The Bell System Technical Journal

The recent development of various methods of modulation such as PCM and PPM which exchange bandwidth for signal-to-noise ratio has intensified the interest in a general theory of communication. A basis for such a theory is contained in the important papers of Nyquist¹ and Hartley² on this subject. In the present paper we will extend the theory to inclu... View full abstract»

THIS paper deals with the mathematical analysis of noise obtained by passing random noise through physical devices. The random noise considered is that which arises from shot effect in vacuum tubes or from thermal agitation of electrons in resistors. Our main interest is in the statistical properties of such noise and we leave to one side many physical results of which Nyquist's law may be given a... View full abstract»

The author was led to the study given in this paper from a consideration of large scale computing machines in which a large number of operations must be performed without a single error in the end result. This problem of “doing things right” on a large scale is not essentially new; in a telephone central office, for example, a very large number of operations are performed while the errors leading ... View full abstract»

THE problems of cryptography and secrecy systems furnish an interesting application of communication theory.¹ In this paper a theory of secrecy systems is developed. The approach is on a theoretical level and is intended to complement the treatment found in standard works on cryptography.² There, a detailed study is made of the many standard types of c... View full abstract»

Correction factors are evaluated for the measurement of sheet resistirities on two-dimensional rectangular and circular samples with the four-point probe. Diffused surface layers can be treated as two-dimensional structures, but the factors are also useful in obtaining body resistivities on thin samples. View full abstract»

We consider the situation in which digital data is to be reliably transmitted over a discrete, memoryless channel (dmc) that is subjected to a wire-tap at the receiver. We assume that the wire-tapper views the channel output via a second dmc). Encoding by the transmitter and decoding by the receiver are permitted. However, the code books used in these operations are assumed to be known by the wire... View full abstract»

In this final installment of the paper we consider the case where the signals or the messages or both are continuously variable, in contrast with the discrete nature assumed until now. To a considerable extent the continuous case can be obtained through a limiting process from the discrete case by dividing the continuum of messages and signals into a large but finite number of small regions and ca... View full abstract»

In this section we use the representations of the noise currents given in section 2.8 to derive some statistical properties of I(t). The first six sections are concerned with the probability distribution of I(t) and of its zeros and maxima. Sections 3.7 and 3.8 are concerned with the statistical properties of the envelope of I(t). Fluctuations of integrals involving I²(t) ar... View full abstract»

In a single crystal of semiconductor the impurity concentration may vary from p-type to n-type producing a mechanically continuous rectifying junction. The theory of potential distribution and rectification for p-n junctions is developed with emphasis on germanium. The currents across the junction are carried by the diffusion of holes in n-type material and electrons in p-type material, resulting ... View full abstract»

We consider the problem of partitioning the nodes of a graph with costs on its edges into subsets of given sizes so as to minimize the sum of the costs on all edges cut. This problem arises in several physical situations — for example, in assigning the components of electronic circuits to circuit boards to minimize the number of connections between boards. This paper presents a heuristic method fo... View full abstract»

We study the transmission properties of a guide consisting of a dielectric rod with rectangular cross section, surrounded by several dielectrics of smaller refractive indices. This guide is suitable for integrated optical circuitry because of its size, single-mode operation, mechanical stability, simplicity, and precise construction. After making some simplifying assumptions, we solve Maxwell's eq... View full abstract»

A coupled wave analysis is given of the Bragg diffraction of light by thick hologram gratings, which is analogous to Phariseau's treatment of acoustic gratings and to the “dynamical” theory of X-ray diffraction. The theory remains valid for large diffraction efficiencies where the incident wave is strongly depleted. It is applied to transmission holograms and to reflection holograms. Spatial modul... View full abstract»

The statistical characteristics of the fields and signals in the reception of radio frequencies by a moving vehicle are deduced from a scattering propagation model. The model assumes that the field incident on the receiver antenna is composed of randomly phased azimuthal plane waves of arbitrary azimuth angles. Amplitude and phase distributions and spatial correlations of fields and signals are de... View full 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 st... View full abstract»

A new radar technique has been developed that provides a solution for the conflicting requirements of simultaneous long-range and high-resolution performance in radar systems. This technique, called Chirp at Bell Telephone Laboratories, recognizes that resolution depends on the transmitted pulse bandwidth. A long high-duty-factor transmitted pulse, with suitable modulation (linear frequency modula... View full abstract»

Measurements of the equivalent parallel conductance of metal-insulator-semiconductor (MIS) capacitors are shown to give more detailed and accurate information about interface states than capacitance measurements. Experimental techniques and methods of analysis are described. From the results of the conductance technique, a realistic characterization of the Si–SiO2interface is developed.... View full abstract»

A complete set of bandlimited functions is described which possesses the curious property of being orthogonal over a given finite interval as well as over (− ∞, ∞). Properties of the functions are derived and several applications to the representation of signals are made. View full abstract»

The problem of wave propagation along a transmission system composed of an overhead wire parallel to the (plane) surface of the earth, in spite of its great technical importance, does not appear to have been satisfactorily solved.1 While a complete solution of the actual problem is impossible, on account of the inequalities in the earth's surface and its lack of conductive homogeneity, the solutio... View full abstract»

After a review of the general aspects of the classical electromagnetic theory several “equivalence” theorems are established and illustrated with a number of examples from the diffraction theory. Then follows a discussion of possible applications of these theorems to radiation problems. The latter part of the paper is devoted to the calculation of the power radiated from an open end of a coaxial p... View full abstract»

The theorem gives the most general form of the driving-point impedance of any network composed of a finite number of self-inductances, mutual inductances, and capacities. This impedance is a pure reactance with a number of resonant and anti-resonant frequencies which alternate with each other. Any such impedance may be physically realized (provided resistances can be made negligibly small) by a ne... View full abstract»

In Some technical problems we are concerned with a current which consists of a sinusoidal component plus a random noise component. A number of statistical properties of such a current are given here. The present paper may be regarded as an extension of Section 3.10 of an earlier paper,1“Mathematical Analysis of Random Noise”, where some of the simpler properties of a sine wave plus rand... View full abstract»

A model of a burst-noise binary channel uses a Markov chain with two states G and B. In state G, transmission is error-free. In state B, the channel has only probability h of transmitting a digit correctly. For suitably small values of the probabilities, p, P of the B $rA G and G $rA B transitions, the model simulates burst-noise channels. Probability formulas relate the parameters p, P, h to easi... View full abstract»

Two algorithms for solving the (symmetric distance) traveling salesman problem have been programmed for a high-speed digital computer. The first produces guaranteed optimal solution for problems involving no more than 13 cities; the time required (IBM 7094 II) varies from 60 milliseconds for a 9-city problem to 1.75 seconds for a 13-city problem. The second algorithm produces precisely characteriz... View full abstract»

The field configurations and propagation constants of the normal modes are determined for a hollow circular waveguide made of dielectric material or metal for application as an optical waveguide. The increase of attenuation due to curvature of the axis is also determined. The attenuation of each mode is found to be proportional to the square of the free-space wavelength λ and inversely proportiona... View full abstract»

The measurement of power spectra is a problem of steadily increasing importance which appears to some to be primarily a problem in statistical estimation. Others may see it as a problem of instrumentation, recording and analysis which vitally involves the ideas of transmission theory. Actually, ideas and techniques from both fields are needed. When they are combined, they provide a basis for devel... View full abstract»