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At least 163 records · Page 9

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.↗

Stability of finite difference models containing two boundaries or interfaces

The stability of finite difference models of hyperbolic initial boundary value problems is connected with the propagation and reflection of parasitic waves. Wave propagation ideas are applied to models containing two boundaires or interfaces, where repeated reflection of trapped wave packets is a potential new source of instability. Various known instability phenomena are accounted for in a unified way. Results show: (1) dissipativity does not ensure stability when three or more formulas are concatenated at a boundary or internal interface; (2) algebraic GKS instabilities can be converted by a second boundary to exponential instabilities only when an infinite numerical reflection coefficient is present; and (3) GKS-stability and P-stability can be established in certain problems by showing that all numerical reflection coefficients have modulus less than 1.

Trefethen, L. N.↗

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.↗

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.↗

Node synchronization for the Viterbi decoder

At very low signal to noise ratios such as those that Voyager 2 will encounter at Uranus, the performance of the Reed-Solomon/Viterbi concatenated coding system could be seriously degraded by loss of node synchronization by the Viterbi decoder. This problem is described and now it can be almost completely avoided with a simple outboard hardware 'node synchronizer'. This device makes statistical decisions about node sync based on the hard quantized undecoded data stream. In a worst case Voyager-like environment, our method will detect and correct a true loss of node sync (thought to be a very rare event) within several hundred bits; many of these false alarms for our technique is on the order several years. Previously announced in STAR as N83-28028

Lorden, G.↗

Standard methods for telemetry and telecommand channel coding

Recommendations being developed by the NASA-ESA Working Group (NEWG) for Space Data Systems Standardization and the Consultative Committee for Space Data Systems (CCSDS) to standardize spacecraft telemetry and command coding are characterized. The telemetry convolutional codes used by JPL, ESA, and GSFC are found to be similar but incompatible, and it is recommended that a secondary capability for the other two schemes be developed at each facility, with the GSFC scheme as the ultimate standard, a periodic convolutional interleaving procedure for use with the NASA Tracking and Data Relay Satellite, and an optional concatenation of the convolutional code with a Reed-Solomon code to achieve up to 6.8 dB of gain. The telecommand-coding approach adopted by CCSDS is based on the schemes in use at JPL and GSFC.

Macmedan, M. L.↗

Coding for reliable satellite communications

Several error control coding techniques for reliable satellite communications were investigated to find algorithms for fast decoding of Reed-Solomon codes in terms of dual basis. The decoding of the (255,223) Reed-Solomon code, which is used as the outer code in the concatenated TDRSS decoder, was of particular concern.

Lin, S.↗

Reed-solomon Code Synchronization Revisited

A concatenated coding consisting of an inner (7, 1/2) convolutional code and an outer (255, 223) Reed-Solomon code was recommended by the Consultative Committee for Space Data Systems for cross-supported space missions. The Reed-Solomon code that was chosen makes use of the Berlekamp encoding algorithm. Some peculiarities of this code that could give rise to synchronization problems are examined. Suggestions are given to alleviate these problems.

Deutsch, L. J.↗

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.↗

In search of a 2-dB coding gain

A recent code search found a (15,1/5), a (14,1/6), and a (15,1/6) convolutional code which, when concatenated with a 10-bit (1023,959) Reed-Solomon (RS) code, achieves a bit-error rate (BER) of 0.000001 at a bit signal-to-noise ratio (SNR) of 0.50 dB, 0.47 dB and 0.42 B, respectively. All of these three codes outperform the Voyager communication system, our baseline, which achieves a BER of 10.000001 at bit SNR of 2.53 db, by more than 2 dB. The 2 dB coding improvement goal was exceeded.

Yuen, J. H.↗

Error control techniques for satellite and space communications

The performance of NASA Telecommand System was analyzed. A random coding approach was taken to determine the optimum code rate to use in forward error correcting (FEC) system with a fixed signal energy to noise power density ration, but no bandwidth constraint. Capacity and cutoff rates of concatened coding systems were determined. A lower bound on the minium distance growth rate between unmerged codewords was obtained for time invarient convolutional codes.

Costello, D. J., Jr.↗

Coding for reliable satellite communications

This research project was set up to study various kinds of coding techniques for error control in satellite and space communications for NASA Goddard Space Flight Center. During the project period, researchers investigated the following areas: (1) decoding of Reed-Solomon codes in terms of dual basis; (2) concatenated and cascaded error control coding schemes for satellite and space communications; (3) use of hybrid coding schemes (error correction and detection incorporated with retransmission) to improve system reliability and throughput in satellite communications; (4) good codes for simultaneous error correction and error detection, and (5) error control techniques for ring and star networks.

Gaarder, N. T.↗

Stability of finite-difference models containing two boundaries or interfaces

The stability of finite difference models of hyperbolic initial boundary value problems is connected with the propagation and reflection of parasitic waves. Wave propagation ideas are applied to models containing two boundaries or interfaces, where repeated reflection of trapped wave packets is a potential new source of instability. Various known instability phenomena are accounted for in a unified way. Results show: (1) dissipativity does not ensure stability when three or more formulas are concatenated at a boundary or internal interface; (2) algebraic GKS instabilities can be converted by a second boundary to exponential instabilities only when an infinite numerical reflection coefficient is present; and (3) GKS-stability and P-stability can be established in certain problems by showing that all numerical reflection coefficients have modulus less than 1.

Trefethen, L. N.↗

Erasure declaring Viterbi decoders

Several methods for realizing erasure declaring Viterbi decoders for the (7,1/2) NASA code are discussed. Only bit oriented algorithms are considered. When such decoders are used in a concatenated system with a (255,223) Reed-Solomon decoder, improvements on the probability of word error of at most 0.1 dB were obtained.

Pollara, F.↗

Error control techniques for satellite and space communications

The performance of bandwidth efficient trellis inner codes using two-dimensional MPSK signal constellations in a NASA concatenated coding is summarized. Work was also continued on trellis coded modulation using multi-dimensional signal sets. Achievable lower bounds on free distance trellis codes were proved and the existence of good trellis coded modulation (TCM) schemes were established for a variety of signal constellations. The performance of TCM schemes on fading channels is being investigated. Preliminary results indicate that bandwidth efficient trellis coding is feasible on such channels, but that the important design parameter is no longer the minimum free Euclidean distance.

Costello, Daniel J., Jr.↗

A VLSI single chip (255,223) Reed-Solomon encoder with interleaver

A single-chip implementation of a Reed-Solomon encoder with interleaving capability is described. The code used was adapted by the CCSDS (Consulative Committee on Space Data Systems). It forms the outer code of the NASA standard concatenated coding system which includes a convolutional inner code of rate 1/2 and constraint length 7. The architecture, leading to this single VLSI chip design, makes use of a bit-serial finite field multiplication algorithm due to E.R. Berlekamp.

Hsu, I. S.↗

Error control techniques for satellite and space communications

Progress made in the following areas is discussed: concatenated codes using bandwidth efficient Trellis inner codes; bounds on the minimum free Euclidean distance of bandwidth efficient Trellis inner codes; performance analysis of bandwidth Trellis codes on channels with phase jitter; construction of bandwidth efficient Trellis codes; and parity retransmission hybrid ARQ using convolutional codes.

Costello, Daniel J., Jr.↗

Solid modelling for the manipulative robot arm (power) and adaptive vision control for space station missions

The structure of a flexible arm derived from concatenation of the Stewart-Table-based links were studied. Solid modeling provides not only a realistic simulation, but is also essential for studying vision algorithms. These algorithms could be used for the adaptive control of the arm, using the well-known algorithms such as shape from shading, edge detection, orientation, etc. Details of solid modeling and its relation to vision based adaptive control are discussed.

Harrand, V.↗