Further Studies of Soft Decision Error Detectors for the Gaussian Channel

This correspondence is an extension of the work in [1] and [2]. We present two new classes of error detectors which utilize symbol reliability information (i.e., soft decision error detectors). First, a simple class of selectively single error correcting error detectors is discussed where the syndrome information is used and where just one single reliability number is compared to a threshold value. These error detectors are simpler than those in [1] and [2], but less powerful. Second, a class of soft decision error detectors with low probability of undetected errors is considered. The reliability information is used to reduce the probability of undetected errors without increasing the repeat request probability (compared to the hard decision error detector). Exponential properties for large signal-to-noise ratios and bounds are calculated for both classes of error detectors. Computer simulations are also presented.     

Reliability evaluation of human operators under stress

This paper presents five newly developed models to predict reliability of human operators performing time continous tasks under stress. Laplace transforms of state probability equations and operator reliability are developed. Mean time to human error (MTTHE) expressions are obtained. In addition specific plots are shown for selective models.     

On the interval reliability of systems modelled by finite semi-Markov processes

In this paper, semi-Markov models of repairable systems are considered whose finite state space is partitioned into two sets, the set of ‘up’ states, U, and the set of ‘down’ states, D. The focus of attention is the system's interval reliability which is defined as the probability of the system being in U throughout a given time interval [t, t + x] where t, x ε [0, +∞) are fixed. Two results in the Laplace transform domain are obtained for the interval reliability. The first one is a closed form expression for the double Laplace transform with respect to both variables t and x. The second result is concerned with a closed form expression of the (single) Laplace transform of the interval reliability with respect to the variable t under the additional assumption that the modelling semi-Markov process is Markovian on U. As an example, the semi-Markov model of a two-unit repairable system is considered. The steady-state behaviour of the system's interval reliability is examined by a Tauberian theorem.     

A Class of Soft Decision Error Detectors for the Gaussian Channel

The main idea of this concise paper is to use symbol reliability information for improving the performance of error detectors. A class of soft decision error detectors (SDED's) is presented, where low weight error patterns are selectively corrected. The reliability numbers govern which error pattern to correct. Asymptotic performance and bounds are derived for the Gaussian channel. It is shown that singleerror correcting SDED's without thresholds have an exponentially lower repeat request probability than the hard decision error detector, but the same exponent in the probability of undetected errors. Detectors with thresholds are also considered. In this case it is possible to contruct an error detector with both better probability of undetected errors and better probability of repeat request than for the hard decision error detector (HDED). Bounds and computer simulations are presented and SDED's are compared to HDED's.     

The Maximum Error in System Reliability Calculations by Using a Subset of the Minimal States

The reliability of a system is evaluated from information about the minimal states, using Poincare's method (inclusion-exclusion). An equation is derived using the minimal paths, which gives the reliability (the probability of system success) as a function of the reliabilities of the components; the unreliability or probability of system failure is obtained by subtracting this from one. Dually, with the minimal cuts, an equation is derived which gives the system unreliability as a function of the unreliabilities of the components; the reliability is obtained by subtracting from one. If some of the minimal states are missing, unknown, or unused, an error is made in the calculation. The probability which is calculated from the minimal states is underestimated and its complement overestimated. In this paper a method is described for determining the maximum error, both absolute and relative, when: 1) the minimal states are all statistically independent (e.g., they have no states in common); and 2) every minimal state has the same probability p, where p is selected so as to maximize the error. It is shown that the error and its associated system probability depend only upon the ratio of the number of minimal states used to the total number of minimal states. A table of errors, system probabilities, and relative errors is given for values of this ratio 0.01 (0.01) 0.99.     

On a reliable data communication broadcast system

This paper describes the design and implementation of a 3 KHz band HF data broadcast communication system, using a quantized frequency modulation, adaptive lattice equalizer together with forward error correcting code (FEC) to obtain a high link reliability and low error rate. A frequency diversity approach is also used in the selection of the timely best carrier frequency, and a microcomputer is implemented into the system for automatic best carrier acquisition, data transmission and clock synchronization, with minimum operator's attention. Extensive field experiments were conducted and experimental results indicate that the system can achieve, for daytime operation, a link reliability of 87–98%, with a probability of error between 10^?4 to 10^?5, depending upon data rate (50, 75bps) and FECs used. For night time operation, the link reliability reduces to from 65–93% with a probability of error down in the order of 10^?3.     

On the performance of peaky capacity-achieving signaling on multipath fading channels

We analyze the error probability of peaky signaling on bandlimited multipath fading channels, the signaling strategy that achieves the capacity of such channels in the limit of infinite bandwidth under an average power constraint. We first derive an upper bound for general fading, then specialize to the case of Rayleigh fading, where we obtain upper and lower bounds that are exponentially tight and, therefore, yield the reliability function. These bounds constitute a strong coding theorem for the channel, as they not only delimit the range of achievable rates, but also give us a relationship among the error probability, data rate, bandwidth, peakiness, and fading parameters, such as the coherence time. They can be used to compare peaky signaling systems to other large bandwidth systems over fading channels, such as ultra-wideband radio and wideband code-division multiple access. We find that the error probability decreases slowly with the bandwidth W; under Rayleigh fading, the error probability varies roughly as W/sup -/spl alpha//, where /spl alpha/>0. With parameters typical of indoor wireless situations, we study the behavior of the upper and lower bounds on the error probability and the reliability function numerically.     

Effect of Mismatch on the Reliability of ON/OFF-Programmable CNNs

In this paper, the reliability of computation of ON/OFF-programmable cellular nonlinear networks (CNNs) is analyzed. This paper redefines the classical concept of robustness (tolerance to physical imperfections) in ON/OFF-programmable CNNs so that it can be used to predict the computation reliability of a physical realization. Also, a systematic approach to improve robustness is described, and guidelines for optimizing reliability with the given resources are given. Random mismatch is identified as the main source of errors in a physical realization. At the presence of random mismatch, we describe the probability of a cell producing an error with specific inputs and the error probability when processing random data. In addition, we show how the error probability could be defined in case the cell needs to work correctly with all possible input combinations.     

Study of the reliability of a binary symmetric channel under non‐Gaussian disturbances

The field of digital and data communications is becoming increasingly dominant because digital transmission offers data processing options and flexibilities not available with analog transmission. The main feature of a digital communication system is that during a finite interval of time, it sends a waveform from a finite set of possible waveform. One of the most important and fundamental models of communications channels is the binary symmetric channel (BSC). An important measure of system performance in a digital communication system is the probability of error. In this paper, the probability of error, the reliability, the entropy and the channel capacity of a BSC model are studied under non‐Gaussian noise disturbances. Namely, Cauchy, Laplace and logistic distributions are considered. It is found that the reliability of the signaling system is low under non‐Gaussian noise distributions compared to the Gaussian noise distribution. Several methods were used to reduce the error probability. The amount of improvement in reliability using the reduction methods is higher in the case of Gaussian noise. In order to achieve high reliability under non‐Gaussian noise distribution, it is required to increase signal‐to‐noise ratio (SNR) and increase number of repetitions when sending the same signal different times. Finally, it is observed that increasing the reliability for Cauchy distribution noise has totally failed based on sending the same signal different times and summing the received signals. Copyright © 2003 John Wiley & Sons, Ltd.     

A new technique in the global reliability of cyclic communications network

The global reliability of a communications network is the probability that given any pair of nodes, there exists a viable path between them. A characterization of connectivity, for a given class of networks, can enable one to find this reliability. Such a characterization is described for a useful class of undirected networks called “daisy-chained” or “braided” networks. This leads to a new method of quickly computing the global reliability of these networks. Asymptotic behavior in terms of component reliability is related to geometric properties of the given graph. Generalization of the technique is discussed.     

Analysis of a two unit standby redundant fail-safe system

This paper evaluates reliability and fail-safety of a two unit cold standby fail-safe redundant system. Three modes of failure—(1) failure due to human error, (2) failure due to unit faults and (3) failure due to switchover faults—are considered. The complete failure states of the system are divided into two categories, fail-safe state and fail-dangerous state. Several fail-safety measures of interest to a fail-safe system designer are defined and evaluated, such as safety function, safety ratio and danger ratio.     

Design and analysis of codes with distance 4 and 6 minimizing the probability of decoder error

The problem of minimization of the decoder error probability is considered for shortened codes of dimension 2 ^m with distance 4 and 6. We prove that shortened Panchenko codes with distance 4 achieve the minimal probability of decoder error under special form of shortening. This shows that Hamming codes are not the best. In the paper, the rules for shortening Panchenko codes are defined and a combinatorial method to minimize the number of words of weight 4 and 5 is developed. There are obtained exact lower bounds on the probability of decoder error and the full solution of the problem of minimization of the decoder error probability for [39,32,4] and [72,64,4] codes. For shortened BCH codes with distance 6, upper and lower bounds on the number of minimal weight codewords are derived. There are constructed [45,32,6] and [79,64,6] BCH codes with the number of weight 6 codewords close to the lower bound and the decoder error probabilities are calculated for these codes. The results are intended for use in memory devices.     

Reliability analysis of non-maintained parallel systems subject to hardware failure and human error

This paper presents four newly developed Markov models to evaluate reliability and mean time to failure of non-maintained parallel systems with hardware failure and human error. The first three models represent two-unit, three-unit and four-unit non-maintained parallel systems, respectively, whereas the fourth model generalises the analysis to a non-maintained n-unit parallel system. System state probability equations and mean time to failure expressions are developed for all four models.     

Reliability of Hamming code transmission versus error probability on message bits

The paper presents an algorithm for the determination of the reliability of Hamming Code transmission against the error probability on message bits incurred during transmission. It establishes that Hamming Code is effective as long as the error probability of transmission line is less than 3%. The accuracy of Hamming Code drops to 90% when the error probability of the line is 8%. The algorithm is useful in adaptive communication circuits and is suitable for VLSI implementation.     

A simulation algorithm for computing failure probability of aconsecutive-k-out-of-r-from-n:F system

An efficient simulation algorithm for computing failure probability of a consecutive-k-out-of-r-from-n:F system (linear or circular) with any component reliability, is presented. The algorithm estimates both the failure probability of the system and the associated uncertainty (error). A complete interpretation of the algorithm results is given through a detailed error analysis     

First-order approximation of the ordered binary-symmetric channel

Soft-decision decoding algorithms of binary linear block codes require reordering of the received symbols within each block in decreasing reliability. Efficient decoding algorithms based on reordering have been devised. This paper presents different results related to the ordering of a sequence of N received symbols with respect to their reliability measure, for BPSK transmission over the AWGN channel model. First, a tight approximation of Pe(i; N), the probability that the hard decision associated with the ith symbol of the ordered sequence is in error, is derived. Then, it is shown that despite the fact that the random variables representing the noise at positions n₁, n₂,...,n_j of the ordering are no longer independent, the events of having a hard decision decoding error at these positions remain almost independent. Pe(n₁,n₂ ,...,n_j; N), the probability that the hard decisions associated with the symbols at positions n₁, n₂,...n_j in the ordered sequence are in error, is thus well approximated from each of the Pe (n_i; N), for i∈[1,j]. Finally, based on the independence of these events, the fully connected 2^N-state BSC representing the channel after ordering is simplified by N independent time-shared 2-state BSCss. This new model allows one to easily and tightly approximate the capacity of the channel after ordering     

Linear dispersion codes for MIMO systems based on frame theory

Multiple-input multiple-output (MIMO) wireless communication systems provide high capacity due to the plurality of modes available in the channel. Existing signaling techniques for MIMO systems have focused primarily on multiplexing for high data rate or diversity for high link reliability. In this paper, we present a new linear dispersion code design for MIMO Rayleigh fading channels. The proposed design bridges the gap between multiplexing and diversity and yields codes that typically perform well both in terms of ergodic capacity as well as error probability. This is important because, as we show, designs performing well from an ergodic capacity point of view do not necessarily perform well from an error probability point of view. Various techniques are presented for finding codes with good error probability performance. Monte Carlo simulations illustrate performance of some example code designs in terms of ergodic capacity, codeword error probability, and bit error probability.     

The Detection of Errors After Error-Correction Decoding

In data transmission and storage systems, combined error correction and detection procedures are often used to provide high reliability. This paper considers the use of separate concatenated codesCandDfor error correction and detection, respectively. It examines the error detection performance of codeDto determine how the probability of undetected error depends on the choice ofCandD. A comparison is made of the probability of undetected error achievable by codeDwith and without error correction, respectively. Asymptotic bounds for low bit error rates are developed which provide criteria to be considered when choosing codesCandD.     

Hierarchical Bayesian reliability analysis using Erlang families of priors and hyperpriors

An hierarchical Bayes approach to reliability estimation for the exponential model with an unknown scale parameter, based on life tests that are terminated after a preassigned number of failures, is considered under the assumptions of squared error loss and Erlang distributions as the prior and hyperprior. The Bayesian estimation of reliability for the case of ‘attribute testing’ is also discussed.