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A highly efficient error correcting code has been selected by NASA as a CCSDS standard: the 16 symbol error correcting Reed Solomon code. A VLSI implementation of this decoder is described in this paper. A total of 4 full custom VLSI chips are needed that correct data in real time at an sustained rate of up to 80 Mbits/second.
Paper extends theory of decoder-error probability for linear maximum-distance separable (MDS) codes. General class of error-correcting codes includes Reed-Solomon codes, important in communications with distant spacecraft, military communications, and compact-disk recording industry. Advancing beyond previous theoretical developments that placed upper bounds on decoder-error probabilities, author derives an exact formula for probability PE(u) that decoder will make error when u code symbols in error.
Reed-Solomon (RS) codes have been part of standard NASA telecommunications systems for many years. RS codes are character-oriented error-correcting codes, and their principal use in space applications has been as outer codes in concatenated coding systems. However, for a given character size, say m bits, RS codes are limited to a length of, at most, 2(exp m). It is known in theory that longer character-oriented codes would be superior to RS codes in concatenation applications, but until recently no practical class of 'long' character-oriented codes had been discovered. In 1992, however, Solomon discovered an extensive class of such codes, which are now called trace-shortened Reed-Solomon (TSRS) codes. In this article, we will continue the study of TSRS codes. Our main result is a formula for the dimension of any TSRS code, as a function of its error-correcting power. Using this formula, we will give several examples of TSRS codes, some of which look very promising as candidate outer codes in high-performance coded telecommunications systems.
A coding scheme is investigated for error control in data communication systems. The scheme is obtained by cascading two error correcting codes, called the inner and outer codes. The error performance of the scheme is analyzed for a binary symmetric channel with bit error rate epsilon <1/2. It is shown that if the inner and outer codes are chosen properly, extremely high reliability can be attained even for a high channel bit error rate. Various specific example schemes with inner codes ranging form high rates to very low rates and Reed-Solomon codes as inner codes are considered, and their error probabilities are evaluated. They all provide extremely high reliability even for very high bit error rates. Several example schemes are being considered by NASA for satellite and spacecraft down link error control.
A Reed Solomon code is a highly efficient error correcting code that NASA will use in future space communication missions. A VLSI implementation of the decoder is presented that accepts data rates of 80 Mbits/second. A total of seven chips are needed and operate with the symbol clock being the system clock for the chip set. Approximately 1.65 billion Galois Field operations per second are achieved with this chip set.
We report a free space laser communication experiment from the satellite laser ranging (SLR) station at NASA Goddard Space Flight Center (GSFC) to the Lunar Reconnaissance Orbiter (LRO) in lunar orbit through the on board one-way Laser Ranging (LR) receiver. Pseudo random data and sample image files were transmitted to LRO using a 4096-ary pulse position modulation (PPM) signal format. Reed-Solomon forward error correction codes were used to achieve error free data transmission at a moderate coding overhead rate. The signal fading due to the atmosphere effect was measured and the coding gain could be estimated.
A coding scheme for error control in data communication systems is investigated. The scheme is obtained by cascading two error-correcting codes, called the inner and outer codes. Its error performance is analyzed for a binary symmetric channel with bit-error rate epsilon less than 1/2. It is shown that, if the inner and outer codes are chosen properly, high reliability can be attained even for a high-channel bit-error rate. Specific examples with inner codes ranging from high rates and Reed-Solomon codes as outer codes are considered, and their error probabilities evaluated. They all provide high reliability even for high bit-error rates, say 0.1-0.01. Several example schemes are being considered for satellite and spacecraft downlink error control.
A coding scheme for error control in data communication systems is investigated. The scheme is obtained by cascading two error correcting codes, called the inner and the outer codes. The error performance of the scheme is analyzed for a binary symmetric channel with bit error rate epsilon < 1/2. It is shown that, if the inner and outer codes are chosen properly, extremely high reliability can be attained even for a high channel bit error rate. Various specific example schemes with inner codes ranging from high rates to very low rates and Reed-Solomon codes are considered, and their probabilities are evaluated. They all provide extremely high reliability even for very high bit error rates, say 0.1 to 0.01. Several example schemes are being considered by NASA for satellite and spacecraft down link error control.
Short-block low-density parity-check (LDPC) codes of a special type are intended to be especially well suited for potential applications that include transmission of command and control data, cellular telephony, data communications in wireless local area networks, and satellite data communications. [In general, LDPC codes belong to a class of error-correcting codes suitable for use in a variety of wireless data-communication systems that include noisy channels.] The codes of the present special type exhibit low error floors, low bit and frame error rates, and low latency (in comparison with related prior codes). These codes also achieve low maximum rate of undetected errors over all signal-to-noise ratios, without requiring the use of cyclic redundancy checks, which would significantly increase the overhead for short blocks. These codes have protograph representations; this is advantageous in that, for reasons that exceed the scope of this article, the applicability of protograph representations makes it possible to design highspeed iterative decoders that utilize belief- propagation algorithms.
A method of using error-correcting codes to obtain data compression, called syndrome-source-coding, is described in which the source sequence is treated as an error pattern whose syndrome forms the compressed data. It is shown that syndrome-source-coding can achieve arbitrarily small distortion with the number of compressed digits per source digit arbitrarily close to the entropy of a binary memoryless source. A universal generalization of syndrome-source-coding is formulated which provides robustly-effective, distortionless, coding of source ensembles.
A method of using error-correcting codes to obtain data compression, called syndrome-source-coding, is described in which the source sequence is treated as an error pattern whose syndrome forms the compressed data. It is shown that syndrome-source-coding can achieve arbitrarily small distortion with the number of compressed digits per source digit arbitrarily close to the entropy of a binary memoryless source. A 'universal' generalization of syndrome-source-coding is formulated which provides robustly effective distortionless coding of source ensembles. Two examples are given, comparing the performance of noiseless universal syndrome-source-coding to (1) run-length coding and (2) Lynch-Davisson-Schalkwijk-Cover universal coding for an ensemble of binary memoryless sources.
We describe novel interleaver and deinterleaver architectures that support bandwidth efficient memory access for decoders of turbo-like codes that are used in conjunction with high order modulations. The presentation focuses on a decoder for serially concatenated pulse-position modulation (SCPPM), which is a forward-error-correction code designed by NASA to support laser communications from Mars at more than 50 megabits-per-second (Mbps). For 64-ary PPM, the new architectures effectively triple the fan-in of the interleaver and fan-out of the deinterleaver, enabling parallelization that doubles the overall throughput. The techniques described here can be readily modified for other PPM orders.
The control system of NASA's Orbital Maneuvering Vehicle (OMV) will employ range/range-rate radar, a forward command link, and a compressed video return link. The video data is compressed by sampling every sixth frame of data; a rate of 5 frames/sec is adequate for the OMV docking speeds. Further axial compression is obtained, albeit at the expense of spatial resolution, by averaging adjacent pixels. The remaining compression is achieved on the basis of differential pulse-code modulation and Huffman run-length encoding. A concatenated error-correction coding system is used to protect the compressed video data stream from channel errors.
Digital electronic still camera part of electronic recording, processing, tansmitting, and displaying system. Removable hard-disk drive in camera serves as digital electronic equivalent of photographic film. Images viewed, analyzed, or transmitted quickly. Camera takes images of nearly photographic quality and stores them in digital form. Portable, hand-held, battery-powered unit designed for scientific use. Camera used in conjunction with playback unit also serving as transmitting unit if images sent to remote station. Remote station equipped to store, process, and display images. Digital image data encoded with error-correcting code at playback/transmitting unit for error-free transmission to remote station.
Codes and coding circuits for automatic error correction in digital computers
In conventional channel coding, all the information symbols of a message are regarded equally significant, and hence codes are devised to provide equal protection for each information symbol against channel errors. However, in some circumstances, some information symbols in a message are more significant than the other symbols. As a result, it is desirable to devise codes with multilevel error-correcting capabilities. In this paper, block codes with multilevel error correcting capabilities, which are also known as unequal error protection (UEP) codes, are investigated. Several classes of UEP codes are constructed. One class of codes satisfies the Hamming bound on the number of parity-check symbols for systematic linear UEP codes and hence is optimal.
A problem in designing semiconductor memories is to provide some measure of error control without requiring excessive coding overhead or decoding time. For example, some 256K-bit dynamic random access memories are organized as 32K x 8 bit-bytes. Byte-oriented codes such as Reed Solomon (RS) codes provide efficient low overhead error control for such memories. However, the standard iterative algorithm for decoding RS codes is too slow for these applications. Some special high speed decoding techniques for extended single and double error correcting RS codes. These techniques are designed to find the error locations and the error values directly from the syndrome without having to form the error locator polynomial and solve for its roots.
Advances made in error-correction coding for deep space communications are described. The code believed to be the best is a (15, 1/6) convolutional code, with maximum likelihood decoding; when it is concatenated with a 10-bit Reed-Solomon code, it achieves a bit error rate of 10 to the -6th, at a bit SNR of 0.42 dB. This code outperforms the Voyager code by 2.11 dB. The use of source statics in decoding convolutionally encoded Voyager images from the Uranus encounter is investigated, and it is found that a 2 dB decoding gain can be achieved.