Asymptotic bounds on optimal noisy channel quantization via randomcoding

Asymptotically optimal zero-delay vector quantization in the presence of channel noise is studied using random coding techniques. First, an upper bound is derived for the average rth-power distortion of channel optimized k-dimensional vector quantization at transmission rate R on a binary symmetric channel with bit error probability ϵ. The upper bound asymptotically equals 2/sup -rRg(ϵ,k,r/). where k/(k +r) [1 - log₂(l +2√(ϵ(1-ϵ))] ⩽g(ϵ,k,r)⩽1) for all ϵ⩾0, lim_ϵ→0 g(ϵ,k,r)=1, and lim_k→∞g(ϵ,k,r)=1. Numerical computations of g(ϵ,k,r) are also given. This result is analogous to Zador's (1982) asymptotic distortion rate of 2^-rR for quantization on noiseless channels. Next, using a random coding argument on nonredundant index assignments, a useful upper bound is derived in terms of point density functions, on the minimum mean squared error of high resolution, regular, vector quantizers in the presence of channel noise. The formula provides an accurate approximation to the distortion of a noisy channel quantizer whose codebook is arbitrarily ordered. Finally, it is shown that the minimum mean squared distortion of a regular, noisy channel VQ with a randomized nonredundant index assignment, is, in probability, asymptotically bounded away from zero     

Cross-layer optimization for video transmission over multirate GMC-CDMA wireless links.

In this paper, we consider the problem of video transmission over wireless generalized multicarrier code division multiple access (GMC-CDMA) systems. Such systems offer deterministic elimination of multiple access interference. A scalable video source codec is used and a multirate setup is assumed, i.e., each video user is allowed to occupy more than one GMC-CDMA channels. Furthermore, each of these channels can utilize a different number of subcarriers. We propose a cross-layer optimization method to select the source coding rate, channel coding rate, number of subcarriers per GMC-CDMA channel and transmission power per GMC-CDMA channel given a maximum transmission power for each video user and an available chip rate. Universal rate distortion characteristics (URDC) are used to approximate the expected distortion at the receiver. The proposed algorithm is optimal in the operational rate distortion sense, subject to the specific setup used and the approximation caused by the use of the URDC. Experimental results are presented and conclusions are drawn.     

Pseudo-Gray coding

A pseudo-Gray code is an assignment of n-bit binary indexes to 2" points in a Euclidean space so that the Hamming distance between two points corresponds closely to the Euclidean distance. Pseudo-Gray coding provides a redundancy-free error protection scheme for vector quantization (VQ) of analog signals when the binary indexes are used as channel symbols on a discrete memoryless channel and the points are signal codevectors. Binary indexes are assigned to codevectors in a way that reduces the average quantization distortion introduced in the reproduced source vectors when a transmitted index is corrupted by channel noise. A globally optimal solution to this problem is generally intractable due to an inherently large computational complexity. A locally optimal solution, the binary switching algorithm, is introduced, based on the objective of minimizing a useful upper bound on the average system distortion. The algorithm yields a significant reduction in average distortion, and converges in reasonable running times. The sue of pseudo-Gray coding is motivated by the increasing need for low-bit-rate VQ-based encoding systems that operate on noisy channels, such as in mobile radio speech communications     

Performance of quantizers on noisy channels using structuredfamilies of codes

Achievable distortion bounds are derived for the cascade of structured families of binary linear channel codes and binary lattice vector quantizers. It is known that for the cascade of asymptotically good channel codes and asymptotically good vector quantizers the end-to-end distortion decays to zero exponentially fast as a function of the overall transmission rate, and is achieved by choosing a channel code rate that is independent of the overall transmission rate. We show that for certain families of practical channel codes and binary lattice vector quantizers, the overall distortion can be made to decay to zero exponentially fast as a function of the square root of transmission rate. This is achieved by carefully choosing a channel code rate that decays to zero as the transmission rate grows. Explicit channel code rate schedules are obtained for several well-known families of channel codes     

Binary lattice vector quantization with linear block codes andaffine index assignments

We determine analytic expressions for the performance of some low-complexity combined source-channel coding systems. The main tool used is the Hadamard transform. In particular, we obtain formulas for the average distortion of binary lattice vector quantization with affine index assignments, linear block channel coding, and a binary-symmetric channel. The distortion formulas are specialized to nonredundant channel codes for a binary-symmetric channel, and then extended to affine index assignments on a binary-asymmetric channel. Various structured index assignments are compared. Our analytic formulas provide a computationally efficient method for determining the performance of various coding schemes. One interesting result shown is that for a uniform source and uniform quantizer, the natural binary code is never optimal for a nonsymmetric channel, even though it is known to be optimal for a symmetric channel     

Optimal resource allocation for Medium Grain Scalable video transmission over MIMO channels

In this paper we investigate an optimal solution for adaptive H.264/SVC video transmission over Multiple-Input Multiple-Output (MIMO) channels.We first write the end-to-end distortion of the H.264/SVC video transmission over a diagonal MIMO channel. The total distortion is expressed following three physical layer parameters: power allocation, modulation spectral efficiency and Error Code Correction (ECC) code rate. Minimizing the total distortion is considered as an optimization problem containing both discrete and continuous variables.We use the Lagrangian method associated with Karush–Kuhn and Tucker conditions to find out the optimal continuous physical layer parameters. Concerting the discrete modulation spectral efficiency and ECC code rate, we exploit information of the MIMO system to remove all suboptimal configurations. Therefore, the optimal power allocation is computed only for a reduced number of discrete configurations.The performance of the proposed solution is evaluated over both statistical and realistic MIMO channels. Results show that the proposed solution performs an optimal resource allocation to achieve the best QoS regardless the channel conditions.     

Two-channel conjugate vector quantizer for noisy channel speechcoding

A two-channel conjugate vector quantizer is proposed in an attempt to reduce quantization distortion for noisy channels. In this quantization, two different codebooks are used. The encoder selects the channel code pair that generates the smallest distortion between the input and the averaged output vectors. These two codebooks are alternately trained by an iterative algorithm which is based on the generalized Lloyd algorithm. Coding experiments show that the proposed scheme has almost the same SNR as a conventional vector quantizer for an error-free channel. On the other hand, it has a significantly higher SNR than the conventional one for a 1% error rate. This scheme also has merits in computational complexity and storage requirements. The scheme is confirmed to be effective for a medium bit-rate speech waveform coder     

A study of vector quantization for noisy channels

Several issues related to vector quantization for noisy channels are discussed. An algorithm based on simulated annealing is developed for assigning binary codewords to the vector quantizer code-vectors. It is shown that this algorithm could result in dramatic performance improvements as compared to randomly selected codewords. A modification of the simulated annealing algorithm for binary codeword assignment is developed for the case where the bits in the codeword are subjected to unequal error probabilities (resulting from unequal levels of error protection). An algorithm for the design of an optimal vector quantizer for a noisy channel is briefly discussed, and its robustness under channel mismatch conditions is studied. Numerical results for a stationary first-order Gauss-Markov source and a binary symmetric channel are provided. It is concluded that the channel-optimized vector quantizer design algorithm, if used carefully, can result in a fairly robust system with no additional delay. The case in which the communication channel is nonstationary (as in mobile radio channels) is studied, and some preliminary ideas for quantizer design are presented     

Soft-decision demodulation design for COVQ over white, colored, andISI Gaussian channels

In this work, the design of a q-bit (scalar and vector) soft-decision demodulator for Gaussian channels with binary phase-shift keying modulation is investigated. The demodulator is used in conjunction with a soft-decision channel-optimized vector quantization (COVQ) system. The COVQ is constructed for an expanded (q>1) discrete channel consisting of the concatenation of the modulator, the Gaussian channel, and the demodulator. It is found that as the demodulator resolution q increases, the capacity of the expanded channel increases, resulting in an improvement of the COVQ performance. Consequently, the soft-decision demodulator is designed to maximize the capacity of the expanded channel. Three Gaussian channel models are considered as follows: (1) additive white Gaussian noise channels; (2) additive colored Gaussian noise channels; and (3) Gaussian channels with intersymbol interference. Comparisons are made with (a) hard-decision COVQ systems, (b) COVQ systems which utilize interleaving, and (c) an unquantized (q=∞) soft-decision decoder proposed by Skoglund and Hedelin (1999). It is shown that substantial improvements can be achieved over COVQ systems which utilize hard decision demodulation and/or channel interleaving. The performance of the proposed COVQ system is comparable with the system by Skoglund and Hedelin-though its computational complexity is substantially less     

Design and analysis of nonbinary LDPC codes for arbitrary discrete-memoryless channels

We present an analysis under the iterative decoding of coset low-density parity-check (LDPC) codes over GF(q), designed for use over arbitrary discrete-memoryless channels (particularly nonbinary and asymmetric channels). We use a random- coset analysis to produce an effect that is similar to output symmetry with binary channels. We show that the random selection of the nonzero elements of the GF(q) parity-check matrix induces a permutation-invariance property on the densities of the decoder messages, which simplifies their analysis and approximation. We generalize several properties, including symmetry and stability from the analysis of binary LDPC codes. We show that under a Gaussian approximation, the entire q-1-dimensional distribution of the vector messages is described by a single scalar parameter (like the distributions of binary LDPC messages). We apply this property to develop extrinsic information transfer (EXIT) charts for our codes. We use appropriately designed signal constellations to obtain substantial shaping gains. Simulation results indicate that our codes outperform multilevel codes at short block lengths. We also present simulation results for the additive white Gaussian noise (AWGN) channel, including results within 0.56 dB of the unrestricted Shannon limit (i.e., not restricted to any signal constellation) at a spectral efficiency of 6 bits/s/Hz.     

The design of joint source and channel trellis waveform coders

The generalized Lloyd algorithm is applied to the design of joint source and channel trellis waveform coders to encode discrete-time continuous-amplitude stationary and ergodic sources operating over discrete memoryless noisy channels. Experimental results are provided for independent and autoregressive Gaussian sources, binary symmetric channels, and absolute error and squared error distortion measures. Performance of the joint codes is compared with the tandem combination of a trellis source code and a trellis channel code on the independent Gaussian source using the squared error distortion measure operating over an additive white Gaussian noise channel. It is observed that the jointly optimized codes achieve performance close to or better than that of separately optimized tandem codes of the same constraint length. Performance improvement via a predictive joint source and channel trellis code is demonstrated for the autoregressive Gaussian source using the squared error distortion measure.     

长码MIMO CDMA信道的一阶聚类盲估计

该文提出了一种长码多输入多输出CDMA系统的信道盲估计方法。使用解相关匹配滤波器作为接收机前端,其输出信号可以剖分为信道矢量张成的线性空间。使用聚类算法提取集合的中心,从而仅利用解相关器输出的一阶统计量便可很好地估计出信道参数。同时对K-均值聚类算法的初始值设定进行了改进以提高收敛速度。所提出的算法有较低的计算复杂度。仿真结果表明该算法的有效性以及对信道阶数过估计有很好的鲁棒性。     

Capacity analysis for finite-state Markov mapping of flat-fading channels

In this paper, time-varying flat-fading channels are modeled as first-order finite-state Markov channels (FSMC). The effect of this modeling on the channel information capacity is addressed. The approximation accuracy of the first-order memory assumption in the Markov model is validated by comparing the FSMC capacity with the channel capacity assuming perfect state information at the receiver side. The results indicate that the first-order Markovian assumption is accurate for normalized Doppler frequencies f/sub d/T /spl lsim/ 0.01, in amplitude-only quantization of the channel gain for noncoherent binary signaling. In phase-only and joint phase and amplitude quantization of the channel gain for coherent binary signaling, the first-order Markovian assumption is accurate for f/sub d/T /spl lsim/ 0.001. Furthermore, the effect of channel quantization thresholds on the FSMC capacity is studied. In high signal-to-noise ratio (SNR) conditions, nonuniform two-level amplitude quantization scheme outperforms equiprobable quantization method by 0.8-1.5 dB.     

Vector Channel Estimation and Multiuser Detection for Multicarrier DS CDMA in Time and Frequency Selective Fading Channels

In a multicarrier direct-sequence code-division multiple access (MC DS CDMA) system, different fading channels for different users and/or different carriers are correlated in general; thus a vector channel model is more appropriate than disjoint scalar channel models. For multiuser MC DS CDMA systems, we propose (1) a generalized vector autoregressive model which accounts for correlation between different user/carrier fading channels, (2) the use of a two-phased algorithm to obtain the proposed model’s parameters, and (3) a receiver structure that consists of a generalized decorrelator followed by maximal-ratio combining (MRC) of uncorrelated carrier channel outputs of each user. The estimated fading coefficients provide the necessary quantities to MRC. The computer simulation results show that the proposed scheme has performance close to the case in which the channel is perfectly known, and outperforms separate scalar channel estimation case.     

快时变OFDM系统中非采样间隔信道的信道估计

摘要：在快时变环境下的OFDM（orthogonal frequency division multiplexing,正交频分复用）系统中,针对非采样间隔信道CIR（channel impulse response,信道冲击响应）能量泄漏和ICI（inter-carrier interference,子载波间干扰）的问题,提出了一种基于分数抽头信道近似的复指数基扩展联合反馈离散傅里叶变换信道估计算法。该算法首先根据基于分数抽头信道近似的复指数基扩展模型计算信道参数,再根据该信道参数计算出快时变环境下OFDM系统的ICI系数,然后将初次消除ICI的信号作为反馈进行离散傅里叶变换,进一步消除噪声和ICI。该算法在一定程度上抑制了CIR能量泄漏,消除了ICI和噪声,有效地近似了实际信道。仿真结果表明,该算法在误比特率和信道均方误差方面均有明显提高。     

大规模MIMO系统上行链路时间-空间结构信道估计算法

针对大规模多入多出(MIMO)系统上行链路非平稳空间相关信道的估计问题,该文利用信道的时间-空间2维稀疏结构信息,应用狄利克雷过程(DP)和变分贝叶斯推理(VBI),设计了一种低导频开销和计算复杂度的信道估计迭代算法,提高了信道估计精度。由于平稳空间相关信道难以适用于大规模MIMO系统,该文借助于狄利克雷过程构建了非平稳空间相关信道先验模型,可将具有空间关联的多个物理信道映射为具有相同时延结构的概率信道,并应用变分贝叶斯推理设计了低导频开销和计算复杂度的信道估计迭代算法。实验结果验证了所提算法的有效性,且具有对系统关键参数鲁棒性的优点。     

Gaussian Approximation Based Mixture Reduction for Joint Channel Estimation and Detection in MIMO Systems

A novel Gaussian approximation based mixture reduction algorithm is proposed for semi-blind joint channel tracking and symbol detection for spatial multiplexing multiple-input multiple-output (MIMO) systems with frequency-flat time-selective channels. The proposed algorithm is based on a modified sequential Gaussian approximation detector (SGA) which takes into account channel uncertainty, and the first order generalized pseudo-Bayesian (GPB1) channel estimator. Simulation results show that the proposed algorithm performs better than the conventional and computationally expensive decision-directed method with Kalman filter based channel estimation and a posteriori probability (APP) symbol detection.     

Raptor codes on binary memoryless symmetric channels

In this paper, we will investigate the performance of Raptor codes on arbitrary binary input memoryless symmetric channels (BIMSCs). In doing so, we generalize some of the results that were proved before for the erasure channel. We will generalize the stability condition to the class of Raptor codes. This generalization gives a lower bound on the fraction of output nodes of degree 2 of a Raptor code if the error probability of the belief-propagation decoder converges to zero. Using information-theoretic arguments, we will show that if a sequence of output degree distributions is to achieve the capacity of the underlying channel, then the fraction of nodes of degree 2 in these degree distributions has to converge to a certain quantity depending on the channel. For the class of erasure channels this quantity is independent of the erasure probability of the channel, but for many other classes of BIMSCs, this fraction depends on the particular channel chosen. This result has implications on the "universality" of Raptor codes for classes other than the class of erasure channels, in a sense that will be made more precise in the paper. We will also investigate the performance of specific Raptor codes which are optimized using a more exact version of the Gaussian approximation technique.     

A moment-based blind method for identification of FIR down-linkDS-CDMA channels

In order to achieve lower bit error rates (BERs), multiuser detection techniques have been proposed. Generally, multiuser detectors can provide excellent performance only when channel parameters are precisely known. In this paper, we propose a moment-based blind method to estimate down-link channels precisely. The mean square error (MSE) expression of the channel vector estimate has been derived. Through simulations, we show the effect of the channel estimation error on the performance of a multiuser detector. In this paper, we also show that finite impulse response (FIR) channels can be blindly identified by using the proposed method and the spreading operation. Since the spreading operation of the code division multiple access (CDMA) can induce cyclostationarity, any FIR channel can be identified by the proposed method. Of course, in order to guarantee identifiability, some conditions on the spreading codes will be satisfied. In this paper, these conditions are also found