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In this paper, we demonstrate a class of low-complexity modulation codes satisfying the (d,k) constraint that offer throughput gains over M-PPM on the order of 10-15%, which translate into SNR gains of .4 - .6 dB.
It has previously been shown that the Reed-Solomon (RS) codes can correct errors beyond the Singleton and Rieger Bounds with an arbitrarily small probability of a miscorrect. That is, an (n,k) RS code can correct more than (n-k)/2 errors. An implementation of such an RS decoder is presented in this paper. An existing RS decoder, the AHA4010, is utilized in this work. This decoder is especially useful for errors which are patterned with a long burst plus some random errors.
A problem in designing semiconductor memories is to provide some measure of error control without requiring excessive coding overhead or decoding time. In LSI and VLSI technology, memories are often organized on a multiple bit (or byte) per chip basis. For example, some 256K-bit DRAM's are organized in 32Kx8 bit-bytes. Byte oriented codes such as Reed Solomon (RS) codes can 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 decoding techniques for extended single-and-double-error-correcting RS codes which are capable of high speed operation are presented. These techniques are designed to find the error locations and the error values directly from the syndrome without having to use the iterative algorithm to find the error locator polynomial.
A detailed discussion of the use of channel coding for error correction, privacy/secrecy, channel separation, and synchronization is presented. Channel coding, in one form or another, is an established and common element in data systems. No analysis and design of a major new system would fail to consider ways in which channel coding could make the system more effective. The presence of channel coding on TDRS, Shuttle, the Advanced Communication Technology Satellite Program system, the JSC-proposed Space Operations Center, and the proposed 30/20 GHz Satellite Communication System strongly support the requirement for the utilization of coding for the communications channel. The designers of the space station data system have to consider the use of channel coding.
The unequal error correction capabilities of binary cyclic codes of composite length are investigated. Under certain conditions, direct sums of concatenated codes have unequal error correction capabilities. By a modified Hartmann and Tzeng algorithm, it is shown that a binary cyclic code of composite length is equivalent to the direct sum of concatenated codes. With this, some binary cyclic unequal error protection (UEP) codes are constructed. Finally, two-level UEP cyclic direct-sum codes are presented which provide error correction capabilities higher than those guaranteed by the Blokh-Zyablov constructions.
Bose-Chaudhuri-Hocquenghem codes for correcting random errors
Recently several day and nighttime links under diverse atmospheric conditions were completed using the Optical Payload for Lasercomm Science (OPALS) flight system on-board the International Space Station (ISS). In this paper we compare measured optical power and its variance at either end of the link with predictions that include atmospheric propagation models. For the 976 nm laser beacon mean power transmitted from the ground to the ISS the predicted mean irradiance of 10's of microwatts per square meter close to zenith and its decrease with range and increased air mass shows good agreement with predictions. The irradiance fluctuations sampled at 100 Hz also follow the expected increase in scintillation with air mass representative of atmospheric coherence lengths at zenith at 500 nm in the 3-8 cm range. The downlink predicted power of 100's of nanowatts was also reconciled within the uncertainty of the atmospheric losses. Expected link performance with uncoded bit-error rates less than 1E-4 required for the Reed-Solomon code to correct errors for video, text and file transmission was verified. The results of predicted and measured powers and fluctuations suggest the need for further study and refinement.
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Shortest sequence of bits likely to be filled with error bursts examined. Algorithm improves synchronization of frames of noisy binary-coded data signals after Viterbi decoding (recovery from "inner" convolutional code used in transmission channel) and before Reed-Solomon or other decoding (recovery from "outer" error-correcting block code). Based on comparisons of sequences of correct and erroneous Viterbi-decoded received bits with known marker sequence denoting beginning of frame of data. Does not require count of number of bits in received sequence disagreeing with corresponding bits in marker sequence.
A concatenated coding scheme for providing very reliable data over mobile-satellite channels at power levels similar to those used for vocoded speech is described. The outer code is a shorter Reed-Solomon code which provides error detection as well as error correction capabilities. The inner code is a 1-D 8-state trellis code applied independently to both the inphase and quadrature channels. To achieve the full error correction potential of this inner code, the code symbols are multiplexed with a pilot sequence which is used to provide dynamic channel estimation and coherent detection. The implementation structure of this scheme is discussed and its performance is estimated.
We investigate methods of coding for a channel subject to a large dead-time constraint, i.e. a constraint on the minimum spacing between transmitted pulses, with the deep-space optical channel as the motivating example.
The trellis structure of linear block codes (LBCs) is discussed. The state and branch complexities of a trellis diagram (TD) for a LBC is investigated. The TD with the minimum number of states is said to be minimal. The branch complexity of a minimal TD for a LBC is expressed in terms of the dimensions of specific subcodes of the given code. Then upper and lower bounds are derived on the number of states of a minimal TD for a LBC, and it is shown that a cyclic (or shortened cyclic) code is the worst in terms of the state complexity among the LBCs of the same length and dimension. Furthermore, it is shown that the structural complexity of a minimal TD for a LBC depends on the order of its bit positions. This fact suggests that an appropriate permutation of the bit positions of a code may result in an equivalent code with a much simpler minimal TD. Boolean polynomial representation of codewords of a LBC is also considered. This representation helps in study of the trellis structure of the code. Boolean polynomial representation of a code is applied to construct its minimal TD. Particularly, the construction of minimal trellises for Reed-Muller codes and the extended and permuted binary primitive BCH codes which contain Reed-Muller as subcodes is emphasized. Finally, the structural complexity of minimal trellises for the extended and permuted, and double-error-correcting BCH codes is analyzed and presented. It is shown that these codes have relatively simple trellis structure and hence can be decoded with the Viterbi decoding algorithm.
The design of a reliable satellite communication link involving the data transfer from a small, low-orbit satellite to a ground station, but through a geostationary satellite, was examined. In such a scenario, the received signal power to noise density ratio increases as the transmitting low-orbit satellite comes into view, and then decreases as it then departs, resulting in a short-duration, time-varying communication link. The optimal values of the small satellite antenna beamwidth, signaling rate, modulation scheme and the theoretical link throughput (in bits per day) have been determined. The goal of this thesis is to choose a practical coding scheme which maximizes the daily link throughput while satisfying a prescribed probability of error requirement. We examine the throughput of both fixed rate and variable rate concatenated forward error correction (FEC) coding schemes for the additive white Gaussian noise (AWGN) channel, and then examine the effect of radio frequency interference (RFI) on the best coding scheme among them. Interleaving is used to mitigate degradation due to RFI. It was found that the variable rate concatenated coding scheme could achieve 74 percent of the theoretical throughput, equivalent to 1.11 Gbits/day based on the cutoff rate R(sub 0). For comparison, 87 percent is achievable for AWGN-only case.
We present a design framework for the implementation for a Low-Density Parity-Check (LDPC) decoders. We employed a scalable decoding architecture for a certain class of structured LDPC codes.
The features of a TDM (time-division multiplexed) link model are described. A PCM telemetry sequence was coded for error correction and multiplexed with a digitized voice channel. An all-digital implementation of a variable-slope delta modulation algorithm was used to digitize the voice channel. The results of extensive testing are reported. The measured coding gain and the system performance over a Gaussian channel are compared with theoretical predictions and computer simulations. Word intelligibility scores are reported as a measure of voice channel performance.
The use of Reed-Solomon (RS) block codes over the pulse position modulated (PPM) frames to obtain the largest degree of error correction is considered. Since RS codes can correct both symbol errors and symbol erasures, a question arises as to the best way to demodulate the PPM laser fields in order to generate the input symbols for the RS decoder. The method selected for demodulating (converting the received laser field to digital symbols) defines the erasure and transmitted symbols of the laser link, and therefore determines the work error probabilities of the system. Several demodulating schemes are considered, and the effect of each on RS decoding performance computed. This computation was carried out for various optical receiver models. It is shown that simple threshold decisioning of pulse slots produces performance that degrades as the background noise increases. This is caused by the generation of too many erasures for the RS decoder to handle. A decision scheme, delta-max demodulation which offers improvement over threshold decisioning by redefining the generation of an erasure is proposed.
An architecture has been designed that integrates formation estimation methodologies, precision formation sensing, and high-bandwidth formation communication into a robust, strap-on system that meets knowledge and communication requirements for the majority of planned, precision formation missions. Specifically, the integrated system supports (a) sub-millimeter metrology, (b) multiple greater than 10 Mbps communication channels over a large, 10 deg field-of-view (FOV), and (c) generalized formation estimation methodologies. The sensing sub-system consists of several absolute, metrology gauges with up to 0.1 mm precision that use amplitude-modulated lasers and a LISA-heritage phase meter. Since amplitude modulation is used, inexpensive and robust diode lasers may be used instead of complex, frequency-stabilized lasers such as for nanometer-level metrology. The metrology subsystem laser transceivers consist of a laser diode, collecting optics, and an avalanche photo diode (APD) for detecting incoming laser signals. The APD is necessary since received power is small due to the large (for optical applications) FOV. The phase meter determines the phase of the incoming amplitude modulations as measured by the APD. This phase is equivalent to time-of-flight and, therefore, distance. By placing three laser transceivers on each spacecraft, 18 clock-offset-corrupted distances are calculated. These measurements are communicated and averaged to obtain nine correct distances between the transceivers. From these correct distances, the range and bearing between spacecraft and their relative attitude are determined. Next, communication is integrated on the laser carrier through spectral separation. Metrology amplitude modulations are limited to the 45-50 MHz band, leaving 0-45 MHz for communication. Through careful design of coding scheme, error correction, and filters, six independent 10 Mbps receive channels are possible. Hence, a spacecraft can simultaneously broadcast at 10 Mbps and listen to six other spacecraft. The integrated sensing and communication architecture has been developed, as have formation estimation methodologies that allow the sensing topology to reconfigure as spacecraft maneuver. A bench-top implementation of the integrated sensing and communication architecture is in progress. The final, multiple sensing/communication systems will be tied together via formation estimation algorithms that are also undergoing further development.
The Hubble Space Telescope Scientific Instrument Control and Data Handling Subsystem (SI C&DH) is designed to interface with five scientific instruments of the Space Telescope to provide ground and autonomous control and collect health and status information using the Standard Telemetry and Command Components (STACC) multiplex data bus. It also formats high throughput science data into packets. The packetized data is interleaved and Reed-Solomon encoded for error correction and Pseudo Random encoded. An inner convolutional coding with the outer Reed-Solomon coding provides excellent error correction capability. The subsystem is designed with the capacity for orbital replacement in order to meet a mission life of fifteen years. The spacecraft computer and the SI C&DH computer coordinate the activities of the spacecraft and the scientific instruments to achieve the mission objectives.