Component Codes Research Articles

Shortened Turbo Product Codes: Encoding Design and Decoding Algorithm

Shortened turbo product codes (TPCs) have already been adopted in many standards. In this paper, we study shortened TPCs from two aspects, namely encoding design and decoding algorithm. To obtain different encoding block sizes, shortened-extended Hamming codes are used as the component codes of product codes in the IEEE 802.16 standard. To design a good structure for the shortened TPC, we compute the undetected error probability of its corresponding component codes. The component codes are shortened-extended Hamming codes, and their optimal generator polynomials are selected in terms of their undetected error probability. For the decoding algorithm, we present an efficient Chase decoding algorithm for shortened TPCs in flat fading channels. In the proposed scheme, the reliability factor used in Pyndiah's scheme is not needed; thus, the decoding complexity is greatly reduced by avoiding the normalization operation of the whole code word at each iteration. Simulation results are also presented to verify the performance of the proposed algorithm.

Using LDPC-Coded Modulation and Coherent Detection for Ultra Highspeed Optical Transmission

We propose the coded modulation schemes for ultrahigh-speed transmission (100 Gb/s and above) by using commercially available components operating at 40 gigasymbols/s. The bit-interleaved coded modulation in combination with the low-density parity-check codes that are used as component codes has been applied. The modulation is based on either M-ary quadrature-amplitude modulation or M-ary phase-shift keying. bits are mapped into the corresponding signal constellation point using either Gray or natural mapping. The coherent detection scheme has been found to outperform the direct detection one and to provide an additional margin much needed for longer transmission distances or for application in an all-optical network scenario.

Performance characteristics and weight distribution analysis of turbo product code with Reed–Muller component codes

In this paper, we present simulation results for Reed–Muller (RM) turbo codes over AWGN and Rayleigh fading channels. We also compare the simulation results of turbo product codes and block turbo codes with RM component codes over an AWGN channel. We show that minimum distance is not important as far as the BER performance of long codes is concerned. The weight distribution of RM codes of different lengths and turbo product codes with first-order RM component codes are obtained and analyzed for their good performance. We show that the weight distribution asymptotically approaches that of random coding as the code length increases.

NEPTUNE: A New Software Platform for Advanced Nuclear Thermal Hydraulics

The NEPTUNE project constitutes the thermal-hydraulic part of the long-term Electricité de France and Commissariat à l’Energie Atomique joint research and development program for the next generation of nuclear reactor simulation tools. This program is also financially supported by the Institut de Radioprotection et Sûreté Nucléaire and AREVA NP. The project aims at developing a new software platform for advanced two-phase flow thermal hydraulics covering the whole range of modeling scales and allowing easy multiscale and multidisciplinary calculations. NEPTUNE is a fully integrated project that covers the following fields: software development, research in physical modeling and numerical methods, development of advanced instrumentation techniques, and performance of new experimental programs.The analysis of the industrial needs points out that three main simulation scales are involved. The system scale is dedicated to the overall description of the reactor. The component or subchannel scale allows three-dimensional computations of the main components of the reactors: cores, steam generators, condensers, and heat exchangers. The current generation of system and component codes has reached a very high level of maturity for industrial applications. The third scale, computational fluid dynamics (CFD) in open medium, allows one to go beyond the limits of the component scale for a finer description of the flows. This scale opens promising perspectives for industrial simulations, and the development and validation of the NEPTUNE CFD module have been a priority since the beginning of the project. It is based on advanced physical models (two-fluid or multifield model combined with interfacial area transport and two-phase turbulence) and modern numerical methods (fully unstructured finite volume solvers). For the system and component scales, prototype developments have also started, including new physical models and numerical methods.In addition to scale-specific developments, the generalized use of multiscale calculations is also expected to be a major means to meet the industrial needs. The coexistence of different simulation scales together with the fast growth of computing power multiplies the computation possibilities. In particular, thanks to the recent progress of CFD tools, one can imagine local zooms in some critical parts of the reactor components. The NEPTUNE multiscale platform will offer advanced coupling functionalities based on state-of-the-art software architecture and new numerical coupling techniques.Finally, despite the existence of a huge worldwide database of two-phase flow experiments, the validation of new physical models (more local, more complex) requires new experimental data. That is the reason why for several years we have been developing new instrumentation techniques such as four-sensor optical probes, X-ray tomography, and hot-wire anemometry. These techniques will be used for new experimental programs (currently being launched) that have been defined in connection with the high-priority industrial applications (departure from nucleate boiling, pressurized thermal shock, loss-of-coolant accident, etc.).

Composition inference for UML class diagrams

Knowing which associations are compositions is important in a tool for the reverse engineering of UML class diagrams. Firstly, recovery of composition relationships bridges the gap between design and code. Secondly, since composition relationships explicitly state a requirement that certain representations cannot be exposed, it is important to determine if this requirement is met by component code. Verifying that compositions are implemented properly may prevent serious program flaws due to representation exposure. We propose an implementation-level composition model based on ownership and a novel approach for identifying compositions in Java software. Our approach is based on static ownership inference; it is parameterized by class analysis and is designed to work on incomplete programs. We present empirical results from two instantiation of our approach. For one of these instantiations, on average 40% of the examined fields account for relationships that are identified as compositions. In addition, we present a precision evaluation which shows that the analysis achieves almost perfect precision--that is, it almost never misses composition relationships. The results indicate that precise identification of interclass relationships can be done with a simple and inexpensive analysis, and thus can be easily incorporated in reverse engineering tools that support iterative model-driven development.

Architecture de turbo-décodeur en blocs entièrement parallèle pour la transmission de données au-delà du Gbit/s

This paper presents a new circuit architecture for turbo decoding, which achieves ultra high data rates when using product codes as error correcting codes. This architecture is able to decode product codes using binary BCH or m-ary Reed Solomon component codes. The major advantage of our full-parallel architecture is that it enables the memory block between each half-iteration to be removed. In fact, the proposed architecture opens the way to numerous applications such as optical transmission. In particular, our block turbo decoding architecture can support optical transmission at data rates above Gbit/s

Parallel Detection of Groupwise Space–Time Codes by Predictive Soft Interference Cancellation

Multiple-input multiple-output (MIMO) techniques promise huge capacity increase in fading channels. Groupwise space-time coding is a tradeoff between complexity and performance. In this letter, the structure of particular component space-time code trellises is exploited, using partial information from a Viterbi decoder of the simultaneously decoded interfering component codes. We have shown that by calculating the a posteriori probabilities of different states of the encoder at each time, and predicting the conditional mean and covariance of interference for the next time index, the system performance can be improved by soft interference cancellation. The word-error rate performance improvement for a system with four transmit and four receive antennas is 1.7 and 1.5 dB for two space-time codes with 8 and 16 states, respectively. In addition, the parallel structure does not have a decoding delay, as in successive interference cancellation, and is highly modular for very-large-scale integration implementation

Application of Randomization Techniques to Space-Time Convolutional Codes

This correspondence introduces a new approach to design space-time convolutional codes (STCCs) with large constellation size in systems with any number of transmit antennas. Our design procedure is based on utilizing quadrature phase-shift keying (QPSK) STCCs as component codes, and, consequently, unlike existing techniques, the search space does not grow exponentially with the constellation size. Our approach is further based on the fact that an ntimesm multiple-input multiple-output (MIMO) system is equivalent to n distinct 1timesm systems. By employing a common design for each individual 1timesm system, we arrive at an approach whose complexity does not grow with the number of transmit antennas. To describe our approach, we first demonstrate that a system employing an STCC can be implemented with only a single transmit antenna when there are multiple receive antennas. The idea is to transmit more than one symbol from a single transmit antenna during a symbol period by superimposing the encoded symbols on top of each other. This objective is achieved by inducing randomness into the system, that creates additional channel paths, called virtual paths. The design of the distributions of the induced random variables is studied for slow Rayleigh and Rician fading channels by utilizing an upper bound on the pairwise block error probability. Simulation results evaluate the performance of this technique for the case of two transmit antennas and several different number of receive antennas, a spectral efficiency of 4 b/s/Hz for slow Rayleigh and Rician fading channels

Presentation and use of a reactive transport code in porous media

The safety assessment of nuclear waste disposals requires an accurate prediction of the radionuclides and chemical species migration through engineered barriers and geological media. It is therefore necessary to develop and assess qualified and validated tools which integrate both the transport mechanisms through the geological media and the chemical mechanisms governing the mobility of radionuclides. Such a reactive transport simulation tool has been developed in the context of the numerical software platform ALLIANCES. Different component codes are available: PHREEQC and CHESS for the chemical part, CAST3M, MT3D and TRACES for the transport part. A coupling scheme has already been implemented, qualified and validated on numerous configurations involving aqueous speciation, dissolution–precipitation, sorption and surface complexation. Presently, the reactive transport numerical tool is used to simulate realistic configurations. This paper presents two of such applications: the migration of uranium in a soil with various redox conditions and the modelling of clay–cement interactions.

Performance of serially concatenated coding schemes for MIMO systems

In this paper, we investigate the performance of serially concatenated space–time coding systems on quasi-static and ideally-interleaved (rapid) Rayleigh fading channels. The considered system uses rate- 1 2 repetition or nonrecursive convolutional codes as the outer code and conventional or super-orthogonal space–time QPSK trellis codes as the inner code. We consider the cases of two transmit and one or two receive antennas with iterative decoding based on the maximum a posteriori (MAP) algorithm. We introduce new low-complexity component code combinations for serially concatenated space–time coding systems providing full diversity and good error performance.

Analysis and design of power-efficient coding schemes with parallel concatenated convolutional codes

In the low signal-to-noise ratio regime, the performance of concatenated coding schemes is limited by the convergence properties of the iterative decoder. Idealizing the model of iterative decoding by an independence assumption, which represents the case in which the codeword length is infinitely large, leads to analyzable structures from which this performance limit can be predicted. Mutual information transfer characteristics of the constituent coding schemes comprising convolutional encoders and soft-in/soft-out decoders have been shown to be sufficient to characterize the components within this model. Analyzing serial and parallel concatenations is possible just by these characteristics. In this paper, we extend the method of extrinsic information transfer charts, that is limited to the case of a concatenation of two component codes, to the case of multiple turbo codes. Multiple turbo codes are parallel concatenations of three or more constituent codes, which, in general, may not be identical and may not have identical code rates. For the construction of low-rate codes, this concept seems to be very favorable, as power efficiencies close to the Shannon limit can be achieved with reasonable complexity

Low-density parity-check codes for 40-gb/s optical transmission systems

In this paper, we compare performance of three classes of forward error correction schemes for 40-Gb/s optical transmission systems. The first class is based on the concatenation of Reed-Solomon codes and this is employed in the state-of-the-art fiber-optics communication systems. The second class is the turbo product codes with Bose-Chaudhuri-Hocquenghen component codes. The application of these codes in optical communication systems was extensively studied by Sab and Lemarie, and Mizuochi The third class is the low-density parity-check (LDPC) codes that have attracted much attention over the past decade. We present enhanced decoding algorithms for Turbo product codes and LDPC codes that use probability density function of output sequences instead of calculating initial likelihood ratios assuming (inaccurate) Gaussian or chi-square approximation. The analysis in this paper shows that the LDPC codes perform better than the other codes in the waterfall region at bit error rates as low as 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-9</sup> . We also presented error floors results obtained by analyzing decoding failures of hard-decision iterative decoders

Multilevel coding in free-space optical MIMO transmission with Q-ary PPM over the atmospheric turbulence channel

We propose an efficient coded modulation scheme for multiple input/multiple output free-space optical systems with Q-ary pulse-position modulation. It is based on multilevel coding and low-density parity-check codes as component codes. The proposed scheme provides excellent coding gain in the regime of strong atmospheric turbulence.

On Unequal Error Protection LDPC Codes Based on Plotkin-Type Constructions

We introduce a new family of unequal error protection (UEP) codes, based on low-density parity-check (LDPC) component codes and Plotkin-type constructions. The codes are decoded iteratively in multiple stages, and the order of decoding determines the level of error protection. The level of UEP among the code bits is also influenced by the choice of the LDPC component codes and by some new reliability features incorporated into the decoding process. The proposed scheme offers a very good tradeoff between code performance on one side and encoding/decoding and storage complexity on the other side. The novel approach to UEP also allows for finding simple approximations for the achievable degrees of UEP, which can be used to govern practical code design implementations

System dependence graph construction for aspect oriented C++

This paper proposes an extended system dependence graph called AspectSDG to represent control and data dependences for AspectC++ programs, and presents an approach for the construction of AspectSDG. This approach decomposes aspect-oriented programs into three parts: component codes, aspect codes, and weaving codes. It constructs program dependence graphs (PDGs) for each part, and then connects the PDGs at call sites to form the complete AspectSDG. The AspectSDG can deal with advice precedence correctly, and represent the additional dependences caused by aspect codes. Based on this model, we introduce how to compute a static slice of an AspectC++ program.

Superposition coding for side-information channels

We present simple, practical codes designed for the binary and Gaussian dirty-paper channels. We show that the dirty-paper decoding problem can be transformed into an equivalent multiple-access decoding problem, for which we apply superposition coding. Our concept is a generalization of the nested lattices approach of Zamir, Shamai, and Erez. In a theoretical setting, our constructions are capable of achieving capacity using random component codes and maximum-likelihood decoding. We also present practical implementations of the constructions, and simulation results for both dirty-paper channels. Our results for the Gaussian dirty-paper channel are on par with the best known results for nested lattices. We discuss the binary dirty- tape channel, for which we present a simple, effective coding technique. Finally, we propose a framework for extending our approach to general Gel'fand-Pinsker channels.

Diversity Analysis for Frequency-Selective MlMO-OFDM Systems With General Spatial and Temporal Correlation Model

In the low signal-to-noise ratio regime, the performance of concatenated coding schemes is limited by the convergence properties of the iterative decoder. Idealizing the model of iterative decoding by an indepen- dence assumption, which represents the case in which the codeword length is infinitely large, leads to analyzable structures from which this perfor- mance limit can be predicted. Mutual information-transfer characteristics of the constituent coding schemes comprising convolutional encoders and soft-in/soft-out decoders have been shown to be sufficient to characterize the components within this model. Analyzing serial and parallel concate- nations is possible just by these characteristics. In this paper, we extend the method of extrinsic information transfer charts that is limited to the case of a concatenation of two component codes, to the case of multiple turbo codes. Multiple turbo codes are parallel concatenations of three or more constituent codes, which, in general, may not be identical and may not have identical code rates. For the construction of low-rate codes, this concept seems to be very favorable, as power efficiencies close to the Shannon limit can be achieved with reasonable complexity. Abstract—In this paper, we present quasi-chaotic schemes for secure digital communication systems, designed over Galois fields with optimal randomness properties. Schemes with the maximum output sequence length (all-zero input response) are presented for different Galois fields. Two coefficients are used to quantitatively measure the proximity of the behavior of these schemes with respect to the ideal white-noise behavior. The proposed schemes outperform those presented by Frey in his paper, and achieve the optimal quasi-chaotic properties available for a given chaotic digital scheme. The proposed schemes have also a very little loss in bit-error rate performance, so that they are a good alternative to the design of systems for which encryption and error correction are important joint goals. They can be implemented with time-variant coefficients in order to highly improve the cryptographic properties of the transmission. Abstract—In this paper, the effect of a general spatial and tem- poral fading correlation structure on the performance of coded mul- tiple-input multiple-output-orthogonal frequency-division multiplexing (MIMO-OFDM) systems is studied. The analysis handles an arbitrary joint transmit-receive spatial correlation model, including the non-Kronecker model. An upper bound on the maximum achievable diversity order for frequency-selective MIMO-OFDM systems with general temporal and spatial correlation is derived. Furthermore, a space-time-frequency code design that can achieve the upper bound for any arbitrarily cor- related channel scenario is provided. The general framework of the analysis includes space-frequency-coded systems as a special case. For the space-frequency-coded MIMO-OFDM system, it is shown that any space-frequency code designed to achieve full diversity in the indepen- dent fading channel can achieve full diversity in an arbitrary spatially correlated channel. The derived analytical results are consistent with those in the existing literature for special correlation structures. Extensive simulation results are provided to confirm the theoretical analysis. Abstract—A new modulation method for linear space-time codes is pro- posed, based on using constellations of different sizes for different symbols. It is shown that the proposed method significantly reduces the complexity of the sphere-decoding algorithm. The complexity reduction is more pro- nounced in high-rate codes, where each code matrix carries a large number of symbols. We also show that the choice of constellation size provides a tradeoff between performance and complexity. Using this, some guidelines for choosing constellation size are presented. As one introduces more con- stellation disparity in the code, the complexity is further reduced, while the performance loss grows. Typically, a complexity reduction of one to two or- ders of magnitude can be achieved at the expense of about 3 dB coding gain. We suggest modification in our design to reduce this loss to about 2 dB.

Low-density parity-check codes for space-time wireless transmission

Irregular low-density parity-check (LDPC) codes have shown exceptionally good performance for single antenna systems over a wide class of channels. In this paper, we investigate their application to multiple antenna systems in flat Rayleigh fading channels. For small transmit arrays, we focus mainly on space-time coding with 2/sup p/-ary LDPC codes, where p equals the number of encoded bits transmitted by the transmit antenna array during each signaling interval. For large transmit arrays, we study a layered space-time architecture using binary LDPC codes as component codes of each layer: We show through simulation that, when applied to multiple antenna systems with high diversity order, LDPC codes of quasi-regular construction are able to achieve higher coding gain and/or diversity gain than previously proposed space-time trellis codes, space-time turbo codes, and convolutional codes in a number of fading conditions. Extending the work of density evolution with Gaussian approximation, we study 2/sup p/-ary LDPC codes on multiple antenna fading channels, and search for the optimum 2/sup p/-ary quasi-regular codes in quasi-static fading. We also show that on fast fading channels, 2/sup p/-ary irregular LDPC codes, though designed for static channels, have superior performance to nonbinary quasiregular codes and binary irregular codes specifically designed for fast fading channels.

Low rate convolutional and turbo codes based on non‐linear cyclic codes

AbstractLow rate convolutional and turbo codes that output non‐linear cyclic (NLC) codewords of length n = 2m, m being a positive integer, are described. These codes have a very low coding rate, which makes them especially suitable for spread spectrum systems where they can be used for simultaneously achieving error correction and bandwidth expansion. Due to the cyclic properties and codeword length of the component codes, branch metrics can be efficiently computed using the fast Fourier transform (FFT), enabling simple implementation of the encoder and decoder. Among the possible NLC base codes, special attention is given to the Tomlinson, Cercas, Hughes (TCH) codes family due to their good autocorrelation properties. It is shown by simulation that the turbo codes schemes studied usually perform better than traditional turbo codes (in this paper the universal mobile telecommunications system (UMTS), rate 1/3 turbo code was used as a reference). This improvement is accomplished at the cost of bandwidth expansion. One of the advantages of the presented solutions over other low rate codes is their ability to improve the synchronization process at the receiver due to the good autocorrelation properties of the available NLC codes (especially TCH codes). A comparison of performance between the UMTS uplink connection and an equivalent system using the proposed codes for a multiuser scenario in a multipath fading channel is presented showing the possibility of capacity increase when using these codes. Copyright © 2006 John Wiley &amp; Sons, Ltd.

Multilevel generalised low-density parity-check codes

Multilevel coding invoking generalised low-density parity-check component codes is proposed, which is capable of outperforming the classic low-density parity check component codes at a reduced decoding latency.