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NASA NTRS1998

Radiation-Driven Warping: Nonisothermal Disks - 2

Recent work by Pringle and by Maloney, Begelman, & Pringle has shown that geometrically thin, optically thick, accretion disks are unstable to warping driven by radiation torque from the central source. This work was confined to isothermal (i.e., surface density Sigma varies as R(sup -3/2) disks. In this paper we generalize the study of radiation-driven warping to include general power-law surface density distributions, Sigma varies as R(sup -delta).We consider the range from Delta = 3/2 (the isothermal case) to Delta = -3/2, which corresponds to a radiation-pressure-supported disk; this spans the range of surface density distributions likely to be found in real astrophysical disks. In all cases there are an infinite number of zero-crossing solutions (i.e., solutions that cross the equator), which are the physically relevant modes if the outer boundary of the disk is required to lie in a specified plane. However, unlike the isothermal disk, which is the degenerate case, the frequency eigenvalues for Delta does not equal 3/2 are all distinct. In all cases the location of the zero moves outward from the steady state (pure precession) value with increasing growth rate; thus, there is a critical minimum size for unstable disks. Modes with zeros at smaller radii are damped. The critical radius and the steady state precession rate depend only weakly on Delta. An additional analytic solution has been found for Delta = 1. The case Delta = 1 divides the solutions into two qualitatively different regimes. For Delta greater than or equal to 1, the fastest growing modes have maximum warp amplitude, close to the disk outer edge, and the ratio of Beta(sub max) to the warp amplitude at the disk inner edge, Beta(sub o), is much greater than 1. For Delta less than 1, Beta(sub max/Beta(sub o) approximately equals 1, and the warp maximum steadily approaches the origin as Delta decreases. This implies that nonlinear effects must be important if the warp extends to the disk inner edge for Delta greater than or equal to 1, but for Delta less than 1 nonlinearity will be important only if the warp amplitude is large at the origin. Because of this qualitative difference in the shapes of the warps, the effects of shadowing of the central source by the warp will also be very different in the two regimes of Delta. This has important implications for radiation-driven warping in X-ray binaries, for which the value of Delta characterizing the disk is likely to be less than unity. In real accretion disks the outer boundary condition is likely to be different from the zero-crossing condition that we have assumed. In accretion disks around massive black holes in active galactic nuclei, the disk will probably become optically thin before the outer disk boundary is reached, whereas in X-ray binaries there will be an outer disk region (outside the circularization radius) in which the inflow velocity is zero but angular momentum is still transported. We show that in both these cases the solutions are similar to the zero-crossing eigenfunctions.

Maloney, Philip R.↗

NASA NTRS1999

Paramagnetic Liquid Bridge in a Gravity-Compensating Magnetic Field

Magnetic levitation was used to stabilize cylindrical columns of a paramagnetic liquid in air between two solid supports. The maximum achievable length to diameter ratio R(sub max) was approx. (3.10 +/- 0.07), very close to the Rayleigh-Plateau limit of pi. For smaller R, the stability of the column was measured as a function of the Bond number, which could be continuously varied by adjusting the strength of the magnetic field. Liquid bridges supported by two solid surfaces have been attracting scientific attention since the time of Rayleigh and Plateau. For a cylindrical bridge of length L and diameter d, it was shown theoretically that in zero gravity the maximum slenderness ratio R (identically = L/d) is pi. The stability and ultimate collapse of such bridges is of interest because of their importance in a number of industrial processes and their potential for low gravity applications. In the presence of gravity, however, the cylindrical shape of an axisymmetric bridge tends to deform, limiting its stability and decreasing the maximum achievable value of R. Theoretical studies have discussed the stability and possible shapes of axisymmetric bridges. Experiments typically are performed in either a Plateau tank, in which the bridge is surrounded by a density-matched immiscible fluid, or in a space-borne microgravity environment. It has been shown, for example, that the stability limit R can be pushed beyond pi by using flow stabilization, by acoustic radiation pressure, or by forming columns in the presence of an axial electric field. In this work, magnetic levitation was used to simulate a low gravity environment and create quasi-cylindrical liquid columns in air. Use of a magnetic field permits us to continuously vary the Bond number B identically equal to (g)(rho)d(exp 2)/4(sigma), where g is the gravitational acceleration, rho is the density of the liquid, and sigma is the surface tension of the liquid in air. The dimensionless Bond number represents the relative importance of external forces acting on the liquid column to those due to surface tension. Our central result is that in a large magnetic field gradient we could create and stabilize columns of mixtures of water and paramagnetic manganese chloride tetrahydrate (MnCl2.4H2O), achieving a length to diameter ratio very close to pi.

Mahajan, Milind P.↗

NASA NTRS1999

Map Algorithms for Decoding Linear Block codes Based on Sectionalized Trellis Diagrams

The MAP algorithm is a trellis-based maximum a posteriori probability decoding algorithm. It is the heart of the turbo (or iterative) decoding which achieves an error performance near the Shannon limit. Unfortunately, the implementation of this algorithm requires large computation and storage. Furthermore, its forward and backward recursions result in long decoding delay. For practical applications, this decoding algorithm must be simplified and its decoding complexity and delay must be reduced. In this paper, the MAP algorithm and its variations, such as Log-MAP and Max-Log-MAP algorithms, are first applied to sectionalized trellises for linear block codes and carried out as two-stage decodings. Using the structural properties of properly sectionalized trellises, the decoding complexity and delay of the MAP algorithms can be reduced. Computation-wise optimum sectionalizations of a trellis for MAP algorithms are investigated. Also presented in this paper are bi-directional and parallel MAP decodings.

Lin, Shu↗

NASA NTRS1998

The Intensity Distribution of Faint Gamma-Ray Bursts Detected with BATSE

We have recently completed a search of 6 years of archival Burst and Transient Source Experiment (BATSE) data for gamma-ray bursts (GRBS) that were too faint to activate the real-time burst detection system running onboard the spacecraft. These "non-triggered" bursts can be combined with the "triggered" bursts detected onboard to produce a GRB intensity distribution that reaches peak fluxes a factor of approximately 2 lower than could be studied previously. The value of the (V/V(max)) statistic (in Euclidean space) for the bursts we detect is 0.177 +/- 0.006. This surprisingly low value is obtained because we detected very few bursts on the 4.096 s and 8.192 s time scales (where most bursts have their highest signal-to-noise ratio) that were not already detected on the 1.024 s time scale. If allowance is made for a power-law distribution of intrinsic peak luminosities, the extended peak flux distribution is consistent with models in which the redshift distribution of the gamma-ray burst rate approximately traces the star formation history of the Universe. We argue that this class of models is preferred over those in which the burst rate is independent of redshift. These results lend support to the conclusions of previous studies predicting that relatively few faint bursts are waiting to be found below the BATSE onboard detection threshold.

Kommers, Jefferson↗

NASA NTRS1999

Data Processing for the Near Earth Asteroid Rendezvous (NEAR), X-ray and Gamma-ray Spectrometer (XGRS) Ground System

An X-ray and Gamma-ray spectrometer (XGRS) is onboard the Near Earth Asteroid Rendezvous (NEAR) spacecraft to determine the elemental composition of the surface of the asteroid 433Eros. The Eros asteroid is highly non-spherical in physical shape and the development of data management and analysis methodologies are in several areas a divergence from traditional remotely sensed geographical information systems techniques. Field of view and asteroid surface geometry must be derived virtually and then combined with real measurements of solar, spectral and instrument calibration information to derive meaningful scientific results. Spatial resolution of planned geochemical maps will be improved from the initial conditions of low statistical significance per integration by repeated surface flyovers and regional spectral accumulation. This paper describes the results of a collaborative effort of design and development of the NEAR XGRS instrument ground system undertaken by participants at the Goddard Space Flight Center, University of Arizona, Cornell University, Applied Physics Laboratory, and Max Plank institute.

McClanahan, Timothy P.↗

NASA NTRS1999

Simulation of the Universal-Time Diurnal Variation of the Global Electric Circuit Charging Rate

A global lightning model that includes diurnal and annual lightning variation, and total flash density versus latitude for each major land and ocean, has been used as the basis for simulating the global electric circuit charging rate. A particular objective has been to reconcile the difference in amplitude ratios [AR=(max-min)/mean] between global lightning diurnal variation (AR approximately equals 0.8) and the diurnal variation of typical atmospheric potential gradient curves (AR approximately equals 0.35). A constraint on the simulation is that the annual mean charging current should be about 1000 A. The global lightning model shows that negative ground flashes can contribute, at most, about 10-15% of the required current. For the purpose of the charging rate simulation, it was assumed that each ground flash contributes 5 C to the charging process. It was necessary to assume that all electrified clouds contribute to charging by means other than lightning, that the total flash rate can serve as an indirect indicator of the rate of charge transfer, and that oceanic electrified clouds contribute to charging even though they are relatively inefficient in producing lightning. It was also found necessary to add a diurnally invariant charging current component. By trial and error it was found that charging rate diurnal variation curves could be produced with amplitude ratios and general shapes similar to those of the potential gradient diurnal variation curves measured over ocean and arctic regions during voyages of the Carnegie Institute research vessels. The comparisons were made for the northern winter (Nov.-Feb.), the equinox (Mar., Apr., Sept., Oct.), the northern summer (May-Aug.), and the whole year.

Mackerras, David↗

NASA NTRS1998

Comment on the Predicted Size of Cycle 23 Based on the Inferred Three-Cycle Quasi-Periodicity of the Planetary Index Ap

Recently, Ahluwalia [1998] reviewed the solar and geomagnetic data for the last 6 decades and remarked that these data "indicate the existence of a three-solar-activity-cycle quasi-periodicity in them." Futhermore, on the basis of this inferred quasi-periodicity, he asserted that cycle 23 represents the initial cycle in a new 3-cycle string, implying that it "will be more modest (a la cycle 17) with an annual mean sunspot number count of 119.3 +/- 30 at the maximum," a prediction that is considerably below the consensus prediction of 160 +/- 30 by Joselyn et al. [1997] and of similar predictions by others based on a variety of predictive techniques. Several major sticking points of Ahluwalia's presentation, however, must be redressed, and these issues form the basis of this comment. In particular, it is shown that Ahluwalia used inappropriate values of the Ap index in his analysis, that the inferred 3-cycle relationship which Ahluwalia claims for both Ap and SSN does not exist for the previous 6-cycle interval (prior to cycle 17) for SSN, that his inferred fit is only of marginal statistical significance (having r = 0.81), and that two alternative precursor fits (both with r = 0.96 or greater) exist which strongly suggest that R max for cycle 23 will be much larger than forecast by Ahluwalia (namely, about 168-187). Thus, caution must be exercised in accepting Ahluwalia's findings.

Hathaway, David H.↗

NASA NTRS1998

Estimating the Size and Timing of Maximum Amplitude for Cycle 23 from Its Early Cycle Behavior

On the basis of the lowest observed smoothed monthly mean sunspot number, cycle 23 appears to have conventionally begun in May 1996, in conjunction with the first appearance of a new cycle, high-latitude spot-group. Such behavior, however, is considered rather unusual, since, previously (based upon the data- available cycles 12-22), the first appearance of a new cycle, high-latitude spot- group has always preceded conventional onset by at least 3 months. Furthermore, accepting May 1996 as the official start for cycle 23 poses a dilemma regarding its projected size and timing of maximum amplitude. Specifically, from the max-min and amplitude-period relationships we infer that cycle 23 should be above average in size and a fast riser, with maximum amplitude occurring before May 2000 (being in agreement with projections for cycle 23 based on precursor information), yet from its initial languid rate of rise (during the first 6 months of the cycle) we infer that it should be below average in size and a slow riser, with maximum amplitude occurring after May 2000. The dilemma vanishes, however, when we use a slightly later-occurring onset. For example, using August 1996, a date associated with a local secondary minimum prior to the rapid rise that began shortly thereafter (in early 1997), we infer that cycle 23's rate of rise is above that for the mean of cycles 1-22, the mean of cycles 10-22 (the modern era cycles), the mean of the modern era'fast risers,' and the largest of the modern era 'slow risers' (i.e., cycle 20), thereby, suggesting that cycle 23 will be both fast-rising and above average in size, peaking before August 2000. Additionally, presuming cycle 23 to be a well- behaved fast-rising cycle (regardless of whichever onset date is used), we also infer that its maximum amplitude likely will measure about 144.0 q+/- 28.8 (from the general behavior found for the bulk of modern era fast risers; i.e., 5 of 7 have had their maximum amplitude to lie within 20% of the mean curve for modern era fast risers). It is apparent, then, that sunspot number growth during 1998 will prove crucial for correctly establishing the size and shape of cycle 23.

Wilson, Robert M.↗

NASA NTRS1999

Simulation of the Universal-Time Diurnal Variation of the Global Electric Circuit Charging Rate

A global lightning model that includes diurnal and annual lightning variation, and total flash density versus latitude for each major land and ocean, has been used as the basis for simulating the global electric circuit charging rate. A particular objective has been to reconcile the difference in amplitude ratios [AR=(max-min)/mean] between global lightning diurnal variation (AR approx. = 0.8) and the diurnal variation of typical atmospheric potential gradient curves (AR approx. = 0.35). A constraint on the simulation is that the annual mean charging current should be about 1000 A. The global lightning model shows that negative ground flashes can contribute, at most, about 10-15% of the required current. For the purpose of the charging rate simulation, it was assumed that each ground flash contributes 5 C to the charging process. It was necessary to assume that all electrified clouds contribute to charging by means other than lightning, that the total flash rate can serve as an indirect indicator of the rate of charge transfer, and that oceanic electrified clouds contribute to charging even though they are relatively inefficient in producing lightning. It was also found necessary to add a diurnally invariant charging current component. By trial and error it was found that charging rate diurnal variation curves in Universal time (UT) could be produced with amplitude ratios and general shapes similar to those of the potential gradient diurnal variation curves measured over ocean and arctic regions during voyages of the Carnegie Institute research vessels.

Mackerras, D.↗

NASA NTRS1999

Data Processing for the Near Earth Asteroid Rendezvous (NEAR), X-Ray and Gamma-Ray Spectrometer (XRS) Ground System

McClanahan, Timothy P.↗

NASA NTRS1999

Hubble Space Telescope observations of Orion Nebula, Helix Nebula, and NGC 6822

This grant covered the major part of the work of the Principal Investigator and his collaborators as a Guaranteed Time Observer on the Hubble Space Telescope. The work done naturally divided itself into two portions the first being study of nebular objects and the second investigation of the interstellar medium between stars. The latter investigation was pursued through a contract with Princeton University, with Professor Lyman Spitzer as the supervising astronomer, assisted by Dr. Ed Fitzpatrick. Following the abrupt death of Professor Spitzer, his responsibilities were shifted to Dr. Fitzpatrick. When Dr. Fitzpatrick relocated to Villanova University the concluding work on that portion of this grant was concluded under a direct service arrangement. This program has been highly successful and the resulting publications in scientific journals are listed below. To the scientist, this is the bottom line, so that I shall simply try to describe the general nature of what was accomplished. There were three nebular programs conducted, one on the Orion Nebula, the second on the Helix Nebula, and the third on NGC 6822. The largest program was that on the Orion Nebula. This involved both HST observations and supporting groundbased observations obtained with a variety of instruments, including the Coude Feed Telescope at the Kitt Peak National observatory in Arizona, the Cerro Tololo observatory in Chile, and the Keck Observatory on Mauna Kea, Hawaii. Moreover, considerable theoretical modeling was done and all of the data analysis was performed at the Rice University in Houston, except for the PI's period of sabbatical leave (6-96 through 7-97) when he was based at the Max Planck Institute for Astronomy in Heidelberg, Germany. The Orion Nebula program was the most productive part, resulting in numerous papers, but more important in the discovery of a new class of objects, for which we coined the name "proplyds". The proplyds are protoplanetary disks surrounding very young stars still in the process of creation. The Orion Nebula is the residual material from a burst of star formation that occurred about 300,000 years ago. Each of these new stars has a surrounding disk of protoplanetary material. The same physics that renders the Nebula so highly visible means that the proto-planetary disks are also quite visible. With the wisdom of hindsight, we now see that this was to be expected and that we should have been searching specifically for this type of object. The discovery of these objects and their subsequent detailed investigation has lead to an accurate assessment of the frequency of protoplanetary disks in young stars and determination of the likelihood of survival of these disks into an era where planets actually form.

Spitzer, Lyman↗

NASA NTRS1994

Empirical Modeling of Plant Gas Fluxes in Controlled Environments

As humans extend their reach beyond the earth, bioregenerative life support systems must replace the resupply and physical/chemical systems now used. The Controlled Ecological Life Support System (CELSS) will utilize plants to recycle the carbon dioxide (CO2) and excrement produced by humans and return oxygen (O2), purified water and food. CELSS design requires knowledge of gas flux levels for net photosynthesis (PS(sub n)), dark respiration (R(sub d)) and evapotranspiration (ET). Full season gas flux data regarding these processes for wheat (Triticum aestivum), soybean (Glycine max) and rice (Oryza sativa) from published sources were used to develop empirical models. Univariate models relating crop age (days after planting) and gas flux were fit by simple regression. Models are either high order (5th to 8th) or more complex polynomials whose curves describe crop development characteristics. The models provide good estimates of gas flux maxima, but are of limited utility. To broaden the applicability, data were transformed to dimensionless or correlation formats and, again, fit by regression. Polynomials, similar to those in the initial effort, were selected as the most appropriate models. These models indicate that, within a cultivar, gas flux patterns appear remarkably similar prior to maximum flux, but exhibit considerable variation beyond this point. This suggests that more broadly applicable models of plant gas flux are feasible, but univariate models defining gas flux as a function of crop age are too simplistic. Multivariate models using CO2 and crop age were fit for PS(sub n), and R(sub d) by multiple regression. In each case, the selected model is a subset of a full third order model with all possible interactions. These models are improvements over the univariate models because they incorporate more than the single factor, crop age, as the primary variable governing gas flux. They are still limited, however, by their reliance on the other environmental conditions under which the original data were collected. Three-dimensional plots representing the response surface of each model are included. Suitability of using empirical models to generate engineering design estimates is discussed. Recommendations for the use of more complex multivariate models to increase versatility are included.

Cornett, Jessie David↗

NASA NTRS1999

Exercise Training During +Gz Acceleration

The overall purpose is to study the effect of passive (without exercise) and active (with exercise) +Gz (head-to-foot) acceleration training, using a short-arm (1.9m radius) centrifuge, on post- training maximal oxygen uptake (VO2 max, work capacity) and 70 deg head-up tilt (orthostatic) tolerance in ambulatory subjects to test the hypothesis that (a) both passive and active acceleration training will improve post-training tilt-tolerance, and (b) there will be no difference in tilt-tolerance between passive and active exercise acceleration training because increased hydrostatic and blood pressures, rather than increased muscular metabolism, will provide the major adaptive stimulus. The purpose of the pilot study was to test the hypothesis that there would be no significant difference in the metabolic responses (oxygen uptake, heart rate, pulmonary ventilation, or respiratory exchange ratio) during supine exercise with moderate +Gz acceleration.

Greenleaf, J. E.↗

NASA NTRS1977

Light-Activated Amino Acid Transport Systems in Halobacterium halobium Envelope Vesicles: Role of Chemical and Electrical Gradients

The accumulation of 20 commonly occurring L-amino acids by cell envelope vesicles of Halobacterium halobium, in response to light-induced membrane potential and an artificially created sodium gradient, has been studied. Nineteen of these amino acids are actively accumulated under either or both of these conditions. Glutamate is unique in that its uptake is driven only by a chemical gradient for sodium. Amino acid concentrations at half-maximal uptake rates (Km) and maximal transport rates (V(sub max) have been determined for the uptake of all 19 amino acids. The transport systems have been partially characterized with respect to groups of amino acids transported by common carriers, cation effects, and relative response to the electrical and chemical components of the sodium gradient, the driving forces for uptake. The data presented clearly show that the carrier systems, which are responsible for uptake of individual amino acids, are as variable in their properties as those found in other organisms, i. e., some are highly specific for individual amino acids, some transport several amino acids competitively, some are activated by a chemical gradient of sodium only, and some function also in the complete absence of such a gradient. For all amino acids, Na(+) and K(+) are both required for maximal rate of uptake. The carriers for L-leucine and L-histidine are symmetrical in that these amino acids are transported in both directions across the vesicle membrane. It is suggested that coupling of substrate transport to metabolic energy via transient ionic gradients may be a general phenomenon in procaryotes.

MacDonald, Russell E.↗

NASA NTRS1977

Transport in Halobacterium Halobium: Light-Induced Cation-Gradients, Amino Acid Transport Kinetics, and Properties of Transport Carriers

Cell envelope vesicles prepared from H. halobium contain bacteriorhodopsin and upon illumination protons are ejected. Coupled to the proton motive force is the efflux of Na(+). Measurements of Na-22 flux, exterior pH change, and membrane potential, Delta(psi) (with the dye 3,3'-dipentyloxadicarbocyanine) indicate that the means of Na(+) transport is sodium/proton exchange. The kinetics of the pH changes and other evidence suggests that the antiport is electrogenic (H(+)/Na(++ greater than 1). The resulting large chemical gradient for Na(+) (outside much greater than inside), as well as the membrane potential, will drive the transport of 18 amino acids. The I9th, glutamate, is unique in that its accumulation is indifferent to Delta(psi): this amino acid is transported only when a chemical gradient for Na(+) is present. Thus, when more and more NaCl is included in the vesicles glutamate transport proceeds with longer and longer lags. After illumination the gradient of H+() collapses within 1 min, while the large Na(+) gradient and glutamate transporting activity persists for 10- 15 min, indicating that proton motive force is not necessary for transport. A chemical gradient of Na(+), arranged by suspending vesicles loaded with KCl in NaCl, drives glutamate transport in the dark without other sources of energy, with V(sub max) and K(sub m) comparable to light-induced transport. These and other lines of evidence suggest that the transport of glutamate is facilitated by symport with Na(+), in an electrically neutral fashion, so that only the chemical component of the Na(+) gradient is a driving force.

Lanyi, Janos K.↗

NASA NTRS2000

Assessment of Low Cycle Fatigue Behavior of Powder Metallurgy Alloy U720

The fatigue lives of modem powder metallurgy disk alloys are influenced by variabilities in alloy microstructure and mechanical properties. These properties can vary as functions of variables the different steps of materials/component processing: powder atomization, consolidation, extrusion, forging, heat treating, and machining. It is important to understand the relationship between the statistical variations in life and these variables, as well as the change in life distribution due to changes in fatigue loading conditions. The objective of this study was to investigate these relationships in a nickel-base disk superalloy, U720, produced using powder metallurgy processing. Multiple strain-controlled fatigue tests were performed at 538 C (1000 F) at limited sets of test conditions. Analyses were performed to: (1) assess variations of microstructure, mechanical properties, and LCF failure initiation sites as functions of disk processing and loading conditions; and (2) compare mean and minimum fatigue life predictions using different approaches for modeling the data from assorted test conditions. Significant variations in life were observed as functions of the disk processing variables evaluated. However, the lives of all specimens could still be combined and modeled together. The failure initiation sites for tests performed at a strain ratio R(sub epsilon) = epsilon(sub min)/epsilon(sub max) of 0 were different from those in tests at a strain ratio of -1. An approach could still be applied to account for the differences in mean and maximum stresses and strains. This allowed the data in tests of various conditions to be combined for more robust statistical estimates of mean and minimum lives.

Gabb, Tomothy P.↗

NASA NTRS1996

Ground Reaction Forces During Locomotion in Simulated Microgravity

Significant losses in bone density and mineral, primarily in the lower extremities have been reported following exposure to weightlessness. Recent investigations suggest that mechanical influences such as bone deformation and strain rate may be critically important in stimulating new bone formation. It was hypothesized that velocity, cadence and harness design would significantly affect lower limb impact forces during treadmill exercise in simulated zero gravity (0G). A ground-based hypogravity simulator was used to investigate which factors affect limb loading during tethered treadmill exercise. A fractional factorial design was used and 12 subjects were studied. The results showed that running on active and passive treadmills in the simulator with a tethering force close to the maximum comfortable level produced similar magnitudes for the peak ground reaction force. It was also found that these maximum forces were significantly lower than those obtained during overground trials, even when the speeds of locomotion in the simulator were 66 % greater than those in 1 G. Cadence had no effect on any of the response variables. The maximum rate of force application (DFDT-Max) was similar for overground running and exercise in simulated 0G, provided that the "weightless subjects ran on a motorized treadmill. These findings have implications for the use of treadmill exercise as a countermeasure for hypokinetic osteoporosis. As the relationship between mechanical factors and osteogenesis becomes better understood, results from human experiments in 0G simulators will help to design in-flight exercise programs that are more closely targeted to generate appropriate mechanical stimuli.

Davis, B. L.↗

NASA NTRS2000

MAP Algorithms for Decoding Linear Block Codes Based on Sectionalized Trellis Diagrams

The maximum a posteriori probability (MAP) algorithm is a trellis-based MAP decoding algorithm. It is the heart of turbo (or iterative) decoding that achieves an error performance near the Shannon limit. Unfortunately, the implementation of this algorithm requires large computation and storage. Furthermore, its forward and backward recursions result in long decoding delay. For practical applications, this decoding algorithm must be simplified and its decoding complexity and delay must be reduced. In this paper, the MAP algorithm and its variations, such as log-MAP and max-log-MAP algorithms, are first applied to sectionalized trellises for linear block codes and carried out as two-stage decodings. Using the structural properties of properly sectionalized trellises, the decoding complexity and delay of the MAP algorithms can be reduced. Computation-wise optimum sectionalizations of a trellis for MAP algorithms are investigated. Also presented in this paper are bidirectional and parallel MAP decodings.

Lui, Ye↗