Showing papers in "Bell System Technical Journal in 1977"
TL;DR: In this paper, the authors consider the possibility that the two fibers of different dimensions are separated in longitudinal direction and are tilted or offset with respect to each other, and the trade-off between slice tolerances with regard to tilt and offset is expressed as an uncertainty principle.
Abstract: This paper analyses losses caused by the misalignment of two fibers joined in a splice. We consider the possibility that the two fibers of different dimensions are separated in longitudinal direction and are tilted or offset with respect to each other. Central to our discussion is the observation that the modes of single-mode fibers are very nearly gaussian in shape regardless of the fiber type step-index or graded-index. The splice losses are thus related to the corresponding losses of gaussian beams. We specify the relation between the actual mode field and the gaussian beam that matches this field optimally. The trade-off between slice tolerances with respect to tilt and offset is expressed as an “uncertainty principle. “ Because of the near-gaussian nature of single-mode fiber fields, our results are immediately applicable to the excitation of single-mode fibers by gaussian-shaped laser beams.
1,134 citations
TL;DR: In this article, an interesting subclass of bandpass signals, where the zero crossings of a bandpass signal determine its sign within a multiplicative constant, is described, and the members may have complex zeros, but it is necessary that h should have no zeros in common with its Hilbert transform other than real simple zeros.
Abstract: An interesting subclass of bandpass signals {h} is described wherein the zero crossings of h determine h within a multiplicative constant. The members may have complex zeros, but it is necessary that h should have no zeros in common with its Hilbert transform h other than real simple zeros. It is then sufficient that the band be less than an octave in width. The subclass is shown to include full-carrier upper-sideband signals (of less than an octave bandwidth). Also it is shown that full-carrier lower-sideband signals have only real simple zeros (for any ratio of upper and tower frequencies) and, hence, are readily identified by their zero crossings. However, under the most general conditions for uniqueness, the problem of actually recovering h from its sign changes appears to be very difficult and impractical.
277 citations
TL;DR: In this paper, an optical time-domain reflectometer that incorporates a gated photomultiplier receiver was proposed to detect extremely weak reflections from fiber breaks (more than 65 dB below the 4-percent reflection of a perfect break).
Abstract: This paper describes an optical time-domain reflectometer that incorporates a gated photomultiplier receiver. The instrument can detect extremely weak reflections from fiber breaks (more than 65 dB below the 4-percent reflection of a perfect break) with 0.5-m distance resolution. In addition, backward Rayleigh scattering, which occurs roughly uniformly along a fiber, can be used to estimate the attenuation vs position within a fiber. Therefore, regions of high attenuation can be located nondestructively from one end of the fiber.
199 citations
TL;DR: In this paper, techniques for reliably estimating the power spectral density function for both small and large samples of a stationary stochastic process are described, particularly successful in cases where the range of the spectrum is large.
Abstract: Techniques for reliably estimating the power spectral density function for both small and large samples of a stationary stochastic process are described. These techniques have been particularly successful in cases where the range of the spectrum is large. The methods are resistant to a moderate amount of contaminated or erroneous data and are well suited for use with auxiliary tests for stationarity and normality. Part I is concerned with background and theoretical considerations while examples from the development and analysis of the WT4 waveguide medium will be discussed in Part II, next issue.
136 citations
TL;DR: In this article, a two-by-two transmission matrix is derived for the acoustic wave amplitudes at the input and output of a surface wave grating, and the external transmission through a saw resonator is found by matrix multiplication.
Abstract: Coupled Surface-Acoustic-Wave (saw) grating resonators are investigated analytically with a transmission-matrix technique, and the measured frequency responses at ∼145 MHz of devices on YZ-LiNbO 3 with Ti-diffused gratings are compared with the theoretical results. Coupled-mode theory is applied to derive the two-by-two transmission matrix relating the acoustic wave amplitudes at the input and output of a surface wave grating. Using the transmission matrices, the external transmission through a saw resonator is found by matrix multiplication. Some fundamental aspects of resonator passband synthesis are introduced by considering the transmission through several acoustically cascaded resonators. Resonator filters where the transducers couple directly to the resonant cavities are treated by developing a description of the transducer that is compatible with the transmission matrix of the grating. The analysis technique is then applied to the familiar two-port resonator-filter. Next, coupled resonator-pairs with a transducer in each cavity are considered in detail for: (i) collinear acoustic coupling, (ii) multistrip coupling, and (iii) transducer coupling. Experimental results are presented for each configuration considered and good agreement with the analytical description is found in each case.
106 citations
TL;DR: Design guidelines, based on results of extensive computer simulations and subjective comparisons, are presented for selection of sub-band coder parameters, and practical considerations for selecting sub-bands under integer-band sampling and multiplexing constraints are discussed.
Abstract: This paper presents a detailed discussion of issues involved in the design of sub-band coders for low-bit-rate speech communications. Specifically, bit rates in the range of 7.2 to 16 kb/s are emphasized. Design guidelines, based on results of extensive computer simulations and subjective comparisons, are presented for selection of sub-band coder parameters. Practical considerations for selecting sub-bands under integer-band sampling and multiplexing constraints are also discussed, and a method for synchronous multiplexing of the sub-band data, without buffering, is proposed. Several examples of sub-band coders for transmission rates of 7.2, 9.6, and 16 kb/s are presented, and the quality of these coders is compared against that of adpcm and adm coders.
68 citations
TL;DR: In this article, a set of simple empirical formulas for converting the distribution of 5-minute rain rates into rain attenuation distributions on 11-GHz radio paths has been deduced from data measured in Georgia.
Abstract: Two methods are described to obtain long-term (≥20 years) distributions of 5-minute point rain rates from data published by the National Climatic Center for U.S. locations. A set of simple empirical formulas for converting the distribution of 5-minute rain rates into rain attenuation distributions on 11-GHz radio paths has been deduced from data measured in Georgia. Additional data measured in several other locations also support this empirical formulation. These simple formulas and 5-minute point rain rate distributions are useful for path engineering of 11-GHz radio. The work on rain rate distributions discussed in the paper derives from approaches suggested by the late W. Y. S. Chen.5,9,16
67 citations
TL;DR: It has been found that a new family of “uniform” (U) permutations (defined by the address mapping i → ki modulo N; k prime to N) is as effective as pseudorandom (pr) permutation in destroying speech intelligibility.
Abstract: This paper presents a study of speech scramblers based on permutations of samples within an N-block. It has been found that a new family of “uniform” (U) permutations (defined by the address mapping i → ki modulo N; k prime to N) is as effective as pseudorandom (pr) permutations in destroying speech intelligibility. Analytical results show the relation between input and scrambled-signal spectra, while computer simulations compare the effects of scrambling on pam samples and on codes based on adm, apcm, and adpcm. Scrambling is increasingly effective in that order, and encoding delays in adpcm can be as low as 1 to 2 ms. Finally, scrambling has been compared with frequency inversion, which corresponds to sign-inversion in every other Nyquist-rate waveform sample.
64 citations
TL;DR: In this paper, the effect of the dominant mode shape with frequency and mode conversion along the horn taper and at waveguide transitions at the horn input on return loss and radiation patterns is investigated.
Abstract: Microwave antennas are often required to carry signals simultaneously over a broad range of frequencies–e.g., the combined td-2 and th common carrier bands encompass a total frequency ratio of about 1.8 to 1 as do the combined 18- and 30-GHz bands. To achieve these bandwidths, an efficient broadband feed horn is required. The corrugated (hybrid-mode) horn is a leading candidate, but it is not immune to some cross-polarization coupling, input reflection, and pattern asymmetry. These problems are introduced mainly by two phenomena: variation of the dominant mode shape with frequency and mode conversion along the horn taper and at waveguide transitions at the horn input. Simple formulas for computing the magnitude of these phenomena and their effects on return loss and radiation patterns are given.
62 citations
TL;DR: In this article, a satellite with a high gain, movable spot beam to communicate with individual earth stations time-sharing a single channel in the tdma (Time-Division Multiple Access) mode is proposed.
Abstract: We propose a satellite with a high gain, movable spot beam to communicate with individual earth stations time-sharing a single channel in the tdma (Time-Division Multiple Access) mode It is estimated that this approach could readily save some 20 dB in the link budget while still providing full US coverage When this 20 dB is apportioned with the objectives of reducing the earth-station antenna size, increasing the satellite capacity, and reducing transmitter power, the effects are dramatic This technique can be combined with a fixed-spot beam system serving major traffic areas This combination can provide both full area coverage as well as multiple reuse of the frequency band A tdma burst organization is proposed, and estimates of burst lengths, beam switching intervals, and buffer storage size are made for a 100-earth-station network operating on a 600 Mb/s channel A phased array antenna with each element irradiating the entire US is employed to form the movable spot-beam This provides an attractive solution even though a closed-loop beam-forming algorithm may be required It appears feasible to construct such an antenna with nearly 50-dB gain capable of forming a spot beam toward any position within the continental United States with a switching time of a few nanoseconds
52 citations
TL;DR: In this paper, a broad class of practical, multimode, circular-symmetric, isotropic, optical fibers having any numerical aperture and any profile dispersion (which is a function of the derivative of the index with respect to the wavelength) was studied.
Abstract: Design criteria to minimize modal dispersion have been found for a broad class of practical, multimode, circular-symmetric, isotropic, optical fibers having any numerical aperture and any profile dispersion (which is a function of the derivative of the index with respect to the wavelength). The impulse-response width of these fibers, the rms width of the impulse response, the optimum profiles to minimize those widths, and the sensitivity to profile departures from ideal are found to be surprisingly simple closed-form generalizations of previous results that are mostly applicable to fibers with small numerical aperture and constant profile dispersion. The minimum impulse-response width of the optimized fiber is a function only of its numerical aperture and consequently is independent of the index profile and of the profile dispersion.
TL;DR: In this article, the authors simplify the coupling theory between two contiguous, parallel, multimode step-index fibers and derive an upper estimate for the overall coupling efficiency between the two fibers.
Abstract: We simplify the coupling theory between two contiguous, parallel, multimode step-index fibers, describe the coupling concept, and derive an upper estimate for the overall coupling efficiency between the two fibers. The maximum coupling obtainable, according to this estimate, is less than 72 percent (−1.5 dB). The coupling efficiency derived for short coupling lengths shows good agreement with experimental results.
TL;DR: A set of pushbuttons on a console may appear to have computer-generated labels temporarily inscribed on them if the button set and computed display are optically combined, for example, by means of a semitransparent mirror.
Abstract: A set of pushbuttons on a console may appear to have computer-generated labels temporarily inscribed on them if the button set and computed display are optically combined, for example, by means of a semitransparent mirror. This combines the flexibility of light buttons with the tactile and kinesthetic feel of physical pushbuttons; it permits a user to interact more directly with a computer program, or a computer-mediated operation, in what subjectively becomes an intimately shared space. A console of this design can serve alternately as a typewriter, computer terminal, text editor, telephone operator's console, or computer-assisted instruction terminal. Each usage may have several modes of operation: training, verbose, abbreviated, and/or special-privilege. Switching from one mode or use to another is done by changing the software rather than hardware; each program controls in its own way the momentary details of visibility, position, label, significance, and function of alt buttons. Several demonstrations are described, including a prototype of a proposed Traffic Service Position System (tsps) console, and an interactive computer terminal resembling a Picturephone® set with a Touch-Tone® pad. Also suggested are combinations of computed displays with x-y tablets and other input devices.
TL;DR: In this article, a corrugated feed with nearly ideal radiation characteristics from 17 GHz to 29 GHz has been built using a novel fabrication technique, where the bandwidth of single-mode operation was maximized by properly choosing the input parameters of the feed.
Abstract: A corrugated feed with nearly ideal radiation characteristics from 17 GHz to 29 GHz has been built using a novel fabrication technique. The bandwidth of single-mode operation was maximized by properly choosing the input parameters of the feed. As a result, only the fundamental mode can propagate at the input from 19 GHz to 28.8 GHz. In this frequency range, the far field is essentially polarized in one direction. At frequencies higher than 28.8 GHz, there is a cross-polarized component caused by an unwanted mode. An approximate calculation of the power in this mode is given. A simple formula for the input reflection coefficient is provided. Results are included that show how to compute mode conversion in a conical taper, cross polarization from a corrugated horn, including contributions from spurious modes, and the reflection coefficient from the smooth-guide to corrugated-guide transition. Comparison of theory and experiment shows good agreement.
TL;DR: It is shown that with the help of a transformation, a (k + 1)-dimensional Markov process that suffices to describe the queueing system may be found, and an equation for the steady-state generating function corresponding to the joint distribution of this vector process is derived.
Abstract: A wide variety of queueing systems with a single server can be modeled by the equation b n+1 = (b n − 1)+ + z n , where b n denotes queue length and z n the input. The usual assumption about the sequence {z n } is that it be a sequence of independent identically distributed (i. i. d.) random variables. However, in many applications, this is not really the case; {z n } is a sequence of correlated random variables. We show that with the help of a transformation, a (k + 1)-dimensional Markov process that suffices to describe the queueing system may be found, where k is the memory of the input process. We derive an equation for the steady-state generating function corresponding to the joint distribution of this vector process. We find that a simple set of equations can be obtained for the marginal distributions. In particular, the steady-state distribution of b n , the queue length, can be obtained without solving for the joint distribution.
TL;DR: Two error detectors are described, one based on correlation measurements, and the other based on sample-to-sample difference measurements, which offer s/n advantages over conventional pcm in the presence of errors and which are more promising both in terms of performance and simplicity of implementation.
Abstract: We consider detection of transmission errors in pcm by means of statistical hypothesis testing of the received quantized sequence. When errors are detected, a median filter is used to smooth waveform discontinuities. We describe two error detectors, one (cdc), based on correlation measurements, and the other (ddc), based on sample-to-sample difference measurements. While both offer s/n advantages over conventional pcm in the presence of errors, ddc is more promising both in terms of performance and simplicity of implementation.
TL;DR: In this paper, a quasioptical feed system for a 7-meter Cassegrain antenna at millimeter wavelengths is described, which is designed to take full advantage of low noise, broadband mixer receivers and will be used for radioastronomical observations at frequencies between 60 GHz and 140 GHz.
Abstract: We describe a quasioptical feed system for use with a 7-meter Cassegrain antenna at millimeter wavelengths. This system is designed to take full advantage of low noise, broadband mixer receivers and will be used for radioastronomical observations at frequencies between 60 GHz and 140 GHz. Two offset parabolic mirrors couple the radiation from the f/D = 5.7 antenna into the receiver feedhorn. A Fabry-Perot resonator operating at oblique incidence is used to inject the local oscillator energy into the signal path and to suppress response at the image frequency. The loss of the Fabry-Perot diplexer is 0.25 dB for the signal, while the coupling loss between the mixer waveguide flange and the main lobe of the antenna pattern should be ≤1 dB.
TL;DR: An investigation was undertaken to determine a suitable set of parameters that would provide a reliable voiced-unvoiced-silence decision across a variety of standard telephone connections, and the use of the Itakura two-pole spectral normalization was investigated to see its effect on the error scores.
Abstract: Recently, a statistical-decision approach to the problem of voiced-unvoiced-silence detection of speech was proposed by Atal and Rabiner. This method was found to perform well on high-quality speech. However, the five speech parameters used in the analysis were not found to be as good for telephone-quality speech. Thus, an investigation was undertaken to determine a suitable set of parameters that would provide a reliable voiced-unvoiced-silence decision across a variety of standard telephone connections. A large number of parameters (70) were included in the investigation, including 12 lpc coefficients, 12 correlation coefficients, 12 parcor coefficients, 12 lpc partial error terms, etc. Many of the parameters were immediately eliminated because they provided almost no separability between the three decision classes. The remaining parameters were used in a knockout optimization to determine the five best parameters to use for a voiced-unvoiced-silence analysis. Various error weights were investigated to see what types of errors occurred and how they could be minimized. Finally, the use of the Itakura two-pole spectral normalization was investigated to see its effect on the error scores.
TL;DR: In this article, the power spectral density function for both small and large samples of a stationary stochastic process was estimated using the WT4 waveguide medium and compared to conventional techniques.
Abstract: In Part I techniques for reliably estimating the power spectral density function for both small and large samples of a stationary stochastic process were described. These techniques have been particularly successful in cases where the range of the spectrum is large. They are resistant to a moderate amount of contaminated or erroneous data. Here these procedures were demonstrated using examples from the development and analysis of the WT4 waveguide medium and compared to conventional techniques.
TL;DR: The multihour technique appears to promise considerable cost benefits in future network designs, and has been implemented in a computer program used in design studies of three end offices in the Los Angeles local network.
Abstract: A procedure is described that is used to engineer traffic networks for more than one hour of point-to-point load data. The procedure differs significantly from existing methods, which are based upon the concept of “economic load on the last trunk” (ECCS). (When the peak-load hours on most routes coincide, however, the procedure reduces to the ECCS method.) This “multihour” procedure has been implemented in a computer program used in design studies of three end offices in the Los Angeles local network. For the cases examined, the multihour technique produced networks whose costs averaged approximately 7 percent below those achieved with the presently used single-hour methods. Thus, the multihour technique appears to promise considerable cost benefits in future network designs.
TL;DR: In this paper, the authors derived a new criterion expressly designed for determining when a given high-order recursive system using saturation arithmetic is free of overflow oscillations, which subsumes certain well-known criteria from the literature on nonlinear systems.
Abstract: Recently we found that, among recursive digital filters using saturation arithmetic to contend with overflow, a fundamental difference exists between second and higher order filters: the latter may sustain large-amplitude overflow oscillations. In this paper we have derived a new criterion expressly designed for determining when a given high-order recursive system using saturation arithmetic is free of overflow oscillations. The new criterion, which is easy to use, follows from this result: we associate with the given system two trigonometric polynomials in θ of degree equal to the order of the given system; if any linear combination of the polynomials with nonnegative weights is positive for all θ in [0, π] then the system is free of all nontrivial periodic oscillations. We prove that the new criterion subsumes certain well-known criteria, such as Tsypkin's criterion, from the literature on nonlinear systems. To illustrate, three classes of special systems are investigated, and in each case the new criterion gives substantial improvements. Finally, the new test is applied in the synthesis of high order sections for a realistic eighth-order system.
TL;DR: In this paper, the authors obtained experimental data describing the statistics of microwave depolarization during multipath fading from a propagation experiment conducted near Atlanta, Georgia, which included 6-and 11-GHz reception on a 26.4-mile path and 15.9-miles path, respectively.
Abstract: Experimental data describing the statistics of microwave depolarization during multipath fading have been obtained from a propagation experiment conducted near Atlanta, Georgia. The experiment included 6- and 11-GHz reception on a 26.4-mile path, and 11-GHz reception on a 15.9-mile path. A theoretical model, suggested by T. O. Mottl, indicates that the interference occasioned by depolarization for a given copolarized signal level is Rice-Nakagami distributed. The theoretically calculated distribution agrees well with the data. The cross-polarization interference consists of a signal-level-dependent component as well as a residual that is independent of the in-line signal level. The residual is Rayleigh distributed with an rms value about 40 dB below the nonfaded in-line signal level, and limits the multipath fade margin of a cochannel dual-polarized digital radio to approximately 30 dB. Calculated multipath outage probabilities for cochannel, dual-polarized, 11-GHz, quaternary-coherent-phase-shift-keyed digital radios with and without space-diversity protection are presented.
TL;DR: This paper presents an overview of the 1A Processor in terms of objectives, design philosophy, major features, and applications in the Bell System.
Abstract: This paper presents an overview of the 1A Processor in terms of objectives, design philosophy, major features, and applications in the Bell System. It also serves as an introduction to the detailed technical papers that follow.
TL;DR: In this article, a plan for the introduction of time-division switching in the intertoll network is outlined, which uses the No. 4 ess as the switching vehicle, and the plan defines a Switched Digital Network (sdn) which can evolve compatibly with the existing Switched Analog Network (san).
Abstract: A plan for the introduction of time-division switching in the intertoll network is outlined. The plan uses the No. 4 ess as the switching vehicle. The plan defines a Switched Digital Network (sdn) which can evolve compatibly with the existing Switched Analog Network (san). The plan introduces 64 kilobits per second time-division multiplexed pcm as a standard switching signal format in the intertoll network. Facilities utilization, trunk design, timekeeping, and maintenance plans which are required for the new format are presented. Effects on intertoll network evolution, particularly voice performance, are assessed.
TL;DR: In this paper, the authors examined the acoustic significance of longitudinal displacement in the self-oscillatory behavior of the vocal cords and inquired into the need for representing this detail in speech synthesis.
Abstract: We examine the acoustic significance of longitudinal displacement in the self-oscillatory behavior of the vocal cords, and inquire into the need for representing this detail in speech synthesis. We use computer techniques and a previously derived model of the vocal cords to study the contribution of longitudinal displacement to the total acoustic volume velocity generated at the vocal cords. This volume velocity is the effective sound source for production of voiced speech. From computational results, and from speech sounds synthesized by the programmed model, we find that the contribution of longitudinal displacement is not significant perceptually, and is not essential for modeling the dominant acoustic properties of voiced speech.
TL;DR: A new descent-type computational algorithm is derived that obtains the unique solution to the minimization of the multihour cost function, which is strictly convex but only piecewise differentiable.
Abstract: Multihour engineering is a technique for designing trunk networks when the hours of peak traffic loads between various pairs of offices do not coincide. A new descent-type computational algorithm for the multihour engineering problem is derived. This algorithm obtains the unique solution to the minimization of the multihour cost function, which is strictly convex but only piecewise differentiable. The noninteger minimum-cost solution is subsequently rounded to the nearest allowable integer solution to give a realizable network. The new algorithm is applied to three numerical examples from the California network. The results are compared with the nonoptimal, nonunique solutions obtained with an earlier algorithm, and with the traditional single-hour solutions.
TL;DR: The No. 4 Electronic Switching System has been planned to provide operational ease in the efficient management of traffic-sensitive equipment for the purpose of maintaining a high quality of service.
Abstract: The No. 4 Electronic Switching System has been planned to provide operational ease in the efficient management of traffic-sensitive equipment for the purpose of maintaining a high quality of service. The network management function has the goal of optimizing the completion of calls during periods of traffic stress. In No. 4 ess, innovative real-time control and surveillance features are provided to meet this goal. Traffic administration involves the activities of personnel in managing the traffic-sensitive equipment in an efficient, timely, and economical fashion. These activities depend upon the collection of data which reflects the operating characteristics of the No. 4 ess, and the reporting of information in a form tailored to the user functions.
TL;DR: A methodology is developed to obtain subjectively optimum quantizers for Hadamard-transformed still pictures and it is indicated that the mmssd quantizers based on subjective visibility of the quantization noise are less companded than the MMSE quantizers.
Abstract: A methodology is developed to obtain subjectively optimum quantizers for Hadamard-transformed still pictures. To exploit the perceptual redundancies that depend upon the local properties of the picture, a small block (2 × 2 × 2, horizontal-vertical-temporal) is used. A series of subjective tests was carried out to determine the visibility of impairment in the reconstructed picture when noise, which simulated the quantization noise, was added to the Hadamard coefficients in the transform domain (H-noise). A design procedure for quantizers was developed using these visibility functions. These quantizers minimize the “mean-square subjective distortion” (mmssd) due to quantization noise. The resulting picture Quality and entropy were compared with that of Max-type quantizers which minimize the “mean-square error” (mmse). This comparison indicates that the mmssd quantizers based on subjective visibility of the quantization noise are less companded than the MMSE quantizers. Also for the same number of quantization levels, pictures coded with mmssd quantizers have better quality and less entropy than the pictures coded with minimum mean-square quantizers.
TL;DR: In this paper, a statistical model for outages that occur in a dual-polarized-frequency radio channel during periods of multipath fading is proposed, and an analytical expression for outage time is obtained.
Abstract: A statistical model for outages that occur in a dual-polarized-frequency radio channel during periods of multipath fading is proposed, and an analytical expression for outage time obtained. The model, which results in Rice-Nakagami statistics for the cochannel interference signal, describes channel outage time as a function of several environmental and radio-system parameters. The formulation obtained allows for efficient parameteric studies to evaluate the importance of these parameters to channel outage time and to examine parameter sensitivity questions. Results of practical significance relative to hardware xpd requirements, maximum hop length, system gain, dependence on geographic environment, and digital terminal performance characteristics are obtained for present 11-GHz QCPSK (quaternary-coherent-phase-shift-keyed) digital radio systems. Estimates of dual-polarized-frequency channel outage time are obtained for a variety of representative system parameter values and compared with expected outage times for a conventional channel. Particular attention is given to the mechanism of channel outages during multipath fading, and several potential means for control and/or reduction of channel outage time are discussed.
TL;DR: This paper considers several methods for the efficient coding of two-level pictures dithered to give the appearance of multiple amplitude levels, and shows how some of the recently developed techniques for coding two- level pictures can be modified to code two-Level ditthered images.
Abstract: This paper consider several methods for the efficient coding of two-level pictures dithered to give the appearance of multiple amplitude levels. In the dithering technique, a multilevel image signal is compared with a position-dependent set of thresholds (called a dither matrix), and, if the image value exceeds the threshold, the two-level output signal is taken to be “white,” otherwise it is taken to be “black.” Spatial correlation present in the original image is not preserved in the two-level picture due to spatial variation of the value of the threshold; and, therefore, standard techniques for coding two-level pictures, such as run-length coding, lose their efficiency. We show how some of our recently developed techniques for coding two-level pictures can be modified to code two-level dithered images. Our computer simulations on a few representative two-level dithered pictures indicate that an entropy between 0.2 to 0.3 bit/pel is possible using our technique. A comparison with some recently proposed techniques by Judice indicates that those schemes result in about 10 to 60 percent higher entropy than our schemes.