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A manual is presented as an aid in using the STEEP32 code. The code is the EXEC 8 version of the STEEP code (STEEP is an acronym for shock two-dimensional Eulerian elastic plastic). The major steps in a STEEP32 run are illustrated in a sample problem. There is a detailed discussion of the internal organization of the code, including a description of each subroutine.
It is shown what choice there is in assigning output digits to transitions of binary rate 1/n code trellis so that the latter will correspond to a convolutional code. A new upper bound on free distance of rate 1/n convolutional codes is also derived, and the results obtained are used to determine the length of the largest input sequence that can conceivably result in an output whose weight is equal to the free distance of a code of rate 1/2.
The implementation and performance evaluation are described for a class of rate (M-1)/M, systematic, convolutional codes being decoded with a simple majority logic decoder. The encoding logic appends one parity bit for each PCM telemetry word. It is shown that over the critical range of received PCM telemetry signal-to-noise ratios, this coding procedure produces a net coding gain of from 1.5 to 2.5 db relative to an equal power transmission of uncoded PCM telemetry. Being a low-redundancy systematic code, it is possible to process this data without convolutional decoding with a small rate loss penalty of about 0.5 db.
Three coding schemes designed for improved data communication are evaluated. Four block codes are evaluated relative to a quality function, which is a function of both the amount of data rejected and the error rate. The Viterbi maximum likelihood decoding algorithm as a decoding procedure is reviewed. This evaluation is obtained by simulating the system on a digital computer. Short constraint length rate 1/2 quick-look codes are studied, and their performance is compared to general nonsystematic codes.
Many recent American unmanned planetary probes have used biorthogonally coded spacecraft-to-earth telemetry links. An examination of the frame-synchronization (sync) techniques employed on these missions revealed that they were not specifically designed for coded data. This led to a consideration of the optimum frame-sync problem for biorthogonally coded data received over the additive white Gaussian noise (AWGN) channel and decoded prior to sync acquisition. A frame-sync algorithm for biorthogonally coded data based on a super-symbol distance rule is proposed, along with a corresponding selection criterion for the sync sequence. It is argued heuristically that this approach is optimum with regard to minimizing the probability of false synchronization.
In this note we investigate the properties of two classes of binary primitive alternant codes that are generalizations of the primitive BCH codes. For these codes we establish certain equivalence and invariance relations and obtain values of d and d*, the minimum distances of the prime and dual codes.
This paper presents the results of a study of the performance of Viterbi-decoded convolutional codes in the presence of nonideal carrier tracking and bit synchronization. A constraint length 7, rate 1/3 convolutional code and parameters suitable for the space shuttle coded communications links are used. Mathematical models are developed and theoretical and simulation results are obtained to determine the tracking and acquisition performance of the system. It is shown that the combined energy-to-noise degradation due to nonideal carrier tracking and bit synchronization over that required for the ideal tracking case can be held to less than 1.5 dB and that combined carrier tracking and bit timing can be acquired in only a few seconds for the parameters and operating ranges of the space shuttle coded communications links.
An approach is shown for using the Huffman algorithm indirectly to prove the optimality of a code for an infinite alphabet if an estimate concerning the nature of the code can be made. Attention is given to nonnegative integers with a geometric probability assignment. The particular distribution considered arises in run-length coding and in encoding protocol information in data networks. Questions of redundancy of the optimal code are also investigated.
Virtually all previously-suggested rate 1/2 binary convolutional codes with KE = 24 are compared. Their distance properties are given; and their performance, both in computation and in error probability, with sequential decoding on the deep-space channel is determined by simulation. Recommendations are made both for the choice of a specific KE = 24 code as well as for codes to be included in future coding standards for the deep-space channel. A new result given in this report is a method for determining the statistical significance of error probability data when the error probability is so small that it is not feasible to perform enough decoding simulations to obtain more than a very small number of decoding errors.
The present, third volume of the final report is a programmer's manual for the code. It provides a listing of the FORTRAN 4 source program; a complete glossary of FORTRAN symbols; a discussion of the purpose and method of operation of each subroutine (including mathematical analyses of special algorithms); and a discussion of the operation of the code on IBM/360 and UNIVAC 1108 systems, including required control cards and the overlay structure used to accommodate the code to the limited core size of the 1108. In addition, similar information is provided to document the programming of the NOZFIT code, which is employed to set up nozzle profile curvefits for use in NATA.
The pseudonoise (PN) code library for the Tracking and Data Relay Satellite System (TDRSS) Services was defined and described. The code library was chosen to minimize user transponder hardware requirements and optimize system performance. Special precautions were taken to insure sufficient code phase separation to minimize cross-correlation sidelobes, and to avoid the generation of spurious code components which would interfere with system performance.
A tabulation of binary systematic convolutional codes with an optimum distance profile for rates 1/3 and 1/4 is given. A number of short rate 1/3 binary nonsystematic convolutional codes are listed. These latter codes are simultaneously optimal for the following distance measures: distance profile, minimum distance, and free distance; they appear attractive for use with Viterbi decoders. Comparisons with previously known codes are made.
The method of solution is a hybrid analytical numerical technique which utilizes eigenvalues and eigenvectors. The method is inherently stable, permitting large time steps even with the best of conductors with the finest of mesh sizes which can provide a factor of five reduction in machine time compared to conventional explicit finite difference methods when structures with small time constants are analyzed over long time periods. This code will find utility in analyzing hypersonic missile and aircraft structures which fall naturally into this class. The code is a completely general one in that problems involving any geometry, boundary conditions and materials can be analyzed. This is made possible by requiring the user to establish the thermal network conductances between nodes. Dynamic storage allocation is used to minimize core storage requirements. This report is primarily a user's manual for CAVE3 code. Input and output formats are presented and explained. Sample problems are included which illustrate the usage of the code as well as establish the validity and accuracy of the method.
Basic information about the computer code STAGS (Structural Analysis of General Shells) is presented to describe to potential users the scope of the code and the solution procedures that are incorporated. Primarily, STAGS is intended for analysis of shell structures, although it has been extended to more complex shell configurations through the inclusion of springs and beam elements. The formulation is based on a variational approach in combination with local two dimensional power series representations of the displacement components. The computer code includes options for analysis of linear or nonlinear static stress, stability, vibrations, and transient response. Material as well as geometric nonlinearities are included. A few examples of applications of the code are presented for further illustration of its scope.
The development of computer codes for calculating dynamic loads in horizontal axis wind turbines was examined, and a brief overview of each code was given. The performance of individual codes was compared against two sets of test data measured on a 100 KW Mod-0 wind turbine. All codes are aeroelastic and include loads which are gravitational, inertial and aerodynamic in origin.
A decoding procedure is described for the (n,k) t-error-correcting Reed-Solomon (RS) code, and an implementation of the (31,15) RS code for the I4-TENEX central system. This code can be used for error correction in large archival memory systems. The principal features of the decoder are a Galois field arithmetic unit implemented by microprogramming a microprocessor, and syndrome calculation by using the g(x) encoding shift register. Complete decoding of the (31,15) code is expected to take less than 500 microsecs. The syndrome calculation is performed by hardware using the encoding shift register and a modified Chien search. The error location polynomial is computed by using Lin's table, which is an interpretation of Berlekamp's iterative algorithm. The error location numbers are calculated by using the Chien search. Finally, the error values are computed by using Forney's method.
An example is provided of two convolutional codes that have the same transmission gain but whose dual codes do not. This shows that no analog of the MacWilliams identity for block codes can exist relating the transmission gains of a convolutional code and its dual.
The performance of certain block codes on a Gaussian channel is evaluated. The BCH codes are markedly superior to convolutional codes currently used for deep space missions. The algorithm is used to derive results, which provides a basis for a simple, almost optimum procedure for decoding these codes.