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In this article, we introduce multiple turbo codes and a suitable decoder structure derived from an approximation to the maximum a posteriori probability (MAP) decision rule, which is substantially different from the decoder for two-code-based encoders. We analyze the effect of interleaver choice on the weight distribution of the code, and we describe simulation results on the improved performance of these new codes.
This article takes a preliminary look at the weight distributions achievable for turbo codes using random, nonrandom, and semirandom permutations. Due to the recursiveness of the encoders, it is important to distinguish between self-terminating and non-self-terminating input sequences. The non-self-terminating sequences have little effect on decoder performance, because they accumulate high encoded weight until they are artificially terminated at the end of the block. From probabilistic arguments based on selecting the permutations randomly, it is concluded that the self-terminating weight-2 data sequences are the most important consideration in the design of constituent codes; higher-weight self-terminating sequences have successively decreasing importance. Also, increasing the number of codes and, correspondingly, the number of permutations makes it more and more likely that the bad input sequences will be broken up by one or more of the permuters. It is possible to design nonrandom permutations that ensure that the minimum distance due to weight-2 input sequences grows roughly as the square root of (2N), where N is the block length. However, these nonrandom permutations amplify the bad effects of higher-weight inputs, and as a result they are inferior in performance to randomly selected permutations. But there are 'semirandom' permutations that perform nearly as well as the designed nonrandom permutations with respect to weight-2 input sequences and are not as susceptible to being foiled by higher-weight inputs.
In this paper the radio loss results for (8920,1/3), (8920,1/6), (1783,1/3) and (1784,1/6) codes are presented. These radio losses were calculated through simulations for a range of data rates. These simulations included both suppressed carrier modulation and residual carrier modulation cases. The radio losses were calculated for a frame error rate of 3 x 10^-4 for (8920,1/3) and (8920,1/6) codes and 3 frame error rate of 6 x 10^-5 for (1764,1/3) and (1784,1/6) codes. The simulations for the residual carrier case were run for loop signal to noise ratios of 13dB, 15dB and 17dB with a loop bandwidth of 10Hz. The simulations for the suppressed carrier case were run for a loop of signal to noise ratio of 17dB. The results of these simulations indicate that the radio losses for turbo codes are low enough to warrant their use in deep space links (maximum of 1dB loss at 17dB loop signal to noise ratio for residual carrier and 1.3dB loss at 17dB loop signal to noise ratio for suppressed carrier at high data rates). Furthermore, these results indicate that by normalizing the radio losses for frame size, loop bandwidth and the loop signal to noise ratio, a single curve could be used for calculating the radio loss for any given data rate at any given loop signal to noise ratio.
A scale model of the NASA/Honeywell Engines Quiet High Speed Fan (QHSF) encountered flutter wind tunnel testing. This report documents aeroelastic calculations done for the QHSF scale model using the blade vibration capability of the TURBO code. Calculations at design speed were used to quantify the effect of numerical parameters on the aerodynamic damping predictions. This numerical study allowed the selection of appropriate values of these parameters, and also allowed an assessment of the variability in the calculated aerodynamic damping. Calculations were also done at 90 percent of design speed. The predicted trends in aerodynamic damping corresponded to those observed during testing.
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A very-large-scale-integrated-circuit (VLSI) turbo decoder has been designed to serve as a compact, high-throughput, low-power, lightweight decoder core of a receiver in a data-communication system. In a typical contemplated application, such a decoder core would be part of a single integrated circuit that would include the rest of the receiver circuitry and possibly some or all of the transmitter circuitry, all designed and fabricated together according to an advanced communication-system-on-a-chip design concept. Turbo codes are forward-error-correction (FEC) codes. Relative to older FEC codes, turbo codes enable communication at lower signal-to-noise ratios and offer greater coding gain. In addition, turbo codes can be implemented by relatively simple hardware. Therefore, turbo codes have been adopted as standard for some advanced broadband communication systems.
Turbo codes can deliver performance that is very close to the Shannon limit. This report investigates algorithms for convolutional turbo codes and block turbo codes. Both coding schemes can achieve performance near Shannon limit. The performance of the schemes is obtained using computer simulations. There are three sections in this report. First section is the introduction. The fundamental knowledge about coding, block coding and convolutional coding is discussed. In the second section, the basic concepts of convolutional turbo codes are introduced and the performance of turbo codes, especially high rate turbo codes, is provided from the simulation results. After introducing all the parameters that help turbo codes achieve such a good performance, it is concluded that output weight distribution should be the main consideration in designing turbo codes. Based on the output weight distribution, the performance bounds for turbo codes are given. Then, the relationships between the output weight distribution and the factors like generator polynomial, interleaver and puncturing pattern are examined. The criterion for the best selection of system components is provided. The puncturing pattern algorithm is discussed in detail. Different puncturing patterns are compared for each high rate. For most of the high rate codes, the puncturing pattern does not show any significant effect on the code performance if pseudo - random interleaver is used in the system. For some special rate codes with poor performance, an alternative puncturing algorithm is designed which restores their performance close to the Shannon limit. Finally, in section three, for iterative decoding of block codes, the method of building trellis for block codes, the structure of the iterative decoding system and the calculation of extrinsic values are discussed.
This report is the documentation of the work performed under the Hypersonic Project of the NASA's Fundamental Aeronautics Program. It was funded through Task Number NNC10E444T under GESS-2 Contract NNC06BA07B. The objective of the task is to develop advanced computational tools for the simulation of multi-stage turbomachinery in support of aeropropulsion. This includes work elements in extending the TURBO code and validating the multi-stage URANS (Unsteady Reynolds Averaged Navier Stokes) simulation results with the experimental data. The unsteady CFD (Computation Fluid Dynamics) calculations were performed in full wheel mode with and without screen generated total pressure distortion at the computational inflow boundary, as well as in single passage phase lag mode for uniform inflow. The experimental data were provided by NASA from the single stage RTA (Revolutionary Turbine Accelerator) fan test program.Significant non-uniform flow condition at the fan-face of the aeropropulsion system is frequentlyencountered in many of the advanced aerospace vehicles. These propulsion systems can be eithera podded or an embedded design employed in HWB (Hybrid Wing Body) airframe concept. It isalso a topic of interest in military applications, in which advanced air vehicles have already deployedsome form of embedded propulsion systems in their design because of the requirementsof compact and low observable inlets. Even in the conventional airframe/engine design, the fancould operate under such condition when the air vehicle is undergoing rapid maneuvering action.It is believed that a better understanding of the fan’s aerodynamic and aeromechanical responseto this type of operating condition or off design operation would be beneficial to designing distortiontolerant blades for improved engine operability.The objective for this research is to assess the capability of turbomachinery code as an analysistool in understanding the effects and evaluating the impact of flow distortion on the aerodynamicand aeromechanical performance of the fan in advanced propulsion systems. Results from thetesting of an advanced fan stage released by NASA are available and will be used here for CFDcode validation. The experiment was performed at NASA’s high speed compressor facility aspart of the RTA (Revolutionary Turbine Accelerator) demonstration project, a joint effort ofNASA Glenn Research Center and GE Aircraft Engines in developing an advanced Mach 4TBCC (Turbine Based Combined Cycle) turbofan/ramjet engine for access to space. Part of thetest was to assess the aerodynamic performance and operability of the fan stage under nonuniforminflow condition. Various flow distortion patterns were created at the fan-face by manipulatingsets of screens placed upstream of the wind tunnel. Measurements at the fan-face willprovide the necessary distortion flow information as the inflow boundary condition for the CFDin a full wheel simulation. Therefore the purpose of this work is to demonstrate the NASA supportedmulti-stage turbomachinery code, TURBO [1-5], in the aerodynamic performance analysisof a modern fan design operating under off design condition, and in particular to validate theCFD results with the RTA fan test data.A brief description of the RTA fan rig configuration is given in the next section, explaining onhow flow distortion were measured in the test and constructed for the CFD at the fan-face. It isfollowed by a section summarizing previous CFD work performed at NASA relevant to the currentfan configuration. A short description of the TURBO code is given next, followed by detailsin the computational model of the fan rig, the required computing resources, and the numericalprocedure for the simulations. The CFD results are presented in the discussion section and finallyconcluding remarks are summarized.
Serially concatenated turbo codes have been proposed to satisfy requirements for low bit- and word-error rates and for low (in comparison with related previous codes) complexity of coding and decoding algorithms and thus low complexity of coding and decoding circuitry. These codes are applicable to such high-level modulations as octonary phase-shift keying (8PSK) and 16-state quadrature amplitude modulation (16QAM); the signal product obtained by applying one of these codes to one of these modulations is denoted, generally, as serially concatenated trellis-coded modulation (SCTCM). These codes could be particularly beneficial for communication systems that must be designed and operated subject to limitations on bandwidth and power. Some background information is prerequisite to a meaningful summary of this development. Trellis-coded modulation (TCM) is now a well-established technique in digital communications. A turbo code combines binary component codes (which typically include trellis codes) with interleaving. A turbo code of the type that has been studied prior to this development is composed of parallel concatenated convolutional codes (PCCCs) implemented by two or more constituent systematic encoders joined through one or more interleavers. The input information bits feed the first encoder and, after having been scrambled by the interleaver, enter the second encoder. A code word of a parallel concatenated code consists of the input bits to the first encoder followed by the parity check bits of both encoders. The suboptimal iterative decoding structure for such a code is modular, and consists of a set of concatenated decoding modules one for each constituent code connected through an interleaver identical to the one in the encoder side. Each decoder performs weighted soft decoding of the input sequence. PCCCs yield very large coding gains at the cost of a reduction in the data rate and/or an increase in bandwidth.
Analytical bounds on the performance of concatenated codes on a tree structure are obtained. Analytical results are applied to examples of parallel concatenation of two codes (turbo codes), serial concatenation of two codes, hybrid concatenation of three codes, and self concatenated codes, over AWGN and fading channels.
In this paper, analytical bounds on the performance of parallel concatenation of two codes, known as turbo codes, and serial concatenation of two codes over fading channels are obtained.
An advanced high-speed fan was recently designed under a cooperative effort between the NASA Glenn Research Center and Honeywell Engines & Systems. The principal design goals were to improve performance and to reduce fan noise at takeoff. Scale models of the Quiet High-Speed Fan were tested for operability, performance, and acoustics. During testing, the fan showed significantly improved noise characteristics, but a self-excited aeroelastic vibration known as flutter was encountered in the operating range. Flutter calculations were carried out for the Quiet High-Speed Fan using a three-dimensional, unsteady aerodynamic, Reynolds-averaged Navier-Stokes turbomachinery code named "TURBO." The TURBO code can accurately model the viscous flow effects that can play an important role in various aeroelastic problems such as flutter with flow separation, flutter at high loading conditions near the stall line (stall flutter), and flutter in the presence of shock and boundary-layer interaction. Initially, calculations were performed with no blade vibrations. These calculations were at a constant rotational speed and a varying mass flow rate. The mass flow rate was varied by changing the backpressure at the exit boundary of the computational domain. These initial steady calculations were followed by aeroelastic calculations in which the blades were prescribed to vibrate harmonically in a natural mode, at a natural frequency, and with a fixed interblade phase angle between adjacent blades. The AE-prep preprocessor was used to interpolate the in-vacuum mode shapes from the structural dynamics mesh onto the computational fluid dynamics mesh and to smoothly propagate the grid deformations from the blade surface to the interior points of the grid. The aeroelastic calculations provided the unsteady aerodynamic forces on the blade surface due to blade vibrations. These forces were vector multiplied with the structural dynamic mode shape to calculate the work done on the blade during one vibration period, then this result was converted to an aerodynamic damping. Flutter occurs when the aerodynamic damping becomes negative, if structural damping is ignored. The results of these aeroelastic calculations are summarized in this plot of aerodynamic damping versus mass flow rate at a constant rotational speed. As the backpressure is increased, the mass flow rate through the fan decreases and the fan operating point moves towards the stall line. The aeroelastic calculations showed that the aerodynamic damping decreases as the stall line is approached, as observed during testing. In addition, the aeroelastic calculations with the TURBO code correctly predicted the aeroelastic parameters: the most unstable vibration mode and interblade phase angle, as observed during testing. The Quiet High-Speed Fan demonstrated significant noise reductions during testing, but flutter imposed limits on its operating range. The accurate calculation of the aeroelastic characteristics using the TURBO code is a significant step toward eliminating flutter from the operating range and toward realizing the benefits of reduced fan noise. The aeroelastic calculations described here were performed under a grant by University of Toledo researchers in collaboration with Glenn's researchers.
In this paper, analytical bounds on the performance of parallel concatenation of two codes, known as turbo codes, and serial concatenation of two codes over fading channels are obtained. Based on this analysis, design criteria for the selection of component trellis codes for MPSK modulation, and a suitable bit-by-bit iterative decoding structure are proposed. Examples are given for throughput of 2 bits/sec/Hz with 8PSK modulation. The parallel concatenation example uses two rate 4/5 8-state convolutional codes with two interleavers. The convolutional codes' outputs are then mapped to two 8PSK modulations. The serial concatenated code example uses an 8-state outer code with rate 4/5 and a 4-state inner trellis code with 5 inputs and 2 x 8PSK outputs per trellis branch. Based on the above mentioned design criteria for fading channels, a method to obtain he structure of the trellis code with maximum diversity is proposed. Simulation results are given for AWGN and an independent Rayleigh fading channel with perfect Channel State Information (CSI).
Turbo codes not only achieve near Shannon-capacity performance, but also have decoders with modest complexity, which is crucial for implementation. So far efficient architectures for decoding of turbo codes have been proposed that is suitable for serial processing. In this paper a novel architecture for very high-speed turbo decoder is presented. The performance of this decoder is illustrated and the tradeoff between speed and efficiency is discussed. It is shown that some decoders can run faster by some order of magnitude while maintaining almost the same processing load.
In this report, we present the results of our recent work on turbo coding in two formats. Appendix A includes the overheads of a talk that has been given at four different locations over the last eight months. This presentation has received much favorable comment from the research community and has resulted in the full-length paper included as Appendix B, 'A Distance Spectrum Interpretation of Turbo Codes'. Turbo codes use a parallel concatenation of rate 1/2 convolutional encoders combined with iterative maximum a posteriori probability (MAP) decoding to achieve a bit error rate (BER) of 10(exp -5) at a signal-to-noise ratio (SNR) of only 0.7 dB. The channel capacity for a rate 1/2 code with binary phase shift-keyed modulation on the AWGN (additive white Gaussian noise) channel is 0 dB, and thus the Turbo coding scheme comes within 0.7 DB of capacity at a BER of 10(exp -5).
The main objective of this paper is to develop new, low complexity turbo codes suitable for bandwidth and power limited systems, for very low bit and word error rate requirements.