the proposed framework is effective to colorize the gray scale facial images to corresponding color ones.     

一种简化的多级译码方法

文中提出了一种简化的多级译码方法。这种译码方法能够在不损害编码系统传输性能的情况下有效地减少译码器的运算量，从而减少译码时延，使高速译码的实时实现成为可能。     

A New Concatenated Coding SystemUsing Multilevel Inner Codes

ＡＮｅｗＣｏｎｃａｔｅｎａｔｅｄＣｏｄｉｎｇＳｙｓｔｅｍＵｓｉｎｇＭｕｌｔｉｌｅｖｅｌＩｎｎｅｒＣｏｄｅｓＷａｎｇＤｕａｎｙｉＡＮＤＹｕｅＧｕａｎｇｘｉｎ（ＤｅｐａｒｔｍｅｎｔｏｆＴｅｌｅｃｏｍｍｕｎｉｃａｔｉｏｎＥｎｇｉｎｅｅｒｉｎｇ，Ｂｅｉｊｉｎ...     

高斯噪声中的参数盲估计

盲信号处理方法中常忽略噪声的影响,而实际问题中噪声的影响是存在的.本文主要讨论了在协方差矩阵未知的加性高斯噪声中混合系数的盲估计问题.本文以最大似然估计为基础,提出一种求解参数的最优化算法,给出了混合矩阵和协方差矩阵的计算式.采用高斯混合模型(GMM)来逼近源信号的概率密度函数,简化了算法中的积分,导出了一种基于EM算法的迭代式.仿真表明,算法不仅能稳定收敛,而且在低信噪比下也能获得良好性能.     

Detection of Modulated Gaussian Signals in Noise

A method using Hermite polynomials is utilized for analyzing the outputs of νth-law devices for inputs of modulated Gaussian signals and zero-mean Gaussian noise. New results are developed for the output correlation functions, and techniques for obtaining closed-form expressions are pointed out. Output signal-to-noise ratios for various input carrier-to-noise-power ratios are calculated, and plots are shown for a single sinusoidal modulating signal. Results are derived to show the existence of a theoretical maximum for the output signal-to-noise ratio. The method can be directly applied for the case of general Fourier expandable signals modulating a Gaussian carrier.     

Hybrid Digital-Analog Coding with Bandwidth Compression for Gaussian Source-Channel Pairs

Three hybrid digital-analog (HDA) systems, denoted by HDA-I, HDA* and HDA-II, for the coding of a memoryless discrete-time Gaussian source over a discrete-time additive memoryless Gaussian channel under bandwidth compression are studied. The systems employ simple linear coding in their analog component and superimpose their analog and digital signals before channel transmission. Information-theoretic upper bounds on the asymptotically optimal mean squared error distortion of the systems are obtained under both matched and mismatched channel conditions. Allocation schemes for distributing the channel input power between the analog and the digital signals are also examined. It is shown that systems HDA* and HDA-II can asymptotically achieve the optimal Shannon-limit performance under matched channel conditions. Low-complexity and low-delay versions of systems HDA-I and HDA-II are next designed and implemented without the use of error correcting codes. The parameters of these HDA systems, which employ vector quantization in conjunction with binary phase-shift keying modulation in their digital part, are optimized via an iterative algorithm similar to the design algorithm for channel-optimized vector quantizers. Both systems have low complexity and low delay, and guarantee graceful performance improvements for high CSNRs. For memoryless Gaussian sources the designed HDA-II system is shown to be superior to the HDA-I designed system. When applied to a Gauss-Markov source under Karhunen-Loeve processing, the HDA-I system is shown to provide considerably better performance.     

Practical Vector Dirty Paper Coding for MIMO Gaussian Broadcast Channels

Recently, the vector dirty paper coding (DPC) achievable rate region has been shown to be the capacity region of a multiple-input multiple-output Gaussian broadcast channel (MIMO GBC). With DPC, the multiuser interference noncausally known at the transmitter can be completely removed. In this paper, we present a vector DPC structure for MIMO GBC. It is a generalization of the single antenna superposition dirty paper coding for the scalar Gaussian dirty paper problem proposed by Bennatan et al. In a theoretical random code setting, this construction is shown to be able to achieve the promised rate performance of the MIMO GBC. We also implement it with existing vector quantizer and capacity-achieving channel coding. Combined with iterative decoding, a design example validates the effectiveness of our methods.     

Hybrid Polynomial Filters for Gaussian and Non-Gaussian Noise Environments

Traditional polynomial filtering theory, based on linear combinations of polynomial terms, is able to approximate important classes of nonlinear systems. The linear combination of polynomial terms, however, yields poor performance in environments characterized by Gaussian and heavy tailed distributions. Weighted median and weighted myriad filters, in contrast, are well known for their outlier suppression and detail preservation properties. It is shown here that the weighted median and weighted myriad methodologies are naturally extended to the polynomial sample case, yielding hybrid filter structures that exploits the higher-order statistics of the observed samples while simultaneously being robust to outliers for both Gaussian and heavy-tailed distributions environments. Moreover, the introduced hybrid polynomial filter classes are well motivated by analysis of cross and square term statistics of Gaussian and heavy-tailed distributions. A presented asymptotic tail mass analysis shows that polynomial terms, both under Gaussian and heavy-tailed noise statistics, have heavier tails than the observed samples, indicating that robust combination methods should be utilized to avoid undue influence of outliers. Further analysis shows weighted median processing of polynomial terms for the Gaussian noise case, and weighted median and weighted myriad processing of cross and square terms, respectively, for the heavy-tailed noise case, are justified from a maximum likelihood perspective. Filters parameter optimization procedures are also presented. Finally, the effectiveness of hybrid filters is demonstrated through simulations that include temporal, spectrum, and bispectrum analysis     

高斯白噪情形下的信噪比测量

在通信系统中,信噪比的测量在业务QoS的配置中,有着举足轻重的地位。信噪比测量的准确性,将直接影响系统的吞吐量。绝大多数系统都可以转化为高斯白噪情形下的信噪比测量。本文考虑了该情形下的通常工程方法,给出了与仿真结果完全吻合的理论闭合表达式,并得出了理论极限。