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NASA NTRS1984

Simulations for Full Unit-memory and Partial Unit-memory Convolutional Codes with Real-time Minimal-byte-error Probability Decoding Algorithm

A program which was written to simulate Real Time Minimal-Byte-Error Probability (RTMBEP) decoding of full unit-memory (FUM) convolutional codes on a 3-bit quantized AWGN channel is described. This program was used to compute the symbol-error probability of FUM codes and to determine the signal to noise (SNR) required to achieve a bit error rate (BER) of 10 to the minus 6th power for corresponding concatenated systems. A (6,6/30) FUM code, 6-bit Reed-Solomon code combination was found to achieve the required BER at a SNR of 1.886 dB. The RTMBEP algorithm was then modified for decoding partial unit-memory (PUM) convolutional codes. A simulation program was also written to simulate the symbol-error probability of these codes.

Vo, Q. D.↗

NASA NTRS1984

Performance analysis of the word synchronization properties of the outer code in a TDRSS decoder

A self-synchronizing coding scheme for NASA's TDRSS satellite system is a concatenation of a (2,1,7) inner convolutional code with a (255,223) Reed-Solomon outer code. Both symbol and word synchronization are achieved without requiring that any additional symbols be transmitted. An important parameter which determines the performance of the word sync procedure is the ratio of the decoding failure probability to the undetected error probability. Ideally, the former should be as small as possible compared to the latter when the error correcting capability of the code is exceeded. A computer simulation of a (255,223) Reed-Solomon code as carried out. Results for decoding failure probability and for undetected error probability are tabulated and compared.

Costello, D. J., Jr.↗

NASA NTRS1984

Automatic finite element generators

The design and implementation of a software system for generating finite elements and related computations are described. Exact symbolic computational techniques are employed to derive strain-displacement matrices and element stiffness matrices. Methods for dealing with the excessive growth of symbolic expressions are discussed. Automatic FORTRAN code generation is described with emphasis on improving the efficiency of the resultant code.

Wang, P. S.↗

NASA NTRS1984

Performance Simulation for Unit-memory Convolutional Codes with Byte-oriented Viterbi Decoding Algorithm

A software package developed to simulate the performance of the byte-oriented Viterbi decoding algorithm for unit-memory (UM) codes on both 3-bit and 4-bit quantized AWGN channels is described. The simulation is shown to require negligible memory and less time than that for the RTMBEP algorith, although they both provide similar performance in terms of symbol-error probability. This makes it possible to compute the symbol-error probability of large codes and to determine the signal-to-noise ratio required to achieve a bit error rate (BER) of 0.000001 for corresponding concatenated systems. A (7, 10/48) UM code, 10-bit Reed-Solomon code combination achieves the required BER at 1.08 dB for a 3-bit quantized channel and at 0.91 dB for a 4-bit quantized channel.

Vo, Q. D.↗

NASA NTRS1984

Coherent Digital Demodulation of a Residual Carrier Signal Using IF Sampling

An analysis is presented of a digital technique for the coherent demodulation of a residual carrier signal with a biphase modulated square wave subcarrier. The processing technique employs the concept of intermediate frequencies IF sampling. An optimum Costas loop is used for subcarrier demodulation and data-aided carrier tracking, i.e., combined Costas and residual carrier tracking. It is shown that the loops perform essentially the same as the corresponding analog loops in terms of signal-to-noise ratio and loop bandwidth. The sampling does not introduce biases or other significant effects on the loops, provided that the loop bandwidth is very small compared to the symbol rate, and that the number of samples per symbol is large compared to inverse loop bandwidth.

Sfeir, R.↗

NASA NTRS1983

The effects of cuing in time-shared tasks

The results of two divided-attention experiments involving the editing of route-way-point displays on an avionics computer unit are reported. Two side tasks were required of the subjects, and either no cue, verbal cues appearing on the CRT, or symbolic cues (lights on the keyboard adjacent to keys to be used) were given to facilitate the primary editing task. Forty female and 30 male undergraduates were trained in the separate and combined tasks and divided randomly into groups of 25 for the cuing tests. A second test with three 10-subject groups was conducted at least one month later to investigate the efficacy of cuing for infrequently used procedures. It is found that only symbolic cuing significantly improved primary-task performance, increasing editing accuracy in the repetitive tests and reducing editing time in the delayed tests. Verbal cuing, probably because it requires additional cognitive effort, has no significant beneficial effect. These results are considered important for designing instruments for work environments requiring the performance of concurrent tasks, and as aircraft cockpits.

Chechile, R. A.↗

NASA NTRS1984

Mathematical models for cochannel interference in FH/MFSK multiple-access systems

FH/MFSK has been proposed for a multiuser spread spectrum digital communication system to combat both self-jamming and intentional jamming. An independence assumption at the energy detector outputs is used to evaluate such a system for a digitized voice mobile radio system (Yue, 1981). This paper presents a correlated model and compares its performance to an independence model under the symbol error probability criterion. A Gaussian process model is also developed for comparison. It is found that the conventional Gaussian approximation is inadequate in predicting the number of users that can be accommodated by an FH/MFSK system using the conventional receiver. Furthermore, for the cases evaluated, the independence model provides an excellent approximation to the correlated model. Additionally, a conditional Chernoff bound is presented for the more general case of frequency-hopping systems with multiple hops per symbol.

Yan, T.-Y.↗

NASA NTRS1986

Fast Reed-Solomon Decoder

High-speed decoder intended for use with Reed-Solomon (RS) codes of long code length and high error-correcting capability. Design based on algorithm that includes high-radix Fermat transform procedure, which is most efficient for high speeds. RS code in question has code-word length of 256 symbols, of which 224 are information symbols and 32 are redundant.

Liu, K. Y.↗

NASA NTRS1985

Digital scrambling for shuttle communication links: Do drawbacks outweigh advantages?

Digital data scrambling has been considered for communication systems using NRZ (non-return to zero) symbol formats. The purpose is to increase the number of transitions in the data to improve the performance of the symbol synchronizer. This is accomplished without expanding the bandwidth but at the expense of increasing the data bit error rate (BER). Models for the scramblers/descramblers of practical interest are presented together with the appropriate link model. The effects of scrambling on the performance of coded and uncoded links are studied. The results are illustrated by application to the Tracking and Data Relay Satellite System links. Conclusions regarding the usefulness of scrambling are also given.

Dessouky, K.↗

NASA NTRS1985

On the binary weight distribution of some Reed-Solomon codes

Consider an (n,k) linear code with symbols from GF(2 sup M). If each code symbol is represented by a m-tuple over GF(2) using certain basis for GF(2 sup M), a binary (nm,km) linear code is obtained. The weight distribution of a binary linear code obtained in this manner is investigated. Weight enumerators for binary linear codes obtained from Reed-Solomon codes over GF(2 sup M) generated by polynomials, (X-alpha), (X-l)(X-alpha), (X-alpha)(X-alpha squared) and (X-l)(X-alpha)(X-alpha squared) and their extended codes are presented, where alpha is a primitive element of GF(2 sup M). Binary codes derived from Reed-Solomon codes are often used for correcting multiple bursts of errors.

Lin, S.↗

NASA NTRS1985

Flowcharting with D-charts

A D-Chart is a style of flowchart using control symbols highly appropriate to modern structured programming languages. The intent of a D-Chart is to provide a clear and concise one-for-one mapping of control symbols to high-level language constructs for purposes of design and documentation. The notation lends itself to both high-level and code-level algorithmic description. The various issues that may arise when representing, in D-Chart style, algorithms expressed in the more popular high-level languages are addressed. In particular, the peculiarities of mapping control constructs for Ada, PASCAL, FORTRAN 77, C, PL/I, Jovial J73, HAL/S, and Algol are discussed.

Meyer, D.↗

NASA NTRS1983

Self-synchronizing outer codes for the TDRSS decoder

In this paper, various aspects of developing a self-synchronizing coding system are discussed for NASA's TDRSS satellite system. The coding system used is a concatenation of a (2, 1, 7) inner convolutional code with a (255,223) Reed-Solomon outer code. The goal is to design the decoder in such a way that both symbol and word synchronization are achieved for the outer code without the need for any separate synchronization patten. The system proposed in this paper uses the properties of the inner (Viterbi) decoder to provide symbol synchronization for the outer code, and maintains word synchronization by making use of a coset code of the Reed-Solomon code.

Lin, S.↗

NASA NTRS1985

Flowcharting with D-charts

Meyer, D. D.↗

NASA NTRS1985

Head-up display (HUD) utility. II - Runway to HUD transitions monitoring eye focus and decision times

An experiment conducted using a head-up display (HUD) suggests that the demonstrated superiority of the HUD over a conventional instrument panel stems from its superior layout of information. A HUD display presents instrument-panel information to pilots in such a way that the symbols appear as a virtual image at optical infinity superimposed on the landscape. In the experiment conducted, the luminance of the display symbology and its angle subtended at the eye remained fixed, while optical distance and gaze angle were varied. Concomitant measures of eye movements, eye accommodative state, and decision-making time concerning airspeed, altitude and runway condition were obtained. It is found that, while looking straight ahead, at zero diopters, the HUD shortens decision time by 80 to 90 msec, not statistically significant at the 0.05 (slope of diopter/gaze interaction) level. The question of a cognitive overload induced by the luminous symbols of the HUD is subsequently addressed.

Weintraub, D. J.↗

NASA NTRS1985

Effect of digital scrambling on satellite communication links

Digital data scrambling has been considered for communication systems using NRZ symbol formats. The purpose is to increase the number of transitions in the data to improve the performance of the symbol synchronizer. This is accomplished without expanding the bandwidth but at the expense of increasing the data bit error rate (BER). Models for the scramblers/descramblers of practical interest are presented together with the appropriate link model. The effects of scrambling on the performance of coded and uncoded links are studied. The results are illustrated by application to the Tracking and Data Relay Satellite System (TDRSS) links. Conclusions regarding the usefulness of scrambling are also given.

Dessouky, K.↗

NASA NTRS1986

Performance analysis of a cascaded coding scheme with interleaved outer code

A cascaded coding scheme for a random error channel with a bit-error rate is analyzed. In this scheme, the inner code C sub 1 is an (n sub 1, m sub 1l) binary linear block code which is designed for simultaneous error correction and detection. The outer code C sub 2 is a linear block code with symbols from the Galois field GF (2 sup l) which is designed for correcting both symbol errors and erasures, and is interleaved with a degree m sub 1. A procedure for computing the probability of a correct decoding is presented and an upper bound on the probability of a decoding error is derived. The bound provides much better results than the previous bound for a cascaded coding scheme with an interleaved outer code. Example schemes with inner codes ranging from high rates to very low rates are evaluated. Several schemes provide extremely high reliability even for very high bit-error rates say 10 to the -1 to 10 to the -2 power.

Lin, S.↗

NASA NTRS1986

Multiple Trellis Coded Modulation (MTCM): An MSAT-X report

Conventional trellis coding outputs one channel symbol per trellis branch. The notion of multiple trellis coding is introduced wherein more than one channel symbol per trellis branch is transmitted. It is shown that the combination of multiple trellis coding with M-ary modulation yields a performance gain with symmetric signal set comparable to that previously achieved only with signal constellation asymmetry. The advantage of multiple trellis coding over the conventional trellis coded asymmetric modulation technique is that the potential for code catastrophe associated with the latter has been eliminated with no additional cost in complexity (as measured by the number of states in the trellis diagram).

Divsalar, D.↗

NASA NTRS1987

The binary weight distribution of the extended (2 sup m, 2 sup m-4) code of Reed-Solomon code over GF(2 sup m) with generator polynomial (x-alpha sup 2) (x-alpha sup 3)

Consider an (n,k) linear code with symbols from GF(2 sup m). If each code symbol is represented by a binary m-tuple using a certain basis for GF(2 sup m), a binary (nm,km) linear code called a binary image of the original code is obtained. A lower bound is presented on the minimum weight enumerator for a binary image of the extended (2 sup m, 2 sup m -4) code of Reed-Solomon code over GF(2 sup m) with generator polynomical (x - alpha)(x- alpha squared)(x - alpha cubed) and its dual code, where alpha is a primitive element in GF(2 sup m).

Lin, Shu↗