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At least 235 records · Page 13

A connection between block and convolutional codes

Convolutional codes of any rate and any constraint length give rise to a sequence of quasi-cyclic codes. Conversely, any quasi-cyclic code may be convolutionally encoded. Among the quasi-cyclic codes are the quadratic residue codes, Reed-Solomon codes and optimal BCH codes. The constraint length K for the convolutional encoding of many of these codes (Golay, (48, 24) QR, etc.) turns out to be surprisingly small. Thus using the soft decoding techniques for convolutional decoding, a new maximum likelihood decoding algorithm for many block codes is established. Conversely an optimal quasi-cyclic code will yield a convolutional encoding with optimal local properties and therefore with good infinite convolutional coding properties.

Solomon, G.↗

Capacity, cutoff rate, and coding for a direct-detection optical channel

It is shown that Pierce's pulse position modulation scheme with 2 to the L pulse positions used on a self-noise-limited direct detection optical communication channel results in a 2 to the L-ary erasure channel that is equivalent to the parallel combination of L completely correlated binary erasure channels. The capacity of the full channel is the sum of the capacities of the component channels, but the cutoff rate of the full channel is shown to be much smaller than the sum of the cutoff rates. An interpretation of the cutoff rate is given that suggests a complexity advantage in coding separately on the component channels. It is shown that if short-constraint-length convolutional codes with Viterbi decoders are used on the component channels, then the performance and complexity compare favorably with the Reed-Solomon coding system proposed by McEliece for the full channel. The reasons for this unexpectedly fine performance by the convolutional code system are explored in detail, as are various facets of the channel structure.

Massey, J. L.↗

Dispersion model studies for Space Shuttle environmental effects activities

The NASA/MSFC REED computer code was developed for predicting concentrations, dosage, and deposition downwind from rocket vehicle launches. The calculation procedures and results of nine studies using the code are presented. Topics include plume expansion, hydrazine concentrations, and hazard calculations for postulated fuel spills.

Source record↗

Practical codes for photon communication

It is shown that even assuming a noiseless model for photon communication for which capacity (measured in nats/photon) is infinite, it is unlikely that a signaling efficiency of even 10 nats/photon could be achieved in practice. Pulse-position modulation plus Reed-Solomon coding is shown to yield practical results in the range of 2 to 3 nats/photon. In addition, a channel model appropriate for the study of noiseless photon communication, referred to as a photon channel, is presented. The use of q-ary pulse position modulation (q-PPM) on the photon channel is investigated. It is shown that q-PPM channel capacity is log q nats/photon, and performance curves (error probability versus signaling efficiency) are given for coded and uncoded q-PPM.

Mceliece, R. J.↗

The 2.5 bit/detected photon demonstration program: Phase 2 and 3 experimental results

The experimental program for laboratory demonstration of and energy efficient optical communication channel operating at a rate of 2.5 bits/detected photon is described. Results of the uncoded PPM channel performance are presented. It is indicated that the throughput efficiency can be achieved not only with a Reed-Solomon code as originally predicted, but with a less complex code as well.

Katz, J.↗

Capacity, cutoff rate, and coding for a direct-detection optical channel

It is shown that when Pierce's pulse-position modulation scheme with 2 to the L power positions (where L is some positive integer) is used on a self-noise-limited direct-detection optical communication channel, there results a (2 to the L power)-ary erasure channel that is equivalent to the parallel combination of L completely correlated binary erasure channels. The capacity of the full channel is the sum of the capacities of the component channels, but the cutoff rate of the full channel is shown to be much smaller than the sum of the cutoff rates. An interpretation of the cutoff rate is given that suggests a complexity advantage in coding separately on the component channels. It is shown that if short-constraint length convolutional codes with Viterbi decoders are used on the component channels, then the performance and complexity compare favorably with the Reed-Solomon coding system proposed by McEliece (1979) for the full channel. The reasons for this unexpectedly fine performance by the convolutional code system are explored in detail, as are various facets of the channel structure.

Massey, J. L.↗

The significance of Cl/P2O5 ratios from lunar samples

The Cl(r)/P2O5 ratios of lunar samples are reported to occur in three groups (Jovanovic and Reed, 1975; etc.). These data have been modeled as representative of three discrete volumes of differentiating magma and correlated with large convection cells and moon-wide heterogeneities. The assumptions inherent to their model are not valid. That the Cl(r)/P2O5 ratio of apatite or a rock is indicative of a magma system is unrealistic. A range of ratios can be generated during the fractionation of a magma. Apatite is not the major Cl- and P-bearing phase in most of the samples analyzed; rust, FeO(OH, Cl) and schreibersite, (FeNi)3P, occur in over 2/3 rds of the Apollo 16 rocks where they constitute 0.1-0.6 modal %, enough to account for most of the Cl(r) and P2O5 analyzed. Due to the complexities and presence of these minerals in soils and breccias, Cl(r)/P2O5 ratios have no real significance in non-igneous samples. However, basaltic rocks alone do not define any statistically significant Cl(r)P2O5 groupings.

Taylor, L. A.↗

Efficient Coding for Optical Communication

Possibility of using photon counting, rather than conventional linear amplification, for optical communications discussed. Study suggests combination of pulse-position modulation and Reed-Solomon coding gives signaling efficiency of 3 to 4 bits/photon.

Mceliece, R. J.↗

The performance of VLA as a telemetry receiver for Voyager planetary encounters

The Very Large Array (VLA) was proposed for use as a supplement to the Deep Space Network (DSN) for telemetry reception at Voyager 2 Uranus and Neptune encounters. The main problem with the use of VLA for telemetry is that it is not capable of producing a continuous stream of data. Gaps of one millisecond follow every 51 milliseconds of data. The effect of these millisecond gaps on coded telemetry is investigated. An upgapped system of the same aperture as the VLA would be capable of handling data rates of 38.4 kbps at Uranus encounter and 19.2 kbps at Neptune encounter. It is shown that VLA with (7, 1/2) convolutional coding (the baseline coding scheme for Voyager) will support a data rate of 10.8 kbps but not 19.2 kbps at both Uranus and Neptune. It is also shown that by implementing Voyager's concatenated Reed-Solomon/convolutional coding capability, data rates of 38.4 kbps and 19.2 kbps would be achievable at Uranus and Neptune respectively. Concatenation also offers a factor of 2 improvement in overall throughput.

Deutsch, L. J.↗

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 rate event) within several hundred bits; many of these false alarms for our technique is on the order several years.

Lorden, G.↗

Aquatic Plants Aid Sewage Filter

Method of wastewater treatment combines micro-organisms and aquatic plant roots in filter bed. Treatment occurs as liquid flows up through system. Micro-organisms, attached themselves to rocky base material of filter, act in several steps to decompose organic matter in wastewater. Vascular aquatic plants (typically, reeds, rushes, cattails, or water hyacinths) absorb nitrogen, phosphorus, other nutrients, and heavy metals from water through finely divided roots.

Wolverton, B. C.↗

Direct-Photon-Detection Communications

Optical communications system based on direct detection of photons rather than heterodyning of carrier with local oscillator. Direct-detection system uses single laser source, pulse-position modulation, and Reed-Solomon coding to protect against burst errors. Conventional photomultiplier tube is receiver. Technology applicable to terrestrial communications.

Lesh, J. R.↗

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.↗

Optical communication with laser diode arrays

The performance of a direct-detection optical communication system in which the laser transmitter sends short optical pulses of selected nonoverlapping center frequencies is analysed. This modulation format, in which a single light pulse is sent in one of M time slots at one of N optical center frequencies, is referred to as color coded optical pulse position modulation (CCPPM). The optimum energy-efficiency of this system, as measured by the channel capacity in nats per photon, exceeds that of ordinary optical pulse position modulation which uses a pulsed laser of fixed optical frequency. Reliable communication at optimal energy efficiency is easily achieved through the use of modest block length Reed-Solomon codes with the code words represented as CCPPM symbols.

Davidson, F.↗

Fast decoding of a d(min) = 6 RS code

A method for high speed decoding a d sub min = 6 Reed-Solomon (RS) code is presented. Properties of the two byte error correcting and three byte error detecting RS code are discussed. Decoding using a quadratic equation is shown. Theorems and concomitant proofs are included to substantiate this decoding method.

Deng, H.↗

An extended d(min) = 4 RS code

A minimum distance d sub m - 4 extended Reed - Solomon (RS) code over GF (2 to the b power) was constructed. This code is used to correct any single byte error and simultaneously detect any double byte error. Features of the code; including fast encoding and decoding, are presented.

Deng, H.↗

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.↗