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     

On the performance of data receivers with a restricted detectiondelay

It is well known that the performance of a data receiver for an intersymbol interference (ISI) channel can depend strongly on the detection delay δ. For a discrete-time communication system, this paper derives a lower bound on the bit-error probability as a function of δ. This “restricted delay bound” is governed by a “restricted-delay distance” d(δ). In many instances, it improves upon Forney's (1972) bound, which is governed by the minimum distance d_min. For instance, for partial-response channels, d(δ) does not converge to d_min even as δ→∞. For channels without spectral zeros, a finite detection delay suffices for d(S) to coincide with d_min. For all finite δ, d(δ) is determined by a finite number of error patterns and may be computed in a straightforward manner. Unlike d_min, d(δ) depends on the phase characteristics of the channel. Minimum phase is proved to maximize d(δ). The lower bound is generalized to discrete-time channels with colored noise and to continuous-time channels. The effect of transforming a continuous-time channel into a discrete-time channel is discussed. Transformation via a matched filter, as in the ISI canceller and a Viterbi detector due to Ungerboeck and MacKechnie (1973), is shown to result in poor restricted-delay properties. Implications of these results are illustrated by means of examples     

一种新的两用户协作分集方案及其性能研究

该文提出了一种基于信道编码和分布式空时分组码级联下的两用户协作分集方案,并且在准静态的瑞利衰落信道下对此方案的系统容量,中断概率以及误比特率进行了理论推导和系统仿真,分别给出了解析表达式和数值结果。通过将信道编码和空时码引入到协作分集中,系统容量得到显著改善,同时中断概率也明显降低。在协作用户间信道存在噪声的情况下,对卷积码与分布式空时分组码级联下的发射方案进行了性能分析和仿真。仿真结果表明：即使协作用户间的信道存在噪声,该文所提方案在各方面都优于传统协作分集,系统容量明显增大,中断概率及误比特率大大降低。     

A simple derivation of the coding theorem and some applications

Upper bounds are derived on the probability of error that can be achieved by using block codes on general time-discrete memoryless channels. Both amplitude-discrete and amplitude-continuous channels are treated, both with and without input constraints. The major advantages of the present approach are the simplicity of the derivations and the relative simplicity of the results; on the other hand, the exponential behavior of the bounds with block length is the best known for all transmission rates between0and capacity. The results are applied to a number of special channels, including the binary symmetric channel and the additive Gaussian noise channel.     

Efficient reconstruction of sequences

We introduce and solve some new problems of efficient reconstruction of an unknown sequence from its versions distorted by errors of a certain type. These erroneous versions are considered as outputs of repeated transmissions over a channel, either a combinatorial channel defined by the maximum number of permissible errors of a given type, or a discrete memoryless channel. We are interested in the smallest N such that N erroneous versions always suffice to reconstruct a sequence of length n, either exactly or with a preset accuracy and/or with a given probability. We are also interested in simple reconstruction algorithms. Complete solutions for combinatorial channels with some types of errors of interest in coding theory, namely, substitutions, transpositions, deletions, and insertions of symbols are given. For these cases, simple reconstruction algorithms based on majority and threshold principles and their nontrivial combination are found. In general, for combinatorial channels the considered problem is reduced to a new problem of reconstructing a vertex of an arbitrary graph with the help of the minimum number of vertices in its metrical ball of a given radius. A certain sufficient condition for solution of this problem is presented. For a discrete memoryless channel, the asymptotic behavior of the minimum number of repeated transmissions which are sufficient to reconstruct any sequence of length n within Hamming distance d with error probability ϵ is found when d/n and ϵ tend to 0 as n→∞. A similar result for the continuous channel with discrete time and additive Gaussian noise is also obtained     

Reliable flow with failures in a network

In communication networks, there is a growing need for ensuring that networks maintain service despite failures. To meet this need, the concept of a δ-reliable channel is introduced; it is a set of communication channels along a set of paths. The δ-reliable channel meets the requirement that if a link or node fails, failure is limited to a maximum of δ·c (c≡total capacity of the channels, and 0<δ⩽1). A δ-reliable flow is such that the maximum number of flow failures is δ·f (f≡value of the flow) if an edge or vertex of a network fails. The max-flow min-cut theorem of δ-reliable flow is demonstrated for the single-commodity case     

Composition bounds for channel block codes

The performance of Channel block codes for a general channel is studied by examining the relationship between the rate of a code, the joint composition of pairs of codewords, and the probability of decoding error. At fixed rate, lower bounds and upper bounds, both on minimum Bhattacharyya distance between codewords and on minimum equivocation distance between codewords, are derived. These bounds resemble, respectively, the Gilbert and the Elias bounds on the minimum Hamming distance between codewords. For a certain large class of channels, a lower bound on probability of decoding error for low-rate channel codes is derived as a consequence of the upper bound on Bhattacharyya distance. This bound is always asymptotically tight at zero rate. Further, for some channels, it is asymptotically tighter than the straight line bound at low rates. Also studied is the relationship between the bounds on codeword composition for arbitrary alphabets and the expurgated bound for arbitrary channels having zero error capacity equal to zero. In particular, it is shown that the expurgated reliability-rate function for blocks of letters is achieved by a product distribution whenever it is achieved by a block probability distribution with strictly positive components.     

A coding theorem for a class of unknown channels

We consider the problem of communication over a channel which is selected 1) in a fashion unknown to the communicator, 2) as a function of past history, 3) from a given set of discrete memoryless channels, and 4) for the purpose of maximizing the degradation in performance. An upperbound on error probability insurable with block coding is obtained which exponentially approaches zero with block length for rates less than capacity. Techniques for the communicator to achieve these results are considered. The design of relatively simple communication techniques for channels with memory and jammed channels are discussed.     

A Study on Universal Codes With Finite Block Lengths

Based on random codes and typical set decoding, an alternative proof of Root and Varaiya's compound channel coding theorem for linear Gaussian channels is presented. The performance limit of codes with finite block length under a compound channel is studied through error bounds and simulation. Although the theorem promises uniform convergence of the probability of error as the block length approaches infinity, with short block lengths the performance can differ considerably for individual channels. Simulation results show that universal performance can be a practical goal as the block lengths become large.     

Performance analysis of orthogonal space-time block codes in spatially correlated MIMO Nakagami fading channels

Orthogonal space-time block coding (STBC) is an open-loop transmit diversity scheme that decouples the multiple-input multiple-output (MIMO) channel, thereby reducing the space-time decoding into a scalar detection process. This characteristic of STBC makes it a powerful tool, achieving full diversity over MIMO fading channels, and requiring little computational cost for both the encoding and decoding processes. In this paper, we exploit the single-input single-output equivalency of STBC in order to analyze its performance over nonselective Nakagami fading channels in the presence of spatial fading correlation. More specifically, we derive exact closed-form expressions for the outage probability and ergodic capacity of STBC, when the latter is employed over spatially correlated MIMO Nakagami fading channels. Moreover, we derive the exact symbol error probability of coherent M-PSK and M-QAM, when these modulation schemes are used along with STBC over such fading channels. The derived formulae are then used to assess the robustness of STBC to spatial correlation by considering general MIMO correlation models and analyzing their effects on the outage probability, ergodic capacity, and symbol error probability achieved by STBC.     

Coding theorems for the nonsynchronized channel

Capacity and error bounds are derived for a memoryless binary symmetric channel with the receiver having no a priori information as to the starting time of the code words. The channel capacity is the same as the capacity of the synchronized channel. For all rates below capacity, the minimum probability of error for the nonsynchronized channel decreases exponentially with the code-block length. For rates near channel capacity, the exponent in the upper bound on the probability of error for the nonsynchronized channel is the same as the corresponding exponent for the synchronized channel. For low rates, the largest exponent obtained for the nonsynchronized channel with conventional block coding is inferior to the exponent obtained for the synchronized channel. Stronger results are obtained for a new form of coding that allows for a Markov dependency between successive code words. Bounds on the minimum probability of error are obtained for unconstrained binary codes and for several classes of parity-check codes and are used to obtain asymptotic distance properties for various classes of binary codes. At certain rates there exist codes whose minimum distance, in the comma-free sense, is not only greater than one, but is proportional to the block length.     

On the robustness of space-time coding techniques based on a general space-time covariance model

The robustness of space-time coding techniques for wireless channels that exhibit both temporal and spatial correlation is investigated. A general space-time covariance model is developed and employed to evaluate the exact pairwise error probability for space-time block codes. The expressions developed for the pairwise error probability are used in conjunction with the union bound to determine an upper bound for the probability of a block error. The block error probability is evaluated for several space-time codes and for wireless channels that exhibit varying degrees of spatial and temporal correlation. Numerical results are presented for a two-dimensional Gaussian scatterer model which has been shown to be consistent with recent field measurements of wireless channels. The results demonstrate that the best-case wireless channel is uncorrelated in both space and time. Correlation between transmission paths, due to insufficient spacing of the transmit antennas or scatterers located in close proximity to the mobile, can result in a significant performance degradation. The conditions that result in uncorrelated transmission paths are quantified in terms of the effective scattering radius and the spacing of the transmit and receive antennas.     

Outage Capacity Optimization for Free-Space Optical Links With Pointing Errors

We investigate the performance and design of free-space optical (FSO) communication links over slow fading channels from an information theory perspective. A statistical model for the optical intensity fluctuation at the receiver due to the combined effects of atmospheric turbulence and pointing errors is derived. Unlike earlier work, our model considers the effect of beam width, detector size, and jitter variance explicitly. Expressions for the outage probability are derived for a variety of atmospheric conditions. For given weather and misalignment conditions, the beam width is optimized to maximize the channel capacity subject to outage. Large gains in achievable rate are realized versus using a nominal beam width. In light fog, by optimizing the beam width, the achievable rate is increased by 80% over the nominal beam width at an outage probability of 10^-5. Well-known error control codes are then applied to the channel and shown to realize much of the achievable gains.     

δ-NARMA neural networks: a new approach to signal prediction

This paper presents a new connectionist architecture for stochastic univariate signal prediction. After a review of related statistical and connectionist models pointing out their advantages and limitations, we introduce the ϵ-NARMA model as the simplest nonlinear extension of ARMA models. These models then provide the units of a MLP-like neural network: the δ-NARMA neural network. The associated learning algorithm is based on an extension of classical backpropagation and on the concept of virtual error. Such networks can be seen as an extension of ARIMA and ARARMA models and face the problem of nonstationary signal prediction. A theoretical study brings understanding of experimental phenomena observed during the δ-NARMA learning process. The experiments carried out on three railroad-related real-life signals suggest that δ-NARMA networks outperform other studied univariate models     

Exponential error bounds for incoherent orthogonal signals (Corresp.)

It is well known that arbitrarily small error probabilities can be obtained at any source rate less than capacity for the band-infinite Gaussian channel by block coding binary digits into either coherent or incoherent orthogonal signals. In this correspondence it is shown that the exponential rate at which the error probability approaches zero with increasing block length is the same for the coherent and incoherent orthogonal signals for any source rate less than channel capacity.     

An optimal scheduling and routing under adaptive spectrum-matching framework for MIMO systems

Multi-users (MUs) along the communication links cause noise and traffic in the channel. The prediction of availability and the optimal usage of channels are the main objectives of the multi-input multi-output (MIMO) system. Several optimisation algorithms select the optimal channel for the users effectively. But the high-error rate and the probability values are the two major problems in traditionally optimised channel selection methods. The bandwidth allotted for information transmission is minimum. Moreover, the outage probability values are maximum in traditional scheduling algorithms. This paper proposes the new optimisation algorithm that predicts the channels for transmission and adaptive spectrum matching concept to predict the suitable channel from allocated bands. Also, the prioritisation on high-spectrum intensity basis assures an efficient data delivery to the receiver. The scheduling of available channels and data prioritisation minimises the error probability rates. This paper investigates the effectiveness of proposed optimal channel utilisation against the different modulation schemes such as three-dimensional complementary codes, linear network coding with the quadrature phase shift keying in terms of the average block error probability and bit error rate.     

Coding for a class of unknown channels

A channel which is selected for each use (without knowledge of past history) to be one of a given set of discrete memoryless channels is to be used by an ignorant communicator, i.e., the transmitter and receiver are assumed to have no knowledge of the particular channels selected. For this situation an upper bound on the insurable average error probability for block codes of length n is obtained which exponentially approaches zero for all rates less than capacity. Communication design techniques for achieving these results are discussed.     

On the undetected error probability of nonlinear binary constantweight codes

The undetected error probability (UEP) of binary (n, 2δ, m) nonlinear constant weight codes over the binary symmetric channel (BSC) is investigated, where n is the blocklength, m is the weight of codeword and 2δ is the minimum distance of the codes. The distance distribution of the (n, 2, m) nonlinear constant weight codes is evaluated. It is proven in this paper that the (5, 2, 2) code, (5, 2, 3) code, (6, 2, 3) code, (7, 2, 4) code, (7, 2, 3) code and (8, 2, 4) code are the only proper error-detecting codes in the (n, 2, m) nonlinear constant weight codes for n⩾5, in the sense that their UEP is increased monotonically with the channel error rate p, of course all these proper codes are m-out-of-n codes. Furthermore, it is conjectured that except for the cases of n⩽4δ, there are no proper error-detecting binary (n, 2δ, m) nonlinear constant weight codes, for n>8 and δ⩾1     

Error probability of coded STBC systems in block fading environments

In this letter, a union bound on the error probability of coded multi-antenna systems over block fading channels is derived. The bound is based on uniform interleaving of the coded sequence prior to transmission over the channel. Using this argument the distribution of error bits over the fading blocks is computed and the corresponding pair wise error probability (PEP) is derived. We consider coded systems that concatenate a binary code with a space-time block code (STBC). Coherent detection is assumed with perfect and imperfect channel state information (CSI) at the receiver, where imperfect CSI is obtained using pilot-aided estimation. Under channel estimation environments, the tradeoff between channel diversity and channel estimation is investigated and the optimal channel memory is approximated analytically. Results show that the performance degradation due to channel memory decreases as the number of transmit antennas is increased. Moreover, the optimal channel memory increases with increasing the number of transmit antennas.