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An error detecting data test set with a pseudorandom bit test pattern is analyzed using generating functions. A modification to the common design that combines the advantages of automatic and manual synchronization modes is proposed; it provides automatic synchronization and records one error count for each bit in error.

This study is concerned with the problem of monitoring the performance of communication links, as indicated by bit error rate, with the objective of detecting as rapidly as possible failures or extreme degradation caused by any source. The monitoring method is based on the use of an artificial threshold for the decision variable and the generation of a measurable "pseudoerror." The study relates pseudoerror probability to true-error probability for two models-one using an analytical-numerical approach and the other using a Monte Carlo simulation. Variation of the parameters in the models adequately approximates the first-order effects of many types of link failure. The results indicate that a monitor indication based on pseudoerror is feasible and has many desirable properties.

The selection of a particular signal set design for a bandwidth-constrained multiple amplitude-and-phase-amplitude-and-phase-shift-keyed (MAPSK) communication system with a linear additive Gaussian noise channel is influenced by a number of factors, such as average and/or peak signal-to-noise ratio for a given error probability, dynamic range of signal amplitudes, simplicity of generation and detection, and number of bit errors per adjacent symbol error (Gray code properties). This paper compares two possible quadrature amplitudes-shift-keyed (QASK) signal sets when the number of bits per symbol is odd (for the even-bit case, the square array is the only viable QASK choice). The "symmetric" QASK version outperforms the "rectangular" QASK set at a very modest implmentation penalty.

An experimental investigation has been performed to assess the feasibility of 8-phase phase-shift-keyed (PSK) signal transmission through a 6-GHz band microwave radio link with a 30-MHz nominal RF bandwidth. Only a portion of this bandwidth is currently being utilized to transmit one analog TV program or 1800channel frequency-division-multiplexed (FDM)/FM telephony. The link has been modified to have a 40-MHz bandwidth for this experiment. The digital modem is a 36-MHz bandwidth, 8-phase coherent PSK (CPSK), 36-Msymbol/s (108 Mbit/s) system. The work which has been performed includes the following: 1) study of the link bit error rate as a function of link carrier-carrier-to-noise ratio (C/N) with the transmitter TWT power output as a parameter; 2) study of the effects of an adjacent 1800-channel carrier (center-to-center separation of 36 MHz) on the error rate of the PSK carrier; and 3) perturbation of the 1800-channel FM carrier top channel noise power ratio (NPR) by an adjacent-channel 8-phase carrier (center-to-center separation of 36 MHz). In addition, experiments have been conducted through a four hop test simulator to examine the cumulative effect of transmission deviations such as group delay and TWT AM-PM transfer effect on the error rate performance for two different TWT power outputs, namely 2 and 4 W.

This paper reports upon the results of tests of the transmission of data over single- and multiple-hop companded delta modulation (DM) systems. The DM coder-decoder (CODEC) was optimized for voice transmission. Modem bit error rate (BER) achievable over the range of 1200-9600 bits/s is presented. A comparison with the performance of pulse code modulation (PCM) is included. The comparison indicates that the two systems are comparable for error-free digital lines but favors the DM system for lines with errors.

Synchronization plays an important role in digital communication networks. A procedure for synchronizing the local clocks in an N -node network is explored in this concise paper. The procedure, termed "discrete control correction," utilizes buffer contents and rates to derive correction signals to the local VCXO's. The system is formulated as a second-order matrix difference equation, which is examined for stability. A two-node network is analyzed as an example, and stability bounds are determined for the control parameters.

Many redundancy removal algorithms employ some sort of run length code. Blocks of timing words are coded with synchronization words inserted between blocks. The probability of incorrectly reconstructing a sample because of a channel error in the timing data is a monotonically nondecreasing function of time since the last synchronization word. In this paper we compute the "probability that the accumulated magnitude of timing errors equal zero" as a function of time since the last synchronization word for a zero-order predictor (ZOP). The result is valid for any data source that can be modeled by a first-order Markov chain and any digital channel that can be modeled by a channel transition matrix. An example is presented.

Quick-look nonsystematic convolutional codes have the property that the information sequence may be recovered from the encoded sequence in straightforward fashion and with a minimum of error amplification. In this concise paper we investigate their relevant characteristics for constraint lengths less than eight and rate \frac{1}{2} and obtain a number of interesting and practically useful results. In particular, for the best of these codes, we derive their free distance and error amplification, their decoded bit error probability when used over the binary symmetric channel in conjunction with Viterbi decoding, and show how they can be employed to measure the channel bit error rate.

In this concise paper we examine the signal design problem associated with a multiple access communication channel in which several binary digital links are operated simultaneously over a common channel. Receiver noise is neglected but the channel is confined in dimension, so that signal crosstalk is the only source of bit errors. An encoder is assumed to exist prior to channel transmission for converting the bit waveforms from all transmitters into a common channel signal available to all receivers. The encoder selects the channel signal during each bit so as to maximize the average detection probability per bit, where the average is taken over all links and all possible bit patterns. Two classes of receivers are considered. In the first the receivers are confined to only signal correlations with the corresponding transmitter signals. In the second the encoder and receivers are matched to arbitrary signal sets. For both type receivers, optimal channel signal selection is shown to be related to minimal hamming distance mappings. Values and bounds for the resulting detection probabilities in terms of numbers of transmitters and channel dimension are reported.

A Percival coil connected between the photodetector and amplifier in the receiver of a digital optical communication system offers the possibility of a reduced signal power requirement for a given bit error rate. When the photodetector is an avalanche diode, the modified receiver requires a lower value of avalanche gain for optimum performance.

A comparison is made of the performance of pure retransmission, forward error correction and hybrid (error detecting/ correcting) schemes for data transmission in a noisy (probability of error, P > 10-4) binary symmetric channel. The performance calculations are based on the use of BCH codes for error detection and correction up to the full correction capability of the code. It is shown that a probability of undetected error of less than 10-9 error/bit, can be achieved by correcting only a few errors while retaining a reasonable throughput and a very low retransmission rate. The best codes in the class considered are specified and the complexity of instrumentation is estimated. Finally, various combinations of possible systems employing half duplex and reverse channel operation are used in a comparison of the transmission schemes. For line error rate worse than 10-4 error /bit, a hybrid system operating with a reverse channel is superior to the other possibilities.

An "inhibited" error-correction decoder is defined as one which inhibits its output of decoded information bits when an uncorrectable error is detected. The output bit error rate, probability of false acceptance, and other performance parameters of inhibited decoders are expressed as responses to uncorrectable errors and the effect of such errors on several error-correction decoders of practical interest is described in terms of the numerical results of a computer simulation.

The performance limitations on the linear control of a linear plant, due to the presence of a feedback channel with finite information capacity, are considered in this paper. This situation may arise in such diverse applications as (a) the remote control of a plant, using a digital data link for feedback, (b) where quantization errors and bit errors of a digital controller may be modelled as occurring in a noisy digital channel in cascade with an ideal controller, and (c) in human-operator modelling, where the sensory feedback channels are characterized by fixed information capacity due to neural noise. The principle result obtained is that, given the state-dimension n of the plant and the channel capacity @e, reliability function E(R), and block encoding time T> >1C, the optimum data-rate R satisfies the equation 2R=nE(R). This rate provides the optimum tradeoff between the effects of quantization errors and message errors. It is seen that R"o"p"t->C as n becomes large, but that good channel performance is retained provided that > >nT.

A synchronization error is said to occur when either a bit which does not belong is detected in a channel between bits which were transmitted, or a bit which was transmitted is never detected at the output. A block code which corrects a single synchronization error per block is presented, and it is shown that this code has, at most, three bits more redundancy than that of an optimal code for this class of errors. The code has the beneficial property that it is possible to separate the information positions from the check positions, and an appropriate method of encoding is shown.

A new approach to asynchronous multiple access communications is presented. The technique, employing orthogonal convolutional coding and Viterbi decoding, is described and its performance characteristics are derived for the case in which other-user interference is the only source of noise. Results indicate that the technique is quite efficient in terms of the number of users supportable at a specified bit error rate in a given system bandwidth. Furthermore, the results of a design study are described, showing that the technique is a practical one to implement.

A simple partitioned Markov chain model is proposed for characterization of the HF channel. It is demonstrated that from the model, the error-burst distribution can be derived with good agreement with simulation results. In this paper the transition probability matrix P of the model is raised to the N th power PN. PNis used to represent the channel after interleaving of degree N . The error-burst distribution after interleaving is derived from PN. The results show again that there is good agreement between calculated and simulated error-burst distribution. It is concluded that the model can be employed to study the effect of interleaving on burst-error channels.

Selection of a particular signal set array for a bandwidthConstrained multiple phase-and-amplitude-shift-keyed (MPASK) communication system for a linear additive Gaussian noise channel requires consideration of factors such as average and/or peak power versus symbol error probability, signal amplitude dynamic range, simplicity of generation and detection, and number of bit errors per symbol error (Gray code properties). A simple technique is presented for generating and optimally detecting the honeycomb (hexagonal.) signal set, i.e., the signal set that has the tightest sphere-packing properties. The symbol and bit error probability performance of this set is compared to other two-dimensional signal sets that have been investigated in the literature, and is shown to be slightly superior from an average power standpoint. The paper concludes with a comparison of all of these signal sets from the standpoint of the factors listed above.

In a satellite time-division multiple-access (TDMA) system, the information is transmitted in bursts from the participating ground stations. In order to establish a time reference in each burst and to determine its origin, special code patterns called unique words (UW) are contained in the bursts. Reliable detection of the UW is the basis for keeping the stations in synchronism and providing high-quality communication links. The influence of miss and false detection of the UW on acquisition and the retention of a stable detection mode are investigated. The tolerable loss of information bursts provides criteria for the detector parameters, and for length and patterns of the UW codes. Practical results obtained during tests on an experimental system are compared with theory.

A synchronization error is said to occur when either a bit which does not belong appears, or is detected in a channel between bits which were transmitted; or a bit which was transmitted is lost or not detected. A model for such a channel will be proposed, and a lower and upper bound on the redundancy necessary to correct a given error rate will be derived. We will consider the case of single synchronization error correction in detail, and stronger bounds will be derived for that case. We will consider multiple adjacent synchronization errors as a special case, and show that the bounds can be tightened in this case as well.

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 block code is presented that will correct an error consisting of the gain or loss of a bit (binary digit) within the block. The code can be generalized to correct the loss or gain of a burst of bits. A further feature is the possibility of correcting additive errors appearing in the vicinity of the bit loss or gain. An additive error is a bit changed from 0 to 1 or from 1 to 0. The code is constructed by inserting a known character into a burst-error-correcting code at periodic intervals. The known character locates the approximate position of the bit loss or gain. At the location a bit is inserted or removed from the block, depending on whether a loss or a gain has occurred. The error-correcting code then corrects the erroneous bits between where the error occurred and where the correction took place.

This paper presents a generalized mathematical model of a PCM/PL system. The analysis demonstrates that any two orthogonal polarizations may be used to represent the binary bits. The generalized approach also facilitates the derivation of the system bit error rate when polarization errors are introduced. Six types of polarization errors are assumed for the discussion. The various cases of polarization errors are presented as operations on the Poincare sphere. These operations are then formalized in terms of the Mueller Matrix theory. The matrix algebra permits the derivation of the bit error-rate curves for the six polarization error cases. Assuming that the atmospheric-induced fading is log normally distributed, the bit error rate for a PCM/PL fading channel is computed.

A new approach to binary-data transmission, termed correlative level coding, is presented, along with practical aspects based on research conducted during the past few years. Following a review of basic data-transmission concepts and definitions, the author discusses the general form of the level-coded correlative techniques, as well as the specific codes with and without carrier modulation. In the error-detection process, it has been found that with this type of system it is unnecessary to introduce redundant digits into the original data stream.

This paper is concerned with the performance of partially coherent digital phase modulation (DPM) systems employing a class of binary signaling waveforms containing a zero crossing within each bit period. The class of waveforms includes the Manchester II bit code and sinusoidal bit code as well as an infinite number of other nonrectangular bit shapes. We wish to study the tradeoff between the RF bandwidth and the probability of bit error P(E) as a function of bit shape. The equation describing the RF power spectrum for these DPM signals is obtained using a two-dimensional Fourier transform technique and is shown to contain both continuous and discrete terms. The spectra are evaluated numerically for a typical bit rate showing the effect of different bit shapes. An original technique is presented for including the effects of modulation interference on the extraction of the carrier-phase reference from these DPM signals using a partially coherent phase-locked-loop receiver. The expression for the P(E) is obtained for the class of signals and is a function of the phase deviation angle and the modulation interference. This expression is evaluated numerically to obtain sets of curves that show the optimal phase deviation angles for five members of the class. The tradeoff between the RF bandwidth and the P(E) is given by a curve that indicates the increase in P(E) for a reduction in RF bandwidth as a function of the bit shape.

This paper analyzes the multiple-access performance of a satellite communications network, in which each subscriber employs a hybrid frequency-time hopping random-access technique for the transmittal of binary information by means of a linear average power limited satellite repeater. The information is repetitively encoded into a number of binary chips. Individual mark and space chips are matched filter envelope detected and pairwise compared; the final binary decision is based upon a majority vote. The present analysis extends previous results by simultaneously taking into account RF phase cancellation effects at the satellite as well as up- and down-link noise. Some numerical results are presented using system parameters typical of a small subscriber net. The multiple-access performance of the frequency-time hopping system is (for the assumed parameters and a bit error rate of 10-5) found to be about 6.6 dB poorer than that of a comparable orthogonal multiple-access system.

Missfle range instrumentation radars are capable of transmitting pulse code groups in which some of the pulses in each group can be used to convey information from the ground to a space vehicle containing a suitable beacon receiver and decoder. Thus, a one-way communication system is provided with only a small increase in ground and vehicle equipment over that required for the tracking function. Since the system is one way, communication reliability becomes of paramount importance. This paper presents a method of computing bit error rates, word error rates, and frame error rates as a function of the SNR at the beacon receiver. The SNR vs range can then be computed by standard methods to obtain the ground-to-vehicle ranges over which reliable communications can be conducted.

This paper discusses a new method of bit synchronization derived from an analog theory to solve the problems involved in receiving a serial train of bits from a remote data communication source. Test results show that accurate frequency and phase information can be derived from the received serial data. The Analog Derived Clock to accomplish this bit synchronization is described, and applications in two-wire (half duplex operation) and four-wire (full duplex operation) communication systems are discussed. Speeds up to 2 Mc/sec using existing digital circuit technology were achieved. The special advantage of the Analog Derived Clock over present clocking techniques is an increase in speed and a reduction in circuitry.

Two problems which arise in the transmission of digital data are message framing and error control. A technique has been developed whereby polynomial coding can be used simultaneously for both error detection and message framing. With this technique, encoded data blocks can be transmitted asynchronously without incorporating any special signals or bit patterns for "start-of-message" and "end-of-message" indications. Erroneously received blocks are automatically deleted from the accepted data stream. The standard systems use a special signal for a start-of-message (SOM) indication at the beginning of each block of data, and independently create and detect a specified format (usually based on parity check sums) to determine when errors have occurred in transmission of the data. In order to achieve high reliability it is necessary to use sophisticated techniques and to devote a large number of transmitted digits to each of these functions. By considering these two problems together a technique which provides a solution to both was found. This technique uses fewer bits than would be required by many conventional approaches to framing to get the same reliability. The error-detection capability which is included is so strong that the mean time between undetected errors is usually dependent on equipment reliability rather than on channel error statistics.

Modern digital computing systems are primarily limited in how densely information may be recorded on the magnetic storage elements by the manner in which the information is retrieved (detected) from these storage facilities. Current systems store information at a density around 1000 bits per inch (bit/in); system elements, other than the detection process, could easily handle densities in excess of 3000 bit/in. This paper describes the signal present at the output of the read-write head and suggests two systems by which detection at high bit densities may be accomplished. The error rate associated with each system is given and the results are applied to a computer system using a magnetic disk file as the storage element. It is demonstrated that these detection procedures can meet the widely accepted standard of one error in one billion bits at reasonable signal-to-noise ratios.

An experimental error control system utilizing a generalized burst-trapping error control technique has been designed, built, and evaluated. Code parameters were chosen such that bursts as long as 1000 bits are likely to be corrected in the presence of a background random bit error rate as large as 3 \times 10^{-3} . In this paper we give a brief description of generalized burst-trapping codes, we discuss the design and implementation of the decoder, and we describe the performance evaluation.

Classical orthogonal frequency division (OFDM) employs fast Fourier transform (FFT) for elimination of inter-symbol interference (ISI) and expansion of time support of the transmitted signals. However FFT could not always be optimal in terms bit error ratio (BER) due channel variations, Doppler Effect, nonlinearities and high peak-to-average power ratio of the signal. Aim of this publication is to experimentally compare different orthogonal transforms and outline impact of these transforms on BER of the communication system with noisy, frequency selective and nonlinear communication channels. Simulation results of OFDM communication systems with equalization and no transform, with FFT, Hadamard and Generalized nonsinusoidal orthogonal transforms are presented. Ill. 5, bibl. 9, tabl. 1 (in English; abstracts in English and Lithuanian).http://dx.doi.org/10.5755/j01.eee.111.5.361

Random bit errors that occur in PCM data during the various phases of the telemetry-data-processing system will not only add a component of mean square error to the experimental data but will also bias it. This paper derives a formula for the bias and describes some of the characteristics of the bias.

In high-speed communication through a medium with time-frequency spread (such as in HF ionospheric, sonic underwater, and voice-quality telephone line transmission), the transmission speed and system errors are determined by an overall system variance (or equivalent noise). This overall variance comprises: 1) the intersymbol interference variance from time spread (or dispersion in the unit impulse response of the medium); 2) the variance from frequency spread (or dispersion it the CW response of the medium); and 3) the variance from channel noise at the receiver. In order to mitigate intersymbol variance from time spread, after discussing some early and limited attempts, a review is made of the general synthesis of the infinite and finite Wiener optimal networks or equalizers using delay lines with feedforward and/or feedback taps (or their shift register digital network counterpart). Also considered are optimal finite feedforward delay line approximations to the Wiener networks, synthesized nonsequentially and sequentially using a steepest descent evolutionary network synthesis, resulting in a monotonically decreasing and convergent overall variance. Applications of these networks are shown in the transmission of speeded-up analog facsimile pictures over unconditioned voice-quality telephone lines. It is shown that the received smeared picture can be refocused or de-smeared, or its time spread mitigated, to allow overall satisfactory high-speed picture transmission. Moreover, in over-the-horizon HF ionospheric analog and/or data transmission, time spread occurs in the form of discrete multi-path reception, such as the familiar ghosts observed in television. A particularly stringent multipath comprises two equal or nearly equal magnitude paths, a situation which is actually observed in HF ionospheric communication between two ships at sea. For this case it is shown that serial data transmission with pulses thin enough to resolve the multipath achieves, with optimal equalization, an irreducible bit error ratio (BER) which is a number of orders of magnitude less than the irreducible BER of the parallel data transmission method used in all contemporary HF modems (modulators and demodulators). Design curves are given showing the intersymbol interference variance from time spread as a function of the number of taps it the delay line correction networks, along with the variance arising from channel noise, and the optimal allocation of both variances for minimal overall BER with a given number of taps for the finite realizable correction networks. Because of frequency spread, the ever-changing unit or impulse response of the medium (e.g., HF ionospheric) causes the correction or equalization networks to become aged, giving rise to frequency spread variance. This is formulated both for determinate and for random changes of the medium unit response. For transmission media having simultaneous time spread and frequency spread, the equivalent overall variance is a simple function of the time-frequency spread product of the medium. These formulas are applied to find the overall minimal BER as a function of the time-frequency product for a contemporary parallel data modem and for a new serial adaptive data transmission system (ADAPTICOM) which periodically in real time and with digital techniques rejuvenates the time spread digital correction networks. It is shown that the transmission limit of communication of the parallel data modem is for a time-frequency spread product of about 1/2000, while that for the new serial adaptive data modem is about ten times larger, or 1/200. As a result, new communication channels are opened up for serial adaptive transmission, such as the HF spectrum below the maximum usable frequency (MUF).

Error control techniques are becoming increasingly important in data transmission systems, since they allow reliable communications over media where the interference is high. Transmission errors can be corrected either by adding redundancy bits to the information to generate an error correcting code, or by automatically retransmitting the message when erroneously received. The relative merits of the two techniques are discussed in terms of both error control and systems compatibility. A class of powerful and easily implemented cyclic error detection and correction codes was recently developed which, in combination with automatic retransmission, should give effective error protection. Once the system reliability requirements are realistically gauged, and the characteristics of the channel interference are known, it is possible to determine a cyclic code best suited to that interference, and to determine a message length for the maximum transfer of information.

Successful development of Broadband over Power Lines (BPL) is obviously a potential solution for wireless communication systems with the existing infrastructure. Multi-Carrier Code Division Multiple Access (MC-CDMA) with Orthogonal Frequency Division Multiplexing (OFDM) modulation technique is a promising solution for a frequency selective fading with impulsive noises of the PLC channel. A linear iterative receiver with a Finite State Markov Channel (FSMC) model is proposed to remove Multiple Access Interference (MAI) and Inter Symbol Interferences (ISI). In this paper we focused on Maximum Likelihood (ML) feedback detection by introducing FSMC to get significant improvement in Bit Error Rate (BER). This model of the receiver is more robust against Gaussian colored and impulsive noises of the PLC channel. Keywords: FSMC; MC-CDMA; OFDM; MAI; ISI DOI: 10.3329/bjsir.v44i4.4595 Bangladesh J. Sci. Ind. Res. 44(4), 441-444, 2009

This paper discusses the problem of multiplexing asynchronous signals which are clocked from independent sources. Two solutions are offered to this problem: one provides a continuous transmission over a fixed period of time proportional to the bit rate integrity duration, and the other utilizes a bit stuffing technique. The former approach is used when the asynchronous signals are clocked from highly stable clocks, and also when the bit rate integrity period is on the order of a few hours. The latter approach is employed when the signal clocks are relatively less stable or the bit rate integrity period is very long. The reliability of these techniques is analyzed, and their efficiencies are evaluated and found to be most satisfactory. Synchronization procedures and probabilities of false lock and failure to lock are also described. In addition, a multiplex system illustrating these techniques is presented. The system multiplexes four input channels at a one megabit rate for each.

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This article describes the results of a data communication experiment designed to investigate the effectiveness of error detection and retransmission in providing high-accuracy data transmission over the switched telephone network. Data were encoded into a Bose-Chaudhuri (31,21) error-detecting code and transmitted at 2000 bits per second by a DATA-PHONE data set 201A over a variety of dialed long-distance connections. Transmitted and received data were compared to obtain error data which were analyzed to obtain an estimate of the error performance of the data set and the effectiveness of the code. The results of this analysis are presented. During the test approximately 6.36 × 107 31-bit code words or 1.97 × 109 bits were transmitted. Of these, 63,002 bits appearing in 29,731 different code words were received incorrectly. Thus, the over-all bit error rate was 3.19 × 10−5 and the word error rate 4.67 × 10−4. The decoder was successful in detecting all but two of the erroneous code words, resulting in an average undetected word error rate of 3.14 × 10−8 or an average of 9.85 × 108 bits between undetected word errors. These results demonstrated that very low undetected error rates can be obtained in practice using an error detection and retransmission system of modest complexity.

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A new coding scheme is presented. In this scheme a given t-error-detectin g code is used for transmission over a noisy channel. When t or less errors are detected, a single request is made via a feedback channel for transmission of additional redundancy to enable the decoder to correct t or less errors. It is shown to be superior to forward error correction in rate and probability of error. For low channel errors the resulting rate is higher than that of retransmission with no significant difference in the probability of error.

The error rate or the probability of error is an important parameter in the design of digital communication systems. In this paper a Gram-Charlier expansion is used to compute the error rate in the presence of intersymbol interference and additive Gaussian noise. The method presented is very useful for numerical computations. We also present expressions for the truncation errors. Rigorous proofs are presented in the Appendix.

Binary decoding of relatively short codes corrupted by Gaussian noise or pulse interference has been considered in applications for which the minimum useful information block length is unity, equal to the information bit capacity of a code, or equal to an integral multiple of the information capacity of a code. The following results pertain to applications which are further characterized by the performance criterion of minimizing error rate and transmitter power, with only minor restrictions on transmission bandwidth and none on channel efficiency (no credit given for error detection): [1] The word error probability for any group error-correcting code is never exceeded by its corresponding bit error probability (for either Gaussian noise or pulse interference). [2] Relatively short codes (10 to 50 information bits) of moderate redundancy (40 to 50 per cent) are available which can reduce bit error rates by factors of 10 to 400, or equivalently, permit 1 to 3 db reductions in transmitter power, when the coded system bit error rate is 10-6(Gaussian noise). [3] These same codes can alternatively reduce word error rates by factors of 10 to 104, or equivalently, permit reductions of 1.5 to 3.7 db in transmitter power, for average word error rates corresponding to values of the quantity E/N_{o} (signal energy per information bit/Gaussian noise power density) in the neighborhood of 8 db for the coded systems. [4] Under worst-case pulse interference, these codes permit 4 to 7 db reductions in transmitter power for average word error rates less than 20 per cent. (Considerably greater improvements result for the pulse interference expected.) [5] All of these codes are easily encoded and decoded.

Assuming bit errors are independently distributed with a constant probability of error p e , it is shown that a simple estimator is highly efficient for estimation of p e . The estimator is based on a simple function of the number of sync words containing no bit errors. The estimator is shown to be maximum likelihood, minimum chi-square, and modified minimum chi-square when the quality index reported is simply the percent of frames containing zero errors. An approximate confidence interval for p e is obtained, and a determination of the number of sync words to observe in order to obtain an approximate confidence interval of fixed length is indicated. The method of scoring which can be used to obtain a more efficient estimator of p e is described.

The word error rate of an ensemble of cryptographic systems is determined. The word error rate is specified as a function of the corresponding plain-text bit error rate. Degradation is defined and computed for the case of phase-shift keying and white Gaussian noise. Finally, the effect of differential encoding on a cryptographic system is investigated.

The performance of perfect codes on the switched telephone network is evaluated in terms of output block error and output bit error probability. By evaluating these codes against experimental data describing the switched telephone network, it is shown that significant improvement in the block error rate is possible, but that only negligible improvement in the bit error rate is obtained even with block lengths as long as 230 bits and with redundancies approaching unity.

In recent years considerable attention has been directed toward digital data communication among machines utilizing the telephone network. Such communication raises many questions concerning the accuracy of transmission attainable. This paper discusses the effectiveness of several error-control techniques. First, the transmission channel is described by three parameters which permit correlation among the errors. A number of errorcorrecting methods are evaluated by a computer simulation technique using the parameters of several hypothetical transmission channels which might be representative of telephone circuits. Emphasis has been placed on the recurrent burst-correcting codes. The performance of these "recurrent" codes, when subjected to actual errors collected from Data-Phone test calls, is compared to the performance of these codes using the assumed channel parameters. Graphs relating the average final error rate after correction to the transmission channel error statistics are shown. The difficulty of extracting channel parameters from real error data is discussed and a method is presented which might permit such calculations. It is concluded that some of the codes considered are capable of reducing the error rates in digital communication considerably. However, most error-control methods are highly sensitive to the particular error statistics found on the transmission channel. An analytical description of the errors found on a transmission channel is needed for the proper evaluation of error-control methods.

This paper introduces two schemes to correct bit errors caused by defective memory cells in high-speed random-access memory systems. The schemes are addressed to word-organized memories produced by the integrated technologies. One of the two schemes calls for encoding of input information and the other does not. The schemes are simple, economical for the technologies concerned, and exhibit a regularity which makes it possible to fabricate the necessary additional hardware within the same technology.

A Kalman filtering algorithm has been applied to the problem of bit synchronization in an M -ary communication system. No synchronizing signal is assumed present; the approach is arranged to determine timing information from the transitions occurring in a pseudorandom sequence of symbols, generated with a fixed but initially unknown bit rate. Procedural steps subdivide naturally into an acquisition phase (block data processing) and a track mode (recursion). The method is supported by sample binary frequency-shift keying (FSK) simulation results, obtained from the output of a 4-pole Butterworth digital filter fed by a random MARK/SPACE sequence plus additive Gaussian noise. Results demonstrate accurate determination of both the bit phase reference time and the bit period. The scope is restricted to high SNR digital communication systems, for which acceptable error rates are obtainable without sophisticated decoding schemes.

The factors influencing the speed at which data can be transmitted, and those determining the error rate, are summarized as an introduction to a statement in respect to error rates measured. Different applications for data transmission are considered in relation to the amount of error correction which may be justified. Various forms of error detection and correction are illustrated, and the probability of undetected errors is considered from a theoretical point of view for a random distribution of errors. These results are then compared with records obtained by practical tests using various redundancy arrangements. It is concluded that there is a substantial advantage in the use of large (500-bit) rather than small (50-bit) blocks for detecting errors. It is also suggested that the practical evidence of error patterns which remain undetected should enable more effective detection designs to be produced.

This paper describes an investigation of channel spacing for multiple biphase-shift-keyed (BPSK) signals accessing a hard-limiter satellite. The effects of intermodulation and modulation spectrum interference on the bit error rate of the active channels were considered. Results and conclusions of experimental errorrate data are presented for various channel spacing arrangements. Of major significance is the formation of rules for the spacing of active channels when six or more BPSK signals are accessing the hard limiter.