Capacity With Causal and Noncausal Side Information: A Unified View

In this correspondence, we identify the common underlying form of the capacity expression that is applicable to both cases where causal or noncausal side information is made available to the transmitter. A genie-aided outerbound is developed that states that when a genie provides n bits of side information to a receiver the resulting capacity improvement cannot be more than n bits. Using the genie-bound we are able to bound the relative capacity advantage of noncausal side information over causal side information for both the single user point-to-point channel as well as the multiple-access channel (MAC) with independent side information at the transmitters. Applications of these capacity bounds are demonstrated through examples of random access channels. Interestingly, the capacity results indicate that the excessive MAC layer overheads common in present wireless systems may be avoided through coding across multiple-access blocks. It is also shown that even one bit of side information at the transmitter can result in unbounded capacity improvement     

Capacity and Random-Coding Exponents for Channel Coding With Side Information

Capacity formulas and random-coding exponents are derived for a generalized family of Gel'fand-Pinsker coding problems. These exponents yield asymptotic upper bounds on the achievable log probability of error. In our model, information is to be reliably transmitted through a noisy channel with finite input and output alphabets and random state sequence, and the channel is selected by a hypothetical adversary. Partial information about the state sequence is available to the encoder, adversary, and decoder. The design of the transmitter is subject to a cost constraint. Two families of channels are considered: 1) compound discrete memoryless channels (CDMC), and 2) channels with arbitrary memory, subject to an additive cost constraint, or more generally, to a hard constraint on the conditional type of the channel output given the input. Both problems are closely connected. The random-coding exponent is achieved using a stacked binning scheme and a maximum penalized mutual information decoder, which may be thought of as an empirical generalized maximum a posteriori decoder. For channels with arbitrary memory, the random-coding exponents are larger than their CDMC counterparts. Applications of this study include watermarking, data hiding, communication in presence of partially known interferers, and problems such as broadcast channels, all of which involve the fundamental idea of binning     

On the Capacity of Time-Varying Channels With Periodic Feedback

The capacity of time-varying channels with periodic feedback at the transmitter is evaluated. It is assumed that the channel-state information (CSI) is perfectly known at the receiver and is fed back to the transmitter at the regular time intervals. The system capacity is investigated in two cases: 1) finite-state Markov channel, and 2) additive white Gaussian noise channel with time-correlated fading. In the first case, it is shown that the capacity is achievable by multiplexing multiple codebooks across the channel. In the second case, the channel capacity and the optimal adaptive coding is obtained. It is shown that the optimal adaptation can be achieved by a single Gaussian codebook, while adaptively allocating the total power based on the side information at the transmitter.     

Capacity Analysis for Continuous Alphabet Channels With Side Information, Part II: MIMO Channels

In this second part of our two-part paper, we consider the capacity analysis for wireless mobile systems with multiple-antenna architectures. We apply the results of the first part to a commonly known baseband, discrete-time multiple-antenna system where both the transmitter and receiver know the channel's statistical law. We analyze the capacity for additive white Gaussian noise (AWGN) channels, fading channels with full channel state information (CSI) at the receiver, fading channels with no CSI, and fading channels with partial CSI at the receiver. For each type of channels, we study the capacity value as well as issues such as the existence, uniqueness, and characterization of the capacity-achieving measures for different types of moment constraints. The results are applicable to both Rayleigh and Rician fading channels in the presence of arbitrary line-of-sight and correlation profiles.     

Multiple-Antenna Signaling Over Fading Channels With Estimated Channel State Information: Capacity Analysis

Multiple-antenna concepts for wireless communication systems promise high spectral efficiencies and improved error rate performance by proper exploitation of the randomness in multipath propagation. In this paper, we investigate the impact of channel uncertainty caused by channel estimation errors on the capacity of Rayleigh and Ricean block-fading channels. We consider a training-based multiple-antenna system that reserves a portion of time to sound the channel. The training symbols are used to estimate the channel state information (CSI) at the receiver by means of an arbitrary linear estimation filter. No CSI is assumed at the transmitter. Our analysis is based on an equivalent system model for training-based multiple-antenna systems which specifies the channel by the estimated (and hence, known) channel coefficients and an uncorrelated, data-dependent, multiplicative noise. This model includes the special cases of perfect CSI and no CSI. We present new upper and lower bounds on the maximum instantaneous mutual information to compute ergodic and outage capacities, and extend previous results to arbitrary (and possibly mismatched) linear channel estimators and to correlated Ricean fading. Several numerical results for single- and multiple-antenna systems with estimated CSI are included as illustration.     

Capacity Analysis for Continuous-Alphabet Channels With Side Information, Part I: A General Framework

Capacity analysis for channels with side information at the receiver has been an active area of interest. This problem is well investigated for the case of finite-alphabet channels. However, the results are not easily generalizable to the case of continuous-alphabet channels due to analytical difficulties inherent with continuous alphabets. In the first part of this two-part paper, we address an analytical framework for capacity analysis of continuous alphabet channels with side information at the receiver. For this purpose, we establish novel necessary and sufficient conditions for weak* continuity and strict concavity of the mutual information. These conditions are used in investigating the existence and uniqueness of the capacity-achieving measures. Furthermore, we derive necessary and sufficient conditions that characterize the capacity value and the capacity-achieving measure for continuous-alphabet channels with side information at the receiver.     

接收机准确估计信道条件下MIMO系统的信道容量分析

文中考虑独立Rayleigh衰落环境下的单用户点对点多输入多输出系统,假定接收端能准确估计信道状态信息,推导出系统的容量公式,相比单天线系统,多天线系统能取得更大的容量,当输入信号是高斯分布时,系统容量随着发射天线和接收天线数目的最小值线性增加,如果发送端完全知道信道状态信息,采用注水原理的功率分配策略,可以获得更高的容量增益,最后推导出各态历经容量的数学表达式.     

LDPC Codes for Flat Rayleigh Fading Channels with Channel Side Information

In this paper, we design capacity approaching lowdensity parity-check (LDPC) codes in the low signal-to-noise ratio (SNR) regime for flat Rayleigh fading channels with channel side information at transmitter and receiver. We use the structure advocated by Caire et al, which uses a single codebook with dynamic power allocation. The extrinsic information transfer (EXIT) function method is used to design the LDPC codes which approach the channel capacities.We also study the EXIT function properties of various demappers.     

快时变环境下OFDM系统中的信道估计

在OFDM系统中,怎样对快时变信道进行较为准确的估计是一个具有挑战性的课题。该文在利用信道基扩展模型的基础上,提出了一种适合于快时变环境下OFDM系统的信道估计方法,并且依据使估计的均方误差最小的准则,推导了相应最优的导频序列,包括最优的导频取值和最优的导频分布。可以证明,最优的导频序列是由一些相邻的等间隔等能量的子序列构成,每个子序列的导频之间满足一定的相位关系。仿真结果表明了所提估计算法在快时变环境下的有效性和采用所推导的最优导频序列进行估计的优越性。     

On the Expected Rate of Slowly Fading Channels With Quantized Side Information

We study a multiple-layer variable-rate system employing quantized feedback to maximize the expected rate over a single-input single-output slowly fading Gaussian channel. The transmitter uses partial channel-state information, which is obtained via an optimized resolution-constrained feedback link, to adapt the power and to assign code layer rates, subject to different power constraints. To systematically design the system parameters, we develop a simple iterative algorithm that successfully exploits results in the study of parallel broadcast channels. We present the necessary and sufficient conditions for single-layer coding to be optimal, irrespective of the number of code layers that the system can afford. Unlike in the ergodic case, even coarsely quantized feedback is shown to improve the expected rate considerably. Our results also indicate that with as little as one bit of feedback information, the role of multilayer coding reduces significantly     

Zero-Error Source–Channel Coding With Side Information

This correspondence presents a novel application of the theta function defined by Lovasz. The problem of coding for transmission of a source through a channel without error when the receiver has side information about the source is analyzed. Using properties of the Lovasz theta function, it is shown that separate source and channel coding is asymptotically suboptimal in general. By contrast, in the case of vanishingly small probability of error, separate source and channel coding is known to be asymptotically optimal. For the zero-error case, it is further shown that the joint coding gain can in fact be unbounded. Since separate coding simplifies code design and use, conditions on sources and channels for the optimality of separate coding are also derived     

On Information Rates of Time-Varying Fading Channels Modeled as Finite-State Markov Channels

We study information rates of time-varying flatfading channels (FFC) modeled as finite-state Markov channels (FSMC). FSMCs have two main applications for FFCs: modeling channel error bursts and decoding at the receiver. Our main finding in the first application is that receiver observation noise can more adversely affect higher-order FSMCs than lower-order FSMCs, resulting in lower capacities. This is despite the fact that the underlying higher-order FFC and its corresponding FSMC are more predictable. Numerical analysis shows that at low to medium SNR conditions (SNR ≲12 dB) and at medium to fast normalized fading rates (0.01 ≲fDT ≲0.10), FSMC information rates are non-increasing functions of memory order. We conclude that BERs obtained by low-order FSMC modeling can provide optimistic results. To explain the capacity behavior, we present a methodology that enables analytical comparison of FSMC capacities with different memory orders. We establish sufficient conditions that predict higher/lower capacity of a reduced-order FSMC, compared to its original high-order FSMC counterpart. Finally, we investigate the achievable information rates in FSMC-based receivers for FFCs. We observe that high-order FSMC modeling at the receiver side results in a negligible information rate increase for normalized fading rates fDT ≲0.01.     

Multiple-Antenna Signaling Over Fading Channels With Estimated Channel State Information: Performance Analysis

Multiple-antenna concepts for wireless communication systems promise high spectral efficiency and low error rates by proper exploitation of the randomness in multipath propagation. In this paper, we investigate the impact of channel uncertainty caused by channel estimation errors on the error rate performance. We consider a training-based multiple-antenna system that reserves a portion of time to sound the channel. Training symbols are used to estimate the channel by means of an arbitrary linear filter at the receiver. No channel state information (CSI) is assumed at the transmitter. We present a new framework to analyze training-based multiple-antenna systems by introducing an equivalent system model that specifies the channel by the estimated (and hence, known) channel coefficients and an uncorrelated, data-dependent, multiplicative noise. We derive the maximum-likelihood (ML) detector and highlight its behavior in the limiting cases of perfect CSI and no CSI, and its relation to several mismatched detectors. We deduce new exact expressions and Chernoff bounds of the pairwise error probability (PEP) used to assess word-error and bit-error rate bounds for ML and mismatched detection. Finally, we review the code design guidelines in terms of the deleterious effect of channel uncertainty for coherent and noncoherent signaling schemes, and present numerical results.     

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。     

Least-Squares Channel Estimation for Mobile OFDM Communication on Time-Varying Frequency-Selective Fading Channels

A least-squares (LS) channel estimation (CE) technique for mobile orthogonal frequency-division multiplexing (OFDM) communications over a rapidly time-varying frequency-selective fading channel is investigated in this paper. The proposed technique keeping the comb-type pilot arrangement can achieve a low error probability by accurately estimating channel impulse response (CIR) and effectively tracking rapid CIR time variations. The LS CE technique proposed here is conducted in the time domain (TD). Meanwhile, a generic estimator is serially performed block by block without assistance from a priori channel information and without increasing computational complexity. By taking advantage of linearly frequency-modulated (LFM) or pseudorandom signals transceived for jointly sounding pilot subchannels, the proposed LS CE can inherently perform pseudonoise (PN) matched filtering (MF) to suppress multipath interference (MPI) caused by frequency-selective fading and intercarrier interference (ICI) resulting from data subchannels. The optimality of the proposed technique is verified by taking Cramer–Rao lower bounds (CRLBs) into comparison both on noise- and interference-dominant signal-to-noise ratio (SNR) conditions. In addition, the dual optimality of the LFM and PN pilot symbols is verified for both TD and frequency-domain (FD) CEs. Furthermore, the proposed technique also exhibits good resistance against residual timing errors occurring with the discrete Fourier transform (DFT) demodulation. Extensive computer simulations in conjunction with statistical derivations show the superiority of the proposed technique.      

Interference Channels With Common Information

In this paper, the interference channel with common information (ICC), in which two senders need deliver not only private messages but also certain common messages to their corresponding receivers, is investigated. An achievable rate region for such a channel is obtained by applying a superposition coding scheme that consists of successive encoding and simultaneous decoding. It is shown that the derived achievable rate region includes or extends several existing results for the interference channels with or without common information. The rate region is then specialized to a class of ICCs in which one sender has no private information to transmit, and a class of deterministic interference channels with common information (DICCs). In particular, the derived rate region is found to be the capacity region for this class of DICCs. Last, the achievable rate region derived for the discrete memoryless ICC is extended to the Gaussian case, in which a numerical example is provided to illustrate the improvement of our rate region over an existing result.     

Time and Frequency Synchronization with Channel Estimation for SC-FDMA Systems Over Time-Varying Channels

The constant amplitude zero autocorrelation sequence based synchronization and its usage in the block-type channel estimation for the single carrier frequency division multiple access (SC-FDMA) systems are vulnerable to the time-varying channels. Therefore, the channel estimation errors limit the performance of SC-FDMA systems in fast fading environments and result an irreducible error floor. In this paper, cyclic prefix based maximum likelihood estimator of time/frequency synchronization with comb-type channel estimation for the SC-FDMA systems are proposed to track the channel variations. Moreover, the residual time/frequency offsets calculations are derived for SC-FDMA systems. Simulation results confirm and illustrate that the proposed receiver is capable of tracking fast fading channel parameters and improving the overall performance as compared with the conventional receiver.     

Capacity of Interference Channels With Partial Transmitter Cooperation

Capacity regions are established for several two-sender, two-receiver channels with partial transmitter cooperation. First, the capacity regions are determined for compound multiple-access channels (MACs) with common information and compound MACs with conferencing. Next, two interference channel models are considered: an interference channel with common information (ICCI) and an interference channel with unidirectional cooperation (ICUC) in which the message sent by one of the encoders is known to the other encoder. The capacity regions of both of these channels are determined when there is strong interference, i.e., the interference is such that both receivers can decode all messages with no rate penalty. The resulting capacity regions coincide with the capacity region of the compound MAC with common information.     

Analysis of Multiple Antenna Systems With Finite-Rate Channel Information Feedback Over Spatially Correlated Fading Channels

This paper employs a high resolution quantization framework to study the effects of finite-rate quantization of the channel state information (CSI) on the performance of MISO systems over correlated fading channels. The contributions of this paper are twofold. First, as an application of the general distortion analysis, tight lower bounds on the capacity loss of correlated MISO systems due to the finite-rate channel quantization are provided. Closed-form expressions for the capacity loss in high-signal-to-noise ratio (SNR) and low-SNR regimes are also provided, and their analysis reveals that the capacity loss of correlated MISO channels is related to that of i.i.d. fading channels by a simple multiplicative factor which is given by the ratio of the geometric mean to the arithmetic mean of the eigenvalues of the channel covariance matrix. Second, this paper extends the general asymptotic distortion analysis to the important practical problem of suboptimal quantizers resulting from mismatches in the distortion functions, source statistics, and quantization criteria. As a specific application, two types of mismatched MISO CSI quantizers are investigated: quantizers whose codebooks are designed with minimum mean square error (MMSE) criterion but the distortion measure is the ergodic capacity loss (i.e., mismatched design criterion), and quantizers with codebook designed with a mismatched channel covariance matrix (i.e., mismatched statistics). Bounds on the channel capacity loss of the mismatched codebooks are provided and compared to that of the optimal quantizers. Finally, numerical and simulation results are presented and they confirm the tightness of theoretical distortion bounds.     

Capacity of the Trapdoor Channel With Feedback

We establish that the feedback capacity of the trapdoor channel is the logarithm of the golden ratio and provide a simple communication scheme that achieves capacity. As part of the analysis, we formulate a class of dynamic programs that characterize capacities of unifilar finite-state channels. The trapdoor channel is an instance that admits a simple closed-form solution.