Binary Communication Research Articles

Communication over fading dispersive channels with feedback

An intermittent on-off noiseless feedback scheme for binary communication over the slow- and fast-fading Rayleigh channels is proposed and analyzed. At high energy-to-noise ratios, doubling the number of feedback iterations yields a 3-dB power saving for the slowly fading channel. Power savings ranging from 1 dB for one feedback iteration to 9 dB for 16 iterations are typical for the fast-fading model. Also for the fast-fading model, by picking the optimum number of forward transmissions for each value of energy-to-noise ratio, the best achievable performance requires approximately 7.5 dB more energy than the minimum predicted by the rate-distortion bound. Also presented is a feedback communication system for wide-sense stationary, uncorrelated-scatterer, fading, and dispersive forward and feedback channels. The model used for both forward and feedback channels is Kennedy's. Upper and lower bounds on the error probability for block orthogonal <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">M</tex> -ary communication are presented for this system.

On the recognition of time-varying patterns using learning procedures

Some recognizers for stochastic time-varying patterns with additive noise are studied. As in binary communication channels with fading, it is supposed that the fluctuation of a pattern (or signal) may be approximated by a stationary Gaussian autoregressive process with known parameters. Each measurement belongs to either of two classes: the pattern plus noise or noise alone. Under these assumptions, optimum dichotomizers with supervized learning are discussed. To the nonsupervised problems, the decision-directed approach and the modified-decision-directed approach are applied. Also some experimental results are presented.

Multiplexed TV and high-data-rate pulse-gated binary modulation communications experiments

Multiplexed TV and high-data-rate pulse-gated binary modulation communications experiments

Binary Synchronous Communications

Binary synchronous communications, in particular the line-control functions, are described. These functions are independent of the devices transmitting and receiving, the mode of transmission, and the transmission code. A mode known as transparent transmission allows the transmission of data, independent of its bit structure. The various aspects of transmission are discussed, including station control, transmission formating, error detection, and error recovery. In addition, the communication control characters are described in detail.

Comparison of Error Probability and Signal-to-Noise Ratio between a Coherent Heterodyne and a Photon-Limited Laser Communications System

The error probability for a coherent heterodyne laser digital communications system is calculated for Poisson signal and local oscillator photon distributions and compared to a photon counting system. It is shown that under optimum conditions, the coherent heterodyne system requires more average signal photons per detection interval than the photon counting system for equal probabilities of error. For a binary communications system with equal zero or one transmit probability, an error probability of </= 10(-3) requires a power S/N approximately 24 for the coherent heterodyne system while only a S/N approximately 3.5 for the photon counting system.

Binary communication over the Gaussian channel using feedback with a peak energy constraint

We consider binary communication over the additive white Gaussian noise channel with no bandwidth constraint on the channel input signals, assuming the availability of a noiseless delayless feedback link. Although the signals at time <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">t</tex> can depend on the noise at times <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">\tau &lt; t</tex> and are therefore random functions, we require that the signal energy never exceed a fixed level. We show that the optimal probability of error is attainable without the use of the feedback channel by using antipodal signals.

Performance of an Ideal Quantum Receiver of a Coherent Signal of Random Phase

An ideal quantum receiver is to detect a coherent narrow-band optical signal in the presence of thermal background radiation. Curves are given both of the average probability of error in a binary communication system transmitting O's (blanks) and 1's (pulses) with equal probabilities, and of the probability of detection for various fixed values of the false-alarm probability.

Some results on error rates for a laser binary communication system

The probability of error is obtained for a simple but fundamental form of a laser binary communication system. The results show that the probability of error is strongly dependent upon absolute signal level as well as signal-to-noise ratio.

The Effect of Atmospheric Scintillation on an Optical Data Channel–Laser Radar and Binary Communications

The effects of scintillation on an optical data channel are analyzed and numerical results presented. Scintillation with a log normal distribution typical of atmospheric optical effects is assumed. The analysis is concerned with the target miss probability of a laser radar and the bit error probability of an optical binary communications link. Results are expressed in terms of a loss factor which is the extra number of dB signal-to-noise ratio necessary to keep the performance in the presence of scintillation up to the level achievable in the absence of scintillation. With even moderately weak scintillation large loss factors are encountered. A brief treatment of the effects of normally distributed scintillation is also presented.

Intermittent Binary Communications in a Rayleigh Fading Medium

The error rate performance of a binary communication system, operating in a Rayleigh fading medium, which possesses the capability of automatically ceasing to operate when the received signal-to-noise ratio falls below a preassigned value is analyzed. Communication systems possessing this capability are shown to perform significantly better than systems which operate continuously in the same medium. It is shown that the intermittent system performance asymptotically, i.e., operation in the total signal environment, approaches the multireceiver performance for the case when the multireceiver is measuring only one path.

Performance of Suboptimum Feedback Functions for Sequential Detection Systems with Feedback

The performances of the optimum and several suboptimum feedback functions for sequential binary communication systems with a feedback link are evaluated and compared in terms of the error probability vs. normalized transmission rate characteristic. Evaluation is also made of nonsequential systems with optimum feedback functions. It is shown that the power advantage attained by the optimum system can be achieved without considerable loss by the suboptimum feedback functions.

A binary channel characterization using partitioned Markov chains

The characterization of binary communication channels using functions of finite-state Markov chains is considered. Two distributions which are relevant to code evaluation, i.e., the error-free run and error-cluster distributions, are derived. It is shown for an N -state model, partitioned into a group of k error-free states and N-k error states, that the general form of the error-free run distribution is the weighted sum of at most k exponentials, and that of the error-cluster distribution the weighted sum of at most N-k exponentials. As evidence of the capability of such models to characterize real communication channels, a simple class of models is investigated and shown experimentally to be capable of representing HF radio statistics.

Performance of binary communication with a noisy phase reference using sequential decoding

For coherent digital communication in a noisy environment, it may not be possible to provide a perfect phase reference. The consequence is a degradation from theoretical coherent performance. This letter derives the performance bounds for convolutional encoding and sequential decoding of binary antipodal signals with a noisy phase reference.

On the design of signals for sequential and nonsequential detection systems with feedback

The design of signals for binary communication systems employing feedback has previously been considered by Turin. A delayless, infinite-bandwidth forward channel disturbed by additive, white, Gaussian noise is assumed. At each instant of time, the log likelihood ratio of the two possible signals is fed back to the transmitter via a noiseless and delayless feedback channel. The forward-channel signals are said to be optimally designed when the feedback information is so utilized that the average (for sequential detection) or fixed (for nonsequential detection) transmission time is minimized, subject to a specified probability of error. Average and peak power constraints are also placed on the signals. Turin has solved the signal design problem for extreme values (i.e., very large or equal to one) of the peak-to-average power constraint ratio. These results are extended in this paper to arbitrary values of the power constraint ratio, for both sequential and nonsequential detection.

Error Probability Estimation Using Bivariate Extreme-Value Theory

Information is ultimately conveyed by the use of some form of decision or threshold device in binary communication systems. Threshold receivers are all basically "signal present" receivers, and are used in both telemetry and command systems for deep space probes and orbital spacecraft. One attack on the problem of experimentally determining bit error rates in such systems is the standard concept of bit error testing, i.e., comparing transmitted and received digital information bit by bit. When either error rates or bit rates are low, considerable test time is required to establish error rates by this method. This paper presents an application of the statistics of extreme values to the problem of estimation of low error probabilities in binary communication systems, with special reference to systems which have "loss-of-lock" indicators. The idea of the extreme-value theory method is to record the maxima within a large group of successive independent samples of the detector analog signal just prior to quantization, and then in turn record a large number of these maxima themselves. Next, the two parameters of the double exponential extreme-value probability distribution are estimated. The probability of exceeding the error threshold is then calculated from knowledge of these two parameters. The presence of a loss-of-lock indicator reduces the error probability at the expense of introducing an "erasure" probability. Techniques are given for estimating both these probabilities using "bivariate" extreme-value theory.

A Comparison of Binary Delay-Lock Tracking-Loop Implementations

The delay-lock loop is a device for tracking the delay difference between two correlated waveforms. It is used as a synchronizing loop for binary communications and tracking. The delay tracking performance is derived for various radio-frequency implementations of the binary delay-lock loop. Amplitude and biphase modulation by pseudorandom sequences are considered. Three types of receivers are analyzed for each modulation: envelope correlation, phase-coherent correlation, and phase-lock demodulation followed by video correlation.

An Optimal Nonlinear Detector for Digital Data Transmission Through Non-Gaussian Channels

The problem of binary synchronous communication in additive non-Gaussian noise is considered. It is shown that, for a class of additive noises, an optimal detector consists of a two-input nonlinear device followed by an integrator and decision box. This system suppresses large excursions from the signal level in an optimal manner before integration of the received signal, so that the effects of large amplitude noise waveforms on the signal decision are minimized. Asymptotic performance characteristics are obtained indicating the relationships between the basic system parameters, signaling waveforms, signal energy, system bandwidth, decision time, noise dispersion, and error probability. Explicit expressions and curves for system performance in large variance (Cauchy distributed) noise are given for various basic signaling waveforms.

On the solution of a quadratic integral equation arising in signal design

This paper considers the solution of a quadratic integral equation of the first kind arising in the design of bandlimited signals for binary communication using simple memory-less correlation detection. The signals are disturbed by additive white Gaussian noise. It is shown that a bandlimited signal can be designed which eliminates intersymbol interference for signalling at Nyquist rate. This signal is a solution to a quadratic integral equation. The existence of the solution, as well as a construction of the solution of this equation, are presented. The method of solution of the integral equation is applicable to a broad class of problems.

On the Reception of Binary Signals in the Presence of a Small Random Delay*

Receiver design for a binary communication system which operates over a linear channel with a random delay is considered. It is assumed that the variance of the random delay is very small and that the rate of growth of its moments is restricted. Under certain smoothness requirements on the received signal an approximation to the test statistic, which is optimum in the Neyman-Pearson sense, is derived for the case of gaussian receiver noise with covariance R(τ) e R(0)eβ$|τ|. It is found that the test statistic, which in general is nonlinear, assumes the linear form of a crosscorrelator when phase reversal signaling is employed. The case where the noise is white and phase reversal signaling is used is investigated. The correlation waveform in this case is found to consist of the expected value of the received signal plus a term dependent on the slope of the signal when the delay is equal to its mean value.

Linear Modeling of Long Underwater Acoustic Paths

The effective treatment of signal-transmission problems requires an analytical representation or “model” of the signal path. Long underwater acoustic-signal paths fall in the class of randomly time-varying dispersive channels, which show approximate linearity and short-term statistical stationarity. A mathematical model for such paths is proposed that is based on the statistical behavior of the time-varying impulse response h (η,τ). This model has sufficient generality to account for the fluctuating dispersive characteristics of underwater paths and their property of increasing attenuation with frequency. Certain constraints may be included, however, so as to provide the model with a high level of mathematical manageability. The effects, of the channel model on the transmission of white noise, stationary random signals, and CW signals are treated. In addition, the use of the complete model in the optimization of a simple binary communication system is illustrated. The detailed treatment is confined to the point-to-point transmission situation although some discussion presented on the more complicated problem of multiple-input/multiple-output channels, including interior reflective and refractive bodies.