Serial concatenated trellis coded modulation with rate-1 inner code
We develop new, low complexity turbo codes suitable for bandwidth and power limited systems, for very low bit and word error rate requirements.
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Serial Turbo Trellis Coded Modulation with Rate 1 Inner Code
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.
Serial Turbo Coded Modulation iterative decoding P↗
Performance complexity tradeoffs for turbo and turbo-like codes
We take a first empirical step toward understanding the performance-complexity tradeoffs that have newly arisen since the advent of turbo codes.
turbo codes coding complexity↗
Low Complexity Turbo-like Codes
This paper addresses the iterative devoding analysis, design, and performance of low complexity turbo like codes.
turbo-like codes iterative decoding analysis conca↗
Investigation of Different Constituent Encoders in a Turbo-code Scheme for Reduced Decoder Complexity
A large number of papers have been published attempting to give some analytical basis for the performance of Turbo-codes. It has been shown that performance improves with increased interleaver length. Also procedures have been given to pick the best constituent recursive systematic convolutional codes (RSCC's). However testing by computer simulation is still required to verify these results. This thesis begins by describing the encoding and decoding schemes used. Next simulation results on several memory 4 RSCC's are shown. It is found that the best BER performance at low E(sub b)/N(sub o) is not given by the RSCC's that were found using the analytic techniques given so far. Next the results are given from simulations using a smaller memory RSCC for one of the constituent encoders. Significant reduction in decoding complexity is obtained with minimal loss in performance. Simulation results are then given for a rate 1/3 Turbo-code with the result that this code performed as well as a rate 1/2 Turbo-code as measured by the distance from their respective Shannon limits. Finally the results of simulations where an inaccurate noise variance measurement was used are given. From this it was observed that Turbo-decoding is fairly stable with regard to noise variance measurement.
Kwatra, S. C.↗
Error-Rate Bounds for Coded PPM on a Poisson Channel
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.
Moision, Bruce↗
Milcom 04 Paper ID# 1158: A New Class of Turbo-like Codes with Efficient and Practical High-speed Decoders
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.
interleaver design↗
Low-Rate Turbo Codes for Deep-Space Communications
It is shown how turbo codes and decoders can be used to improve the coding gain for deep-space communications, while decreasing the decoding complexity with respect to the large constraint length convolutional codes currently in use. Similar code constructions were used to build multiple-encoder turbo codes. This generalizes the turbo decoding concept to a truly distributed decoding system.
turbo codes deep-space communications coding decod↗
Implementation of a Coded Modulation for Deep Space Optical Communications
We present a field programmable gate array code (FPGA) implementation of a turbo-like decoder for a serially concatenated pulse-position modulation (SCPPM) code. NASA a developed this coded modulation scheme for deep space communications from Mars. Under a nominal mission condition, the decoder complexity by iteratively decoding the modulation and SCPPM coded system can operate within a one dB signal energy gap from capacity. The structure of SCPPM makes direct application of the conventional turbo decoding algorithm very inefficient. Here, we describe techniques to increase the throughput and performance of a hardware SCPPM decoder. using our optimizations, we demonstrate a 6 mega-bits per second (Mbps) decoder realization on a single FPGA. Extension toa higher data rate decoder using multiple FPGAs is readily achievable. Similar codes designed for the optical channel can benefit from our optimization techniques.
modulation↗
Serial-Turbo-Trellis-Coded Modulation with Rate-1 Inner Code
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.
Divsalar, Dariush↗
Low complexity serially concatenated coding for the deep space optical channel
We illustrate the performance of low-complexity serially concatenated codes designed for the deep space optical channel.
turbo codes optical communications↗
Numerical Simulation of Complex Turbomachinery Flows
An unsteady, multiblock, Reynolds Averaged Navier Stokes solver based on Runge-Kutta scheme and Pseudo-time step for turbo-machinery applications was developed. The code was validated and assessed against analytical and experimental data. It was used to study a variety of physical mechanisms of unsteady, three-dimensional, turbulent, transitional, and cooling flows in compressors and turbines. Flow over a cylinder has been used to study effects of numerical aspects on accuracy of prediction of wake decay and transition, and to modify K-epsilon models. The following simulations have been performed: (a) Unsteady flow in a compressor cascade: Three low Reynolds number turbulence models have been assessed and data compared with Euler/boundary layer predictions. Major flow features associated with wake induced transition were predicted and studied; (b) Nozzle wake-rotor interaction in a turbine: Results compared to LDV data in design and off-design conditions, and cause and effect of unsteady flow in turbine rotors were analyzed; (c) Flow in the low-pressure turbine: Assessed capability of the code to predict transitional, attached and separated flows at a wide range of low Reynolds numbers and inlet freestream turbulence intensity. Several turbulence and transition models have been employed and comparisons made to experiments; (d) leading edge film cooling at compound angle: Comparisons were made with experiments, and the flow physics of the associated vortical structures were studied; and (e) Tip leakage flow in a turbine. The physics of the secondary flow in a rotor was studied and sources of loss identified.
Chernobrovkin, A. A.↗
Hardware Implementation of Serially Concatenated PPM Decoder
A prototype decoder for a serially concatenated pulse position modulation (SCPPM) code has been implemented in a field-programmable gate array (FPGA). At the time of this reporting, this is the first known hardware SCPPM decoder. The SCPPM coding scheme, conceived for free-space optical communications with both deep-space and terrestrial applications in mind, is an improvement of several dB over the conventional Reed-Solomon PPM scheme. The design of the FPGA SCPPM decoder is based on a turbo decoding algorithm that requires relatively low computational complexity while delivering error-rate performance within approximately 1 dB of channel capacity. The SCPPM encoder consists of an outer convolutional encoder, an interleaver, an accumulator, and an inner modulation encoder (more precisely, a mapping of bits to PPM symbols). Each code is describable by a trellis (a finite directed graph). The SCPPM decoder consists of an inner soft-in-soft-out (SISO) module, a de-interleaver, an outer SISO module, and an interleaver connected in a loop (see figure). Each SISO module applies the Bahl-Cocke-Jelinek-Raviv (BCJR) algorithm to compute a-posteriori bit log-likelihood ratios (LLRs) from apriori LLRs by traversing the code trellis in forward and backward directions. The SISO modules iteratively refine the LLRs by passing the estimates between one another much like the working of a turbine engine. Extrinsic information (the difference between the a-posteriori and a-priori LLRs) is exchanged rather than the a-posteriori LLRs to minimize undesired feedback. All computations are performed in the logarithmic domain, wherein multiplications are translated into additions, thereby reducing complexity and sensitivity to fixed-point implementation roundoff errors. To lower the required memory for storing channel likelihood data and the amounts of data transfer between the decoder and the receiver, one can discard the majority of channel likelihoods, using only the remainder in operation of the decoder. This is accomplished in the receiver by transmitting only a subset consisting of the likelihoods that correspond to time slots containing the largest numbers of observed photons during each PPM symbol period. The assumed number of observed photons in the remaining time slots is set to the mean of a noise slot. In low background noise, the selection of a small subset in this manner results in only negligible loss. Other features of the decoder design to reduce complexity and increase speed include (1) quantization of metrics in an efficient procedure chosen to incur no more than a small performance loss and (2) the use of the max-star function that allows sum of exponentials to be computed by simple operations that involve only an addition, a subtraction, and a table lookup. Another prominent feature of the design is a provision for access to interleaver and de-interleaver memory in a single clock cycle, eliminating the multiple clock-cycle latency characteristic of prior interleaver and de-interleaver designs.
Moision, Bruce↗
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↗
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↗
Multi-Zone Liquid Thrust Chamber Performance Code with Domain Decomposition for Parallel Processing
Computational Fluid Dynamics (CFD) has considerably evolved in the last decade. There are many computer programs that can perform computations on viscous internal or external flows with chemical reactions. CFD has become a commonly used tool in the design and analysis of gas turbines, ramjet combustors, turbo-machinery, inlet ducts, rocket engines, jet interaction, missile, and ramjet nozzles. One of the problems of interest to NASA has always been the performance prediction for rocket and air-breathing engines. Due to the complexity of flow in these engines it is necessary to resolve the flowfield into a fine mesh to capture quantities like turbulence and heat transfer. However, calculation on a high-resolution grid is associated with a prohibitively increasing computational time that can downgrade the value of the CFD for practical engineering calculations. The Liquid Thrust Chamber Performance (LTCP) code was developed for NASA/MSFC (Marshall Space Flight Center) to perform liquid rocket engine performance calculations. This code is a 2D/axisymmetric full Navier-Stokes (NS) solver with fully coupled finite rate chemistry and Eulerian treatment of liquid fuel and/or oxidizer droplets. One of the advantages of this code has been the resemblance of its input file to the JANNAF (Joint Army Navy NASA Air Force Interagency Propulsion Committee) standard TDK code, and its automatic grid generation for JANNAF defined combustion chamber wall geometry. These options minimize the learning effort for TDK users, and make the code a good candidate for performing engineering calculations. Although the LTCP code was developed for liquid rocket engines, it is a general-purpose code and has been used for solving many engineering problems. However, the single zone formulation of the LTCP has limited the code to be applicable to problems with complex geometry. Furthermore, the computational time becomes prohibitively large for high-resolution problems with chemistry, two-equation turbulence model, and two-phase flow. To overcome these limitations, the LTCP code is rewritten to include the multi-zone capability with domain decomposition that makes it suitable for parallel processing, i.e., enabling the code to run every zone or sub-domain on a separate processor. This can reduce the run time by a factor of 6 to 8, depending on the problem.
Homayun K. Navaz↗
Herative Decoding of Serially Concatenated Codes with Interleavers and Comparison with Turbo Codes
A serially concatenated code with interleaver consists of the cascade of an outer encoder, an interleaver permuting the outer codewords bits, and an inner encoder whose input words are the permuted outer codewords.
low-complexity iterative decoding simulation compa↗
Transfer Factors for the FRMAC Assessment Manual and Turbo FRMAC to Improve Radiological Dose Assessment
The Turbo FRMAC analysis tool is used to perform complex calculations to quickly evaluate radiological consequences and aid in decision making during an emergency response by assessing impacts to the public, workers, and the food supply. Turbo FRMAC calculations are based on methods established by the Federal Radiological Monitoring and Assessment Center (FRMAC). To be able to assess impacts, input data called transfer factors that describe radionuclide uptake by local plants and animals are required. During the code application exercises in late 2016, identifying, finding, and validating nonstandard transfer factors proved to be time consuming and diverted the teams’ activity away from other critical tasks. As a result, a task was undertaken to dramatically expand the list of available transfer factors (food and non-food) and incorporate these factors into Turbo FRMAC. This will ultimately result in improved efficiency of the assessment team to perform calculations during times when the FRMAC is activated and provide more defensible, vetted data from which to calculate results. As a result of these and subsequent exercises, transfer factors were needed for the following items: bell peppers, Christmas tree, deer, flowers, fresh cucumbers, tomatoes, grapefruit, lichens, mushrooms, oranges, snap beans, squash, strawberries, sugarcane for sugar and seed, sweet corn, tea, tobacco, tree bark, and watermelon. To expand the applicability of the information tables, generic transfer data were also provided for common categories and recommendations were made for expanding the list of chemicals based on chemical similarity. The data presented in this report were compiled from recent literature with most of the data encompassing the period from 2000 to 2018. The following radionuclides were targeted during the literature search: elements associated with reactor accidents or nuclear detonations (Sr 89/90, Cs 134/137, Ce 141/144, Ru 103/106, I 129/131/133, Pu 238/239, Am 241, Zr 95, and Nb 95) and elements associated with industrial accidents or dirty bombs (Ir 192 and Co 60). Data from other elements were evaluated if they were identified during the literature search. In addition, reports were evaluated that were recommended by the research consultants. For each plant or animal transfer factor, the goal was to determine the geometric mean, the geometric standard deviation, the minimum, the maximum, and the number of measurements used. If only one measurement was available that was presented as the mean. Concentration ratios with large geometric standard deviations (GSDs) were generally the result of a paucity of measurements or a few disparate measurements. Measurement disparity was observed for data from different soil types. The geometric mean (GM) is a good reference value for planning and responses purposes, but the location-specific concentrations are unlikely to be similar to the model results. Recommendations for further work include: segregating the data to reflect the influence of soil type, developing approaches to incorporate animal data based on aggregated transfer measurements, and including data for foliar deposition on plants.
61 RADIATION PROTECTION AND DOSIMETRY↗