Bit Geometrically Uniform Encoders: A Sustematic Approach to the Design of Serially Concatenated Trellis Coded Modulation
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Bit Geometrically Uniform Encoders uniform bit err↗
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Error coding simulations in C
When data is transmitted through a noisy channel, errors are produced within the data rendering it indecipherable. Through the use of error control coding techniques, the bit error rate can be reduced to any desired level without sacrificing the transmission data rate. The Astrionics Laboratory at Marshall Space Flight Center has decided to use a modular, end-to-end telemetry data simulator to simulate the transmission of data from flight to ground and various methods of error control. The simulator includes modules for random data generation, data compression, Consultative Committee for Space Data Systems (CCSDS) transfer frame formation, error correction/detection, error generation and error statistics. The simulator utilizes a concatenated coding scheme which includes CCSDS standard (255,223) Reed-Solomon (RS) code over GF(2(exp 8)) with interleave depth of 5 as the outermost code, (7, 1/2) convolutional code as an inner code and CCSDS recommended (n, n-16) cyclic redundancy check (CRC) code as the innermost code, where n is the number of information bits plus 16 parity bits. The received signal-to-noise for a desired bit error rate is greatly reduced through the use of forward error correction techniques. Even greater coding gain is provided through the use of a concatenated coding scheme. Interleaving/deinterleaving is necessary to randomize burst errors which may appear at the input of the RS decoder. The burst correction capability length is increased in proportion to the interleave depth. The modular nature of the simulator allows for inclusion or exclusion of modules as needed. This paper describes the development and operation of the simulator, the verification of a C-language Reed-Solomon code, and the possibility of using Comdisco SPW(tm) as a tool for determining optimal error control schemes.
Noble, Viveca K.↗
Bandwidth efficient CCSDS coding standard proposals
The basic concatenated coding system for the space telemetry channel consists of a Reed-Solomon (RS) outer code, a symbol interleaver/deinterleaver, and a bandwidth efficient trellis inner code. A block diagram of this configuration is shown. The system may operate with or without the outer code and interleaver. In this recommendation, the outer code remains the (255,223) RS code over GF(2 exp 8) with an error correcting capability of t = 16 eight bit symbols. This code's excellent performance and the existence of fast, cost effective, decoders justify its continued use. The purpose of the interleaver/deinterleaver is to distribute burst errors out of the inner decoder over multiple codewords of the outer code. This utilizes the error correcting capability of the outer code more efficiently and reduces the probability of an RS decoder failure. Since the space telemetry channel is not considered bursty, the required interleaving depth is primarily a function of the inner decoding method. A diagram of an interleaver with depth 4 that is compatible with the (255,223) RS code is shown. Specific interleaver requirements are discussed after the inner code recommendations.
Costello, Daniel J., Jr.↗
Analysis of space telescope data collection systems
The Multiple Access (MA) communication link of the Space Telescope (ST) is described. An expected performance bit error rate is presented. The historical perspective and rationale behind the ESTL space shuttle end-to-end tests are given. The concatenated coding scheme using a convolutional encoder for the outer coder is developed. The ESTL end-to-end tests on the space shuttle communication link are described. Most important is how a concatenated coding system will perform. This is a go-no-go system with respect to received signal-to-noise ratio. A discussion of the verification requirements and Specification document is presented, and those sections that apply to Space Telescope data and communications system are discussed. The Space Telescope System consists of the Space Telescope Orbiting Observatory (ST), the Space Telescope Science Institute, and the Space Telescope Operation Control Center. The MA system consists of the ST, the return link from the ST via the Tracking and Delay Relay Satellite system to White Sands, and from White Sands via the Domestic Communications Satellite to the STOCC.
Ingels, F. M.↗
Soft-Input Soft-Output Modules for the Construction and Distributed Iterative Decoding of Code Networks
Soft-input soft-output building blocks (modules) are presented to construct and iteratively decode in a distributed fashion code networks, a new concept that includes, and generalizes, various forms of concatenated coding schemes.
iterative decoding turbo codes serial concatenated↗
Cut-off rate calculations for the outer channel in a concatenated cooling system
Concatenated codes were long used as a practical means of achieving long block or constraint lengths for combating errors on very noisy channels. The inner and outer encoders are normally separated by an interleaver, so that decoded error bursts coming from the inner decoder are randomized before entering the outer decoder. The effectiveness of this interleaver is examined by calculating the cut-off rate of the outer channel seen by the outer decoder with and without interleaving. Interleaving never hurts the performance of a concatenated code, and when the inner code rate is near the cut-off rate of the inner channel, interleaving significantly improves code performance.
Herro, M. A.↗
A reduced complexity highly power/bandwidth efficient coded FQPSK system with iterative decoding
Based on a representation of FQPSK as a trellis-coded modulation, this paper investigates the potential improvement in power efficiency obtained from the application of simple outer codes to form a concatenated coding arrangement with iterative decoding.
FQPSK digital communications iterative decoding ba↗
Serial concatenated trellis coded modulation with rate-1 inner code
We develop new, low complexity turbo codes suitable for bandwidth and power limited systems, for very low bit and word error rate requirements.
code↗
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.↗
Enhanced decoding for the Galileo low-gain antenna mission: Viterbi redecoding with four decoding stages
The Galileo low-gain antenna mission will be supported by a coding system that uses a (14,1/4) inner convolutional code concatenated with Reed-Solomon codes of four different redundancies. Decoding for this code is designed to proceed in four distinct stages of Viterbi decoding followed by Reed-Solomon decoding. In each successive stage, the Reed-Solomon decoder only tries to decode the highest redundancy codewords not yet decoded in previous stages, and the Viterbi decoder redecodes its data utilizing the known symbols from previously decoded Reed-Solomon codewords. A previous article analyzed a two-stage decoding option that was not selected by Galileo. The present article analyzes the four-stage decoding scheme and derives the near-optimum set of redundancies selected for use by Galileo. The performance improvements relative to one- and two-stage decoding systems are evaluated.
Dolinar, S.↗
Error control techniques for satellite and space communications
This report focuses on the results obtained during the PI's recent sabbatical leave at the Swiss Federal Institute of Technology (ETH) in Zurich, Switzerland, from January 1, 1995 through June 30, 1995. Two projects investigated various properties of TURBO codes, a new form of concatenated coding that achieves near channel capacity performance at moderate bit error rates. The performance of TURBO codes is explained in terms of the code's distance spectrum. These results explain both the near capacity performance of the TURBO codes and the observed 'error floor' for moderate and high signal-to-noise ratios (SNR's). A semester project, entitled 'The Realization of the Turbo-Coding System,' involved a thorough simulation study of the performance of TURBO codes and verified the results claimed by previous authors. A copy of the final report for this project is included as Appendix A. A diploma project, entitled 'On the Free Distance of Turbo Codes and Related Product Codes,' includes an analysis of TURBO codes and an explanation for their remarkable performance. A copy of the final report for this project is included as Appendix B.
Costello, Daniel J., Jr.↗
Soft-decision decoding techniques for linear block codes and their error performance analysis
The first paper presents a new minimum-weight trellis-based soft-decision iterative decoding algorithm for binary linear block codes. The second paper derives an upper bound on the probability of block error for multilevel concatenated codes (MLCC). The bound evaluates difference in performance for different decompositions of some codes. The third paper investigates the bit error probability code for maximum likelihood decoding of binary linear codes. The fourth and final paper included in this report is concerns itself with the construction of multilevel concatenated block modulation codes using a multilevel concatenation scheme for the frequency non-selective Rayleigh fading channel.
Lin, Shu↗
Serial Concatenation of Interleaved Codes: Performance Analysis, Design and Iterative Decoding
In this paper, upper bounds to the average maximum-likelihood bit error probability of serially concatenated coding schemes are derived, design guidelines for the outer and inner codes that maximize the interleaver gain are presented, and finally, a highly-performing iterative decoding algorithm is proposed.
Concatenation↗
Performance of concatenated Reed-Solomon/Viterbi channel coding
The concatenated Reed-Solomon (RS)/Viterbi coding system is reviewed. The performance of the system is analyzed and results are derived with a new simple approach. A functional model for the input RS symbol error probability is presented. Based on this new functional model, we compute the performance of a concatenated system in terms of RS word error probability, output RS symbol error probability, bit error probability due to decoding failure, and bit error probability due to decoding error. Finally we analyze the effects of the noisy carrier reference and the slow fading on the system performance.
Divsalar, D.↗
The effects of Reed-Solomon code shortening on the performance of coded telemetry systems
The theory of Reed-Solomon code shortening in general was developed and the degradation due to shortening in the context of concatenated coding was qualified. It is shown that in the NASA/ESA concatenated system, significant degradations occur only when N 180. A Reed-Solomon code was concatenated with an inner (7, 1/2) convolutional code. Under some circumstances, it would be desirable to use a shorter outer code word length. For example, the format of the data coming from science instruments on board a spacecraft may lend itself naturally to a word length of 200 symbols rather than 223. To accommodate such code word lengths, the Reed-Solomon code can be shortened to an (N, N-32) code where N can be any integer between 33 and 255. Shortening the code, however, changes its performance. On one hand, the amount of redundancy per information symbol increases. Because of this increased redundancy, the amount of energy per information symbol is decreased by code shortening. The overall effect is to degrade the performance of the code.
Deutsch, L. J.↗
Iterative demodulation and decoding of coded non-square QAM
Simulation results show that, with iterative demodulation and decoding, coded NS-8QAM performs 0.5 dB better than standard 8QAM and 0.7 dB better than 8PSK at BER= 10(sup -5), when the FEC code is the (15, 11) Hamming code concatenated with a rate-1 accumulator code, while coded NS-32QAM performs 0.25 dB better than standard 32QAM.
iterative decoding QAM bit error rate capacity↗
Multilevel Concatenated Block Modulation Codes for the Frequency Non-selective Rayleigh Fading Channel
This paper is concerned with construction of multilevel concatenated block modulation codes using a multi-level concatenation scheme for the frequency non-selective Rayleigh fading channel. In the construction of multilevel concatenated modulation code, block modulation codes are used as the inner codes. Various types of codes (block or convolutional, binary or nonbinary) are being considered as the outer codes. In particular, we focus on the special case for which Reed-Solomon (RS) codes are used as the outer codes. For this special case, a systematic algebraic technique for constructing q-level concatenated block modulation codes is proposed. Codes have been constructed for certain specific values of q and compared with the single-level concatenated block modulation codes using the same inner codes. A multilevel closest coset decoding scheme for these codes is proposed.
Lin, Shu↗
Deep space communications, weather effects, and error control
Deep space telemetry is and will remain signal-to-noise limited and vulnerable to interference. A need exists to increase received signal power and decrease noise. This includes going to Ka-band in the mid-1990's to increase directivity. The effects of a wet atmosphere can increase the noise temperature by a factor of 5 or more, even at X-band, but the order of magnitude increase in average data rate obtainable at Ka-band relative to X-band makes the increased uncertainty a good trade. Lowbit error probabilities required by data compression are available both theoretically and practically with coding, at an infinitesimal power penalty rather than the 10 to 15 dB more power required to reduce error probabilities without coding. Advances are coming rapidly in coding, as with the new constraint-length 15 rate 1/4 convolutional code concatenated with the already existing Reed-Solomon code to be demonstrated on Galileo. In addition, high density spacecraft data storage will allow selective retransmissions, even from the edge of the Solar System, to overcome weather effects. In general, deep space communication was able to operate, and will continue to operate, closer to theoretical limits than any other form of communication. These include limits in antenna area and directivity, system noise temperature, coding efficiency, and everything else. The deep space communication links of the mid-90's and beyond will be compatible with new instruments and compression algorithms and represent a sensible investment in an overall end-to-end information system design.
Posner, Edward C.↗