Fading channels: information-theoretic and communications aspects

In this paper we review the most peculiar and interesting information-theoretic and communications features of fading channels. We first describe the statistical models of fading channels which are frequently used in the analysis and design of communication systems. Next, we focus on the information theory of fading channels, by emphasizing capacity as the most important performance measure. Both single-user and multiuser transmission are examined. Further, we describe how the structure of fading channels impacts code design, and finally overview equalization of fading multipath channels     

An information-theoretic framework for deriving canonical decision-feedback receivers in Gaussian channels

A framework is presented that allows a number of known results relating feedback equalization, linear prediction, and mutual information to be easily understood. A lossless, additive decomposition of mutual information in a general class of Gaussian channels is introduced and shown to produce an information-preserving canonical decision-feedback receiver. The approach is applied to intersymbol interference (ISI) channels to derive the well-known minimum mean-square error (MMSE) decision-feedback equalizer (DFE). When applied to the synchronous code-division multiple-access (CDMA) channel, the result is the MMSE (or signal-to-interference ratio (SIR) maximizing) decision-feedback detector, which is shown to achieve the channel sum-capacity at the vertices of the capacity region. Finally, in the case of the asynchronous CDMA channel we are able to give new connections between information theory, decision-feedback receivers, and structured factorizations of multivariate spectra.     

An information-theoretic view of network management

We present an information-theoretic framework for network management for recovery from nonergodic link failures. Building on recent work in the field of network coding, we describe the input-output relations of network nodes in terms of network codes. This very general concept of network behavior as a code provides a way to quantify essential management information as that needed to switch among different codes (behaviors) for different failure scenarios. We compare two types of recovery schemes, receiver-based and network-wide, and consider two formulations for quantifying network management. The first is a centralized formulation where network behavior is described by an overall code determining the behavior of every node, and the management requirement is taken as the logarithm of the number of such codes that the network may switch among. For this formulation, we give bounds, many of which are tight, on management requirements for various network connection problems in terms of basic parameters such as the number of source processes and the number of links in a minimum source-receiver cut. Our results include a lower bound for arbitrary connections and an upper bound for multitransmitter multicast connections, for linear receiver-based and network-wide recovery from all single link failures. The second is a node-based formulation where the management requirement is taken as the sum over all nodes of the logarithm of the number of different behaviors for each node. We show that the minimum node-based requirement for failures of links adjacent to a single receiver is achieved with receiver-based schemes.     

Uniform power allocation in MIMO channels: a game-theoretic approach

When transmitting over multiple-input-multiple-output (MIMO) channels, there are additional degrees of freedom with respect to single-input-single-output (SISO) channels: the distribution of the available power over the transmit dimensions. If channel state information (CSI) is available, the optimum solution is well known and is based on diagonalizing the channel matrix and then distributing the power over the channel eigenmodes in a "water-filling" fashion. When CSI is not available at the transmitter, but the channel statistics are a priori known, an optimal fixed power allocation can be precomputed. This paper considers the case in which not even the channel statistics are available, obtaining a robust solution under channel uncertainty by formulating the problem within a game-theoretic framework. The payoff function of the game is the mutual information and the players are the transmitter and a malicious nature. The problem turns out to be the characterization of the capacity of a compound channel which is mathematically formulated as a maximin problem. The uniform power allocation is obtained as a robust solution (under a mild isotropy condition). The loss incurred by the uniform distribution is assessed using the duality gap concept from convex optimization theory. Interestingly, the robustness of the uniform power allocation also holds for the more general case of the multiple-access channel.     

An information-theoretic analysis of cutaneous receptor responses

Two prevalent underlying assumptions related to cutaneous receptor research are that receptor responses are conditionally independent given the stimulus, and that stimulus information is encoded through a mean rate code. In this paper, an information-theoretic technique that can be used to test these assumptions is developed and presented. Results are presented from experiments designed to evaluate the efficiency of mean rate codes and the independence of receptor discharges recorded from cutaneous receptor afferent neurons.     

An information-theoretic proof of Burg's maximum entropy spectrum

It is known that the maximum entropy stationary Gaussian stochastic process, subject to a finite number of autocorrelation constraints, is the Gauss-Markov process of appropriate order. The associated spectrum is Burg's maximum entropy spectral density. We pose a somewhat broader entropy maximization problem, in which stationarity and normality are not assumed, and shift the burden of proof from the previous focus on the calculus of variations and time series techniques to a string of information-theoretic inequalities. This results in an elementary proof of greater generality.     

Robust decoding for timing channels

To transmit information by timing arrivals to a single-server queue, we consider using the exponential server channel's maximum likelihood decoder. For any server with service times that are stationary and ergodic with mean 1/μ seconds, we show that the rate e ^-1μ nats per second (capacity of the exponential server timing channel) is achievable using this decoder. We show that a similar result holds for the timing channel with feedback. We also show that if the server jams communication by adding an arbitrary amount of time to the nominal service time, then the rate e^-1μ₁μ₂/(μ₁+μ ₂) nats per second is achievable with random codes, where the nominal service times are stationary and ergodic with mean 1/μ₁ seconds, and the arithmetic mean of the delays added by the server does not exceed 1/μ₂ seconds. This is a model of an arbitrarily varying channel where the current delay and the current input can affect future outputs. We also show the counterpart of these results for single-server discrete-time queues     

A formal model for proving hardware timing properties and identifying timing channels

Timing channels are becoming a critical threat to hardware security. When exploited, secret information can be revealed by analyzing the execution time statistically. There are a variety of methods for detecting timing channels such as statistical analysis, testing and formal verification. However, existing methods cannot guarantee that the timing channels can be identified due to limited test coverage or high performance overhead. In this work, we introduce a novel model for evaluating timing variations of the hardware design. Furthermore, we propose a systematical solution that integrates time label enhanced tracking logic and formally verifies the timing invariant property of hardware designs in order to identify hardware timing channels. We demonstrate our solution on several hardware implementations, including arithmetic units, cryptographic cores and cache. The proof results show that our solution can detect hardware timing channels effectively.     

瑞利衰落信道下改进的OFDM符号定时算法

对相干OFDM系统中结合循环前缀和导频信息的传统符号定时同步算法进行了分析和研究,提出了一种改进的符号定时同步算法.此算法相对于传统算法由于更加有效的利用了观察样本信息,具有更大的定时同步范围.同时考虑时间偏移参数在若干OFDM符号区间内不变,给出了一种利用连续多个OFDM符号的算法,以提高定时同步的准确度.仿真验证了所提出算法在瑞利衰落信道下可以有效地改进传统算法的定时性能.     

NRZ timing recovery technique for band-limited channels

Nonreturn-to-zero (NRZ) data, when transmitted over band-limited channels, suffer from the lack of zero crossings because the elongated tail of each pulse interferes with subsequent ones, causing intersymbol interference (ISI). An NRZ timing recovery technique working with a decision-feedback equalizer (DFE) recovers the clock from the equalized waveform and enables data transmission at a rate ten times higher than the channel bandwidth. The proposed timing recovery technique uses a data-triggered low-jitter phase detector to sustain phase locking even with 600 missing transitions, A data rate of 30 Mb/s in 3-MHz bandwidth is demonstrated with a peak-peak clock jitter of 2 ns using 2-μm CMOS     

Gait probability image: An information-theoretic model of gait representation

In this paper, we propose a new probabilistic gait representation to characterize human walking for recognition by gait. The approach obtains the binomial distribution of every pixel in a gait cycle. Organizing the binomial distribution of all pixels in the gait image, we obtain the gait signature, which we denote as the Gait Probability Image (GPI). In the recognition stage, symmetric Kullback–Leibler divergence is used to measure the information theoretical distance between gait signatures. The experimental results reveal that GPI achieves promising recognition rates. Besides that, experiments on different walking speeds demonstrate that GPI is robust to slight variation in walking speed.     

An information-theoretic framework for field monitoring using autonomously mobile sensors

We consider a mobile sensor network monitoring a spatio-temporal field. Given limited caches at the sensor nodes, the goal is to develop a distributed cache management algorithm to efficiently answer queries with a known probability distribution over the spatial dimension. First, we propose a novel distributed information theoretic approach assuming knowledge of the distribution of the monitored phenomenon. Under this scheme, nodes minimize an entropic utility function that captures the average amount of uncertainty in queries given the probability distribution of query locations. Second, we propose a correlation-based technique, which only requires knowledge of the second-order statistics, relaxing the stringent constraint of a priori knowledge of the query distribution, while significantly reducing the computational overhead. We show that the proposed approaches considerably improve the average field estimation error. Further, we show that the correlation-based technique is robust to model mismatch in case of imperfect knowledge of the underlying generative correlation structure.     

An information-theoretic approach for design and analysis ofrooted-tree-based multicast key management schemes

Previous literature presents several seemingly different approaches to rooted-tree-based multicast key distribution schemes that try to minimize the user key storage while providing efficient member deletion. In this paper, we show that the user key storage on rooted trees can be systematically studied using basic concepts from information theory. We show that the rooted-tree-based multicast key distribution problem can be posed as an optimization problem that is abstractly identical to the optimal codeword length selection problem in information theory. In particular, we show that the entropy of member deletion statistics quantifies the optimal value of the average number of keys to be assigned to a member. We relate the sustainable key length to statistics of member deletion event and the hardware bit generation rate. We then demonstrate the difference between the key distribution on rooted trees and the optimal codeword length selection problem with an example of a key distribution scheme that attains optimality but fails to prevent user collusion     

Coarse recovery of carrier frequency and symbol timing in multibeam satellite channels

A multibeam concept under full frequency reuse is a major prerequisite for high throughput satellite systems. The resulting interference problems might be tackled by appropriately designed precoding or multiuser detection schemes. However, before such powerful techniques are applicable, the most important transmission parameters have to be recovered successfully. In the context of this paper, a feedback structure for joint control of carrier frequency and symbol timing is investigated for a multibeam scenario, which has been developed in some previous work by the authors for a single user link. It is to be noticed that we describe a recovery method for a multibeam satellite network with suitably selected interference mitigation techniques; as a consequence, all cochannels are assumed to be aligned in frequency and time to the reference beam; other signal models are out of scope and not addressed in this contribution.     

Code timing acquisition for DS-CDMA in fading channels bydifferential correlations

We propose simple and efficient algorithms for the code timing acquisition in the direct-sequence code-division multiple-access communication system. The essential assumption is that a preamble or an unmodulated pilot channel is available for the desired user. Then the correlation matrix R(τ) of the sampled data, where τ is suitably chosen time lag, contains the timing information only of desired user, while the contributions of uncorrelated interferers and noise are suppressed out. Hence, compared to the conventional approach, more interference suppression is achieved. Coarse delay estimates are then obtained by a matched filter (MF) or multiple signal classification-type approaches. In the latter case, only L eigenvectors are computed, where L is the number of resolvable paths. If only one path exists, an additional procedure is proposed to both approaches, by which the estimation accuracy is greatly improved with negligible increase in computation. More precisely, the chip timing offset due to chip-asynchronous sampling can be determined by solving a system of two second-order polynomials for each chip interval. Therefore, only at most 2C hypotheses are needed, where C is the processing gain. All the proposed methods are computationally quite simple, containing mainly MF-operations, or at most computation of only few eigenvectors. Mean acquisition time analysis is carried out semi-analytically. Numerical experiments speaks for the possibility of achieving significant performance gains compared to conventional acquisition, especially in the presence of strong multiple-access interference, making them attractive options to be attached for the next generation mobile receivers     

The information-theoretic capacity of discrete-time queues

The information-theoretic capacity of continuous-time queues was analyzed recently by Anantharam and Verdu (see ibid. vol.42, p.4-18, 1996). Along similar lines, we analyze the information-theoretic capacity of two models of discrete-time queues. The first model has single packet arrivals and departures in a time slot and independent packet service times, and is the discrete-time analog of the continuous-time model analyzed by Anantharam and Verdu. We show that in this model, the geometric service time distribution plays a role analogous to that of the exponential distribution in continuous-time queues, in that, among all queues in this model with a given mean service time, the queue with geometric service time distribution has the least capacity. The second model allows multiple arrivals in each slot, and the queue is modeled as serving an independent random number of packets in each slot. We obtain upper and lower bounds on the capacity of queues with an arbitrary service distribution within this model, and show that the bounds coincide in the case of the queue that serves a geometrically distributed number of packets in each slot. We also discuss the extremal nature of the geometric service distribution within this model     

An information-theoretic approach to spectral variability,similarity, and discrimination for hyperspectral image analysis

A hyperspectral image can be considered as an image cube where the third dimension is the spectral domain represented by hundreds of spectral wavelengths. As a result, a hyperspectral image pixel is actually a column vector with dimension equal to the number of spectral bands and contains valuable spectral information that can be used to account for pixel variability, similarity and discrimination. We present a new hyperspectral measure, the spectral information measure (SIM), to describe spectral variability and two criteria, spectral information divergence and spectral discriminatory probability for spectral similarity and discrimination, respectively. The spectral information measure is an information-theoretic measure which treats each pixel as a random variable using its spectral signature histogram as the desired probability distribution. Spectral information divergence (SID) compares the similarity between two pixels by measuring the probabilistic discrepancy between two corresponding spectral signatures. The spectral discriminatory probability calculates spectral probabilities of a spectral database (library) relative to a pixel to be identified so as to achieve material identification. In order to compare the discriminatory power of one spectral measure relative to another, a criterion is also introduced for performance evaluation, which is based on the power of discriminating one pixel from another relative to a reference pixel. The experimental results demonstrate that the new hyperspectral measure can characterize spectral variability more effectively than the commonly used spectral angle mapper (SAM)     

A Bayesian maximum-likelihood sequence estimation algorithm for apriori unknown channels and symbol timing

It is shown that the optimum demodulator for the case of an a priori unknown channel and symbol timing can be approximated using a modified Viterbi algorithm (VA), in which the branch metrics are obtained from the conditional innovations of a bank of extended Kalman filters (EKFs). Each EKF computes channel and timing estimates conditioned on one of the survivor sequences in the trellis. It is also shown that the minimum-variance channel and timing estimates can be approximated by a sum of conditional EKF estimates, weighted by the VA metrics. Simulated bit error rate (BER) results and averaged-squared channel/timing error trajectories are presented, with estimation errors compared to the Cramer-Rao lower bound. The BER performance of the modified VA is also shown to be superior to that obtained using a decision-directed channel/timing estimation algorithm     

宽带无线信道精细时延和响应联合估计方法

研究适用于无线信道测量的定时偏移和信道联合估计方法.发射机发送具有循环前缀结构的导频信号段.接收机根据粗同步信号确定快速傅里叶变换的窗口起始位置.利用改进时域最小二乘信道估计和变换域滤波,获得高精度的信道估计值.对频域接收导频信号段的定时偏移进行精细估计,对定时偏移量进行滤波并累加.最后,对频域接收导频信号段进行定时偏移补偿.信道估计器、定时延迟偏移精细估计器与补偿单元三者构成迭代相干延迟锁定环路.仿真结果表明：采用迭代相干联合估计方法进行精细定时延迟估计的性能明显优于非相干方法.     

An information-theoretic criterion for intrasubject alignment of FMRI time series: motion corrected independent component analysis

A three-dimensional image registration method for motion correction of functional magnetic resonance imaging (fMRI) time-series, based on independent component analysis (ICA), is described. We argue that movement during fMRI data acquisition results in a simultaneous increase in the joint entropy of the observed time-series and a decrease in the joint entropy of a nonlinear function of the derived spatially independent components calculated by ICA. We propose this entropy difference as a reliable criterion for motion correction and refer to a method that maximizes this as motion-corrected ICA (MCICA). Specifically, a given motion-corrupted volume may be corrected by determining the linear combination of spatial transformations of the motion-corrupted volume that maximizes the proposed criterion. In essence, MCICA consists of designing an adaptive spatial resampling filter which maintains maximum temporal independence among the recovered components. In contrast with conventional registration methods, MCICA does not require registration of motion-corrupted volumes to a single reference volume which can introduce artifacts because corrections are applied without accounting for variability due to the task-related activation. Simulations demonstrate that MCICA is robust to activation level, additive noise, random motion in the reference volumes and the exact number of independent components extracted. When the method was applied to real data with minimal estimated motion, the method had little effect and, hence, did not introduce spurious changes in the data. However, in a data series from a motor fMRI experiment with larger motion, preprocessing the data with the proposed method resulted in the emergence of activation in primary motor and supplementary motor cortices. Although mutual information (MI) was not explicitly optimized, the MI between all subsequent volumes and the first one was consistently increased for all volumes after preprocessing the data with MCICA. We suggest MCICA represents a robust and reliable method for preprocessing of fMRI time-series corrupted with motion.