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The density evolution method is used to analyze the performance and optimize the structure of parallel and serial turbo codes, and generalized serial concatenations of mixtures of different outer and inner codes. Design examples are given for mixture codes.
We take a first empirical step toward understanding the performance-complexity tradeoffs that have newly arisen since the advent of turbo codes.
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.
This paper presents a concatenated turbo coding system in which a Reed-Solomom outer code is concatenated with a binary turbo inner code. In the proposed system, the outer code decoder and the inner turbo code decoder interact to achieve both good bit error and frame error performances. The outer code decoder helps the inner turbo code decoder to terminate its decoding iteration while the inner turbo code decoder provides soft-output information to the outer code decoder to carry out a reliability-based soft-decision decoding. In the case that the outer code decoding fails, the outer code decoder instructs the inner code decoder to continue its decoding iterations until the outer code decoding is successful or a preset maximum number of decoding iterations is reached. This interaction between outer and inner code decoders reduces decoding delay. Also presented in the paper are an effective criterion for stopping the iteration process of the inner code decoder and a new reliability-based decoding algorithm for nonbinary codes.
This paper addresses the iterative devoding analysis, design, and performance of low complexity turbo like codes.
A new deep space transponder is being developed by the Jet Propulsion Laboratory for NASA. The Spacecraft Transponding Modem (STM) implements the standard transponder functions and the channel service functions that have previously resided in spacecraft Command/Data Subsystems. The STM uses custom ASICs, MMICs, and MCMs to reduce the active device parts count to 70, mass to I kg, and volume to 524 cc. The first STMs will be flown on missions launching in the 2003 time frame. The STM tracks an X-band uplink signal and provides both X-band and Ka-band downlinks, either coherent or non-coherent with the uplink. A NASA standard Command Detector Unit is integrated into the STM, along with a codeblock processor and a hardware command decoder. The decoded command codeblocks are output to the spacecraft command/data subsystem. Virtual Channel 0 (VC-0) (hardware) commands are processed and output as critical controller (CRC) commands. Downlink telemetry is received from the spacecraft data subsystem as telemetry frames. The STM provides the following downlink coding options: the standard CCSDS (7-1/2) convolutional coding, ReedSolomon coding with interleave depths one and five, (15-1/6) convolutional coding, and Turbo coding with rates 1/3 and 1/6. The downlink symbol rates can be linearly ramped to match the G/T curve of the receiving station, providing up to a 1 dB increase in data return. Data rates range from 5 bits per second (bps) to 24 Mbps, with three modulation modes provided: modulated subcarrier (3 different frequencies provided), biphase-L modulated direct on carrier, and Offset QPSK. Also, the capability to generate one of four non-harmonically related telemetry beacon tones is provided, to allow for a simple spacecraft status monitoring scheme for cruise phases of missions. Three ranging modes are provided: standard turn around ranging, regenerative pseudo-noise (PN) ranging, and Differential One-way Ranging (DOR) tones. The regenerative ranging provides the capability of increasing the ground received ranging SNR by up to 30 dB. Two different avionics interfaces to the command/data subsystem's data bus are provided: a MIL STD 1553B bus or an industry standard PCI interface. Digital interfaces provide the capability to control antenna selection (e.g., switching between high gain and low gain antennas) and antenna pointing (for future steered Ka-band antennas).
It is well known that the BER performance of a parallel concatenated turbo-code improves roughly as 1/N, where N is the information block length. However, it has been observed by Benedetto and Montorsi that for most parallel concatenated turbo-codes, the FER performance does not improve monotonically with N. In this report, we study the FER of turbo-codes, and the effects of their concatenation with an outer code. Two methods of concatenation are investigated: across several frames and within each frame. Some asymmetric codes are shown to have excellent FER performance with an information block length of 16384. We also show that the proposed outer coding schemes can improve the BER performance as well by eliminating pathological frames generated by the iterative MAP decoding process.
This paper describes coupled receiver-decoder architectures for suppressed carrier convolutionally-coded signals and residual carrier turbo-coded signals.
Equations for computing tight bounds on error rates for coded pulse-position modulation (PPM) on a Poisson channel at high signal-to-noise ratio have been derived. These equations and elements of the underlying theory are expected to be especially useful in designing codes for PPM optical communication systems. The equations and the underlying theory apply, more specifically, to a case in which a) At the transmitter, a linear outer code is concatenated with an inner code that includes an accumulator and a bit-to-PPM-symbol mapping (see figure) [this concatenation is known in the art as "accumulate-PPM" (abbreviated "APPM")]; b) The transmitted signal propagates on a memoryless binary-input Poisson channel; and c) At the receiver, near-maximum-likelihood (ML) decoding is effected through an iterative process. Such a coding/modulation/decoding scheme is a variation on the concept of turbo codes, which have complex structures, such that an exact analytical expression for the performance of a particular code is intractable. However, techniques for accurately estimating the performances of turbo codes have been developed. The performance of a typical turbo code includes (1) a "waterfall" region consisting of a steep decrease of error rate with increasing signal-to-noise ratio (SNR) at low to moderate SNR, and (2) an "error floor" region with a less steep decrease of error rate with increasing SNR at moderate to high SNR. The techniques used heretofore for estimating performance in the waterfall region have differed from those used for estimating performance in the error-floor region. For coded PPM, prior to the present derivations, equations for accurate prediction of the performance of coded PPM at high SNR did not exist, so that it was necessary to resort to time-consuming simulations in order to make such predictions. The present derivation makes it unnecessary to perform such time-consuming simulations.
A new decoder is being developed by the Jet Propulsion Laboratory for NASA's Deep Space Network. This unit will decode the new turbo codes, which have recently been approved by the Consultative Committee for Space Data Systems (CCSDS). Turbo codes provide up to 0.8 dB improvement in Eb/No over the current best codes used by deep space missions.
As available bandwidth for communication applications becomes scarce, bandwidth-efficient modulation and coding schemes become ever important. Since their discovery in 1993, turbo codes (parallel concatenated convolutional codes) have been the center of the attention in the coding community because of their bit error rate performance near the Shannon limit. Serial concatenated convolutional codes have also been shown to be as powerful as turbo codes. In this dissertation, we introduce algorithms for designing bandwidth-efficient rate r = k/(k + 1),k = 2, 3,..., 16, parallel and rate 3/4, 7/8, and 15/16 serial concatenated convolutional codes via puncturing for BPSK/QPSK (Binary Phase Shift Keying/Quadrature Phase Shift Keying) channels. Both parallel and serial concatenated convolutional codes have initially, steep bit error rate versus signal-to-noise ratio slope (called the -"cliff region"). However, this steep slope changes to a moderate slope with increasing signal-to-noise ratio, where the slope is characterized by the weight spectrum of the code. The region after the cliff region is called the "error rate floor" which dominates the behavior of these codes in moderate to high signal-to-noise ratios. Our goal is to design high rate parallel and serial concatenated convolutional codes while minimizing the error rate floor effect. The design algorithm includes an interleaver enhancement procedure and finds the polynomial sets (only for parallel concatenated convolutional codes) and the puncturing schemes that achieve the lowest bit error rate performance around the floor for the code rates of interest.
NASA's Advanced Subsonic Technology (AST) program is developing new technologies to increase the fuel efficiency of commercial aircraft engines, improve the safety of engine operation, and reduce engine emissions and noise. With the development of new designs for ducted fans, compressors, and turbines to achieve these goals, a basic aeroelastic requirement is that there should be no flutter or high resonant blade stresses in the operating regime. To verify the aeroelastic soundness of these designs, we need an accurate prediction and analysis code. Such a two-dimensional viscous propulsion aeroelastic code, named TURBO-AE, is being developed at the NASA Lewis Research Center. The TURBO-AE aeroelastic code is based on a three-dimensional unsteady aerodynamic Euler/Navier-Stokes turbomachinery code TURBO, developed under a grant from NASA Lewis. TURBO-AE can model viscous flow effects that play an important role in certain aeroelastic problems, such as flutter with flow separation (or stall flutter) and flutter in the presence of shock and boundary-layer interaction. The structural dynamics representation of the blade in the TURBO-AE code is based on a normal mode representation. A finite element analysis code, such as NASTRAN, is used to calculate in-vacuum vibration modes and the associated natural frequency. A work-per-cycle approach is used to determine aeroelastic (flutter) stability. With this approach, the motion of the blade is prescribed to be a harmonic vibration in a specified in vacuum normal mode. The aerodynamic forces acting on the vibrating blade and the work done by these forces on the vibrating blade during a cycle of vibration are calculated. If positive work is being done on the blade by the aerodynamic forces, the blade is dynamically unstable, since it will extract energy from the flow, leading to an increase in the amplitude of the blade's oscillation. Initial calculations have been done for a configuration representative of the Energy Efficient Engine fan rotor. The accompanying figure shows the work-per-cycle after each cycle of vibration. It can be seen that the work-per-cycle does not vary much after the fourth cycle. The negative sign of the converged work-per-cycle shows that the fan blade is dynamically stable and will not flutter. TURBO-AE will provide a useful aeroelastic prediction/analysis capability for engine manufacturers. It will reduce design cycle times by allowing new blade designs to be verified for aeroelastic soundness before blades are built and tested. With this prediction capability, it will be possible to build thinner, lighter, and faster rotating blades without encountering aeroelastic problems like stall flutter and high-cycle fatigue due to forced vibrations.
A pre-release version of the Navier-Stokes solver (TURBO) was obtained from MSU. Along with Dr. Milind Bakhle of the University of Toledo, subroutines for aeroelastic analysis were developed and added to the TURBO code to develop versions 1 and 2 of the TURBO-AE code. For specified mode shape, frequency and inter-blade phase angle the code calculates the work done by the fluid on the rotor for a prescribed sinusoidal motion. Positive work on the rotor indicates instability of the rotor. The version 1 of the code calculates the work for in-phase blade motions only. In version 2 of the code, the capability for analyzing all possible inter-blade phase angles, was added. The version 2 of TURBO-AE code was validated and delivered to NASA and the industry partners of the AST project. The capabilities and the features of the code are summarized in Refs. [1] & [2]. To release the version 2 of TURBO-AE, a workshop was organized at NASA Lewis, by Dr. Srivastava and Dr. M. A. Bakhle, both of the University of Toledo, in October of 1996 for the industry partners of NASA Lewis. The workshop provided the potential users of TURBO-AE, all the relevant information required in preparing the input data, executing the code, interpreting the results and bench marking the code on their computer systems. After the code was delivered to the industry partners, user support was also provided. A new version of the Navier-Stokes solver (TURBO) was later released by MSU. This version had significant changes and upgrades over the previous version. This new version was merged with the TURBO-AE code. Also, new boundary conditions for 3-D unsteady non-reflecting boundaries, were developed by researchers from UTRC, Ref. [3]. Time was spent on understanding, familiarizing, executing and implementing the new boundary conditions into the TURBO-AE code. Work was started on the phase lagged (time-shifted) boundary condition version (version 4) of the code. This will allow the users to calculate non-zero interblade phase angles using, only one blade passage for analysis.
A coding system uses a serially concatenated coder driving an interleaver, which drives a trellis coder. This combination, while similar to a turbo coder, produces certain different characteristics.
We develop new, low complexity turbo codes suitable for bandwidth and power limited systems, for very low bit and word error rate requirements.
This paper presents a coupled analysis of the interaction between mainpath and secondary flowpaths in gas turbines using transient simulations. Some of the topics include: 1) Need for Coupled Analysis; 2) Primary-Secondary Coupling Schematic; 3) Secondary Flow Requirement; 4) Objectives of Present Methodology; 5) Current Methodologies Recap; 6) Proposed Coupled Code Methodology; 7) Description of SCISEAL Code; 8) Description of Turbo Code; 9) Code Coupling/Interface Issues; and 10) Current Interface Strategy. This paper is presented in viewgraph form.
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Serial concatenated trellis coded modulation (SCTCM) includes an outer coder, an interleaver, a recursive inner coder and a mapping element. The outer coder receives data to be coded and produces outer coded data. The interleaver permutes the outer coded data to produce interleaved data. The recursive inner coder codes the interleaved data to produce inner coded data. The mapping element maps the inner coded data to a symbol. The recursive inner coder has a structure which facilitates iterative decoding of the symbols at a decoder system. The recursive inner coder and the mapping element are selected to maximize the effective free Euclidean distance of a trellis coded modulator formed from the recursive inner coder and the mapping element. The decoder system includes a demodulation unit, an inner SISO (soft-input soft-output) decoder, a deinterleaver, an outer SISO decoder, and an interleaver.