Unstructured Codes Research Articles

Computing Sum of Sources Over a Classical-Quantum MAC

We consider the task of communicating a generic bivariate function of two classical correlated sources over a Classical-Quantum Multiple Access Channel (CQ-MAC). The two sources are observed at the encoders of the CQ-MAC, and the decoder aims at reconstructing a bivariate function from the received quantum state. We first propose a coding scheme based on asymptotically good algebraic structured codes, in particular, nested coset codes, and provide a set of sufficient conditions for the reconstruction of the function of the sources over a CQ-MAC. The proposed technique enables the decoder to recover the desired function without recovering the sources themselves. We further improve this by employing a coding scheme based on a classical superposition of algebraic structured codes and unstructured codes. This coding scheme allows exploiting the symmetric structure common amongst the sources and also leverage the asymmetries. We derive a new set of sufficient conditions that strictly enlarges the largest known set of sources whose function can be reconstructed over any given CQ-MAC, and identify examples demonstrating the same. We provide these conditions in terms of single-letter quantum information-theoretic quantities.

Synthetic Turbulence Generation for High-Order Scale-Resolving Simulations on Unstructured Grids

An extended version of the synthetic eddy method for generation of synthetic turbulence has been developed via a source term formulation and implemented in the open-source cross-platform solver PyFR. The method caters for the full space-dependent anisotropy of the target turbulent length scales, and it is agnostic of the space and time discretization of the underlying solver, which can be incompressible or compressible. Moreover, the method does not require each solution point to communicate with nearest neighbors; thus, it is well suited for modern, massively parallel, high-order unstructured codes which support mixed and possibly curved elements. The method has been applied to two test cases: incompressible plane channel flow at and compressible flow over an SD7003 aerofoil at , , and . The channel flow case was run on three topologically different meshes composed of hexahedra, prisms, and a combination of prisms and tetrahedra, respectively. Almost identical results have been obtained on the three meshes. Results also show that taking into account the anisotropy of the turbulent length scales can reduce the development length. For the SD7003 aerofoil case, the injection of synthetic turbulence improves agreement between numerical and experimental results.

PARAMETRIC STUDY OF PARALLEL BLOCK JACOBI / SOURCE ITERATION HYBRID METHODS IN 2-D CARTESIAN GEOMETRY AND CONSTRUCTION OF THE INTEGRAL TRANSPORT MATRIX METHOD MATRICES VIA GREEN’S FUNCTIONS

Parallel Block Jacobi (PBJ) [1] is an asynchronous spatial domain decomposition with application in solving the neutron transport equation due to its extendibility to massively parallel solution in unstructured spatial meshes (grids) without the use of the computationally complex and expensive sweeps required by the Source Iteration (SI) method in these applications. [2] However, PBJ iterative methods suffer a lack of iterative robustness in problems with optically thin cells, [1] which we have previously demonstrated to be a consequence of PBJ’s asynchronicity. To mitigate this effect, we have developed multiple PBJ / SI hybrid methods which employ a PBJ method (Parallel Block Jacobi - Integral Transport Matrix Method (PBJ-ITMM) or Inexact Parallel Block Jacobi (IPBJ)) along with SI. [3,4] In this work, we perform a parametric study to determine performance of numerous PBJ / SI hybrid methods as a function of multiple problem parameters. This parametric study reached 5 main conclusions: 1) our hybrid approach is more effective with PBJ-ITMM than with IPBJ, 2) for PBJ-ITMM, there is a hybrid method that mitigates the aforementioned iterative slowdown in optically thin cells without diminishing the method’s potential parallelism in unstructured grids, 3) this hybrid method is most effective in problems with large, continuous regions of very thin cells, 4) the best performing hybrid method consistently executes within a factor of ten slower than current state-of-the-art acceleration methods that are not efficiently extendable to the massively parallel regime, and 5) both PBJ-ITMM and IPBJ are observed to be viable approaches for our desired applications. In the pursuit of implementing PBJ-ITMM in unstructured grids, we conclude with a description of the Green’s Function ITMM Construction (GFIC) algorithm, which allows for the ITMM matrices to be constructed using the pre-existing SI sweep algorithm already present in unstructured grid SN transport codes.

Quasi Structured Codes for Multi-Terminal Communications

A new class of structured codes called quasi group codes (QGCs) is introduced. A QGC is a subset of a group code. In contrast with the group codes, QGCs are not closed under group addition. The parameters of the QGC can be chosen, such that the size of $\mathcal {C}+\mathcal {C}$ is equal to any number between $|\mathcal {C}|$ and $|\mathcal {C}|^{2}$ . We analyze the performance of a specific class of QGCs. This class of QGCs is constructed by assigning single-letter distributions to the indices of the codewords in a group code. Then, the QGC is defined as the set of codewords whose index is in the typical set corresponding to these single-letter distributions. The asymptotic performance limits of this class of QGCs are characterized using single-letter information quantities. Corresponding covering and packing bounds are derived. It is shown that the point-to-point channel capacity and optimal rate-distortion function are achievable using QGCs. Coding strategies based on QGCs are introduced for three fundamental multi-terminal problems: the Korner-Marton problem for modulo prime-power sums, computation over the multiple access channel (MAC), and MAC with distributed states. For each problem, a single-letter achievable rate-region is derived. It is shown, through examples, that the coding strategies improve upon the previous strategies based on the unstructured codes, linear codes, and group codes.

Achievable Rate Region for Three User Discrete Broadcast Channel Based on Coset Codes

We consider the problem of developing coding techniques and deriving achievable rate regions for discrete memoryless broadcast channels with three receivers (3-DBC). We begin by identifying a novel vector additive 3-DBC for which we characterize an upper bound on the the largest achievable rate region based on unstructured codes, henceforth referred to as $\pmb {\mathscr {U}}\mathcal {M}$ -region. We propose a coding technique based on coset codes that yield an achievable rate triple not contained within $\pmb {\mathscr {U}}\mathcal {M}$ -region. We generalize the proposed coding technique using a new ensemble of codes— partitioned coset codes (PCC)—containing both empirical and algebraic properties, and evaluate its performance to derive an achievable rate region for the general 3-DBC. The new elements in this derivation are binning and joint typicality encoding and decoding of statistically correlated PCCs. We validate the utility of this technique by identifying non-additive instances of 3-DBC for which the proposed coding techniques based on PCC yield strictly larger rates.

An Achievable Rate Region Based on Coset Codes for Multiple Access Channel With States

We prove that the ensemble the nested coset codes built on finite fields achieves the capacity of arbitrary discrete memoryless point-to-point channels. Exploiting it's algebraic structure, we develop a coding technique for communication over general discrete multiple access channel with channel state information distributed at the transmitters. We build an algebraic coding framework for this problem using the ensemble of Abelian group codes and thereby derive a new achievable rate region. We identify non-additive and non-symmteric examples for which the proposed achievable rate region is strictly larger than the one achievable using random unstructured codes.

Partial parallel encoding and algorithmic construction of non-binary structured IRA codes

The non-binary (NB) Irregular Repeat Accumulate (IRA) codes, as a subclass of NB LDPC codes, potentially have an excellent error-correcting performance. They are also known to provide linear complexity of encoding, but the basic encoding method with the serial rate-1 accumulator significantly limits the encoder throughput. Then the objective of the research presented in this paper is to develop an encoding method providing significantly increased throughput of an NB-IRA encoder altogether with a flexible code construction methods for the structured (S-NB-IRA) codes eligible for the proposed encoding method. For this purpose, we reformulate the classic encoding algorithm to fit into the partial parallel encoder architecture. We propose the S-NB-IRA encoder block diagram and show that its estimated throughput is proportional to the submatrix size of the parity check matrix, which guarantees a wide complexity-throughput tradeoff. Then, in order to facilitate the S-NB-IRA coding systems design, we present a computer search algorithm for the construction of good S-NB-IRA codes. The algorithm aims at optimizing the code graph topology along with selecting an appropriate non-binary elements in the parity check matrix. Numerical results show that the constructed S-NB-IRA codes significantly outperform the binary IRA and S-IRA codes, while their performance is similar to the best unstructured NB-LDPC codes.

Security gap analysis of some LDPC coded transmission schemes over the flat and fast fading Gaussian wire-tap channels

It is known that the error rate can be used as a measure of reliability and security over the wire-tap channel when practical, finite length codes are used for transmission, and the security gap is an error rate based metric able to jointly treat these two aspects. In this paper, we consider several low-density parity-check (LDPC) coded transmissions, which represent the state of the art for transmissions over the wire-tap channel and we assess and compare their security gap performance. We consider two kinds of wire-tap channels: the flat and the fast fading wire-tap channels with additive white Gaussian noise. As a reference, we use the progressive edge growth (PEG) algorithm for the design of unstructured LDPC codes and compare its performance with that of four approaches for designing structured LDPC codes. We analyze both systematic and non-systematic transmissions and show that some structured code design techniques are able to achieve comparable or even better performance than the PEG algorithm over the considered channels, while taking advantage of their simpler encoding and decoding procedures.

Inflow Turbulence Generation for Eddy-Resolving Simulations of Turbomachinery Flows

A simple variant of recycling and rescaling method to generate inflow turbulence using unstructured grid computational fluid dynamics (CFD) codes is presented. The method has been validated on large eddy simulation (LES) of spatially developing flat plate turbulent boundary layer. The proposed rescaling algorithm is based on the momentum thickness which is more robust and essentially obviates the need of finding the edge of the turbulent boundary layer in unstructured grid codes. Extension of this algorithm to hybrid Reynolds-Averaged Navier-Stokes (RANS) LES type of approaches and for wall-bounded turbomachinery flows is also discussed. Results from annular diffuser with different inflow boundary layer characteristics are presented as an example application to show the utility of such an algorithm.

Constrained Codes for Joint Energy and Information Transfer

In various wireless systems, such as sensor RFID networks and body area networks with implantable devices, the transmitted signals are simultaneously used both for information transmission and for energy transfer. In order to satisfy the conflicting requirements on information and energy transfer, this paper proposes the use of constrained run-length limited (RLL) codes in lieu of conventional unconstrained (i.e., random-like) capacity-achieving codes. The receiver's energy utilization requirements are modeled stochastically, and constraints are imposed on the probabilities of battery underflow and overflow at the receiver. It is demonstrated that the codewords' structure afforded by the use of constrained codes enables the transmission strategy to be better adjusted to the receiver's energy utilization pattern, as compared to classical unstructured codes. As a result, constrained codes allow a wider range of trade-offs between the rate of information transmission and the performance of energy transfer to be achieved.

On the implementation of low-dissipative Runge–Kutta projection methods for time dependent flows using OpenFOAM®

Open source computational fluid dynamics (CFD) codes provide suitable environments for implementation, testing and rapid dissemination of algorithms typically used for large-eddy simulations (LES) and direct numerical simulations (DNS). In particular, it is important to test low-dissipative algorithms in unstructured codes of industrial relevance. In the present paper, the implementation of incompressible, explicit Runge–Kutta (RK) based projection methods into the OpenFOAM® library is discussed. We search for low-dissipative alternatives to the second order time integration methods which are commonly used together with the standard pressure correction approach PISO (Pressure Implicit with Splitting of Operators) in many commercial and open source codes including OpenFOAM®. The practical implementation of the projection methods in OpenFOAM® is provided together with theory. The method is tested with the classical fourth order RK-method and the accelerated third order RK-method. Four numerical experiments are carried out in order to cross-validate the solvers and in order to investigate the drawbacks/benefits of the solution approaches. The test problems are: (1) 2d lid driven cavity flow at Re=2500, (2) DNS of 3d turbulent channel flow at Reτ=180, (3) LES of a 3d mixing layer, and (4) the 2d inviscid Taylor–Green vortex. The RK-methods are benchmarked against the standard OpenFOAM® LES/DNS solver based on the PISO pressure correction method. The results indicate that the RK projection methods provide low-dissipative alternatives to the PISO method. The turbulent test cases show also that the RK-methods have a good computational efficiency.

An Area-Efficient Reconfigurable LDPC Decoder with Conflict Resolution

Based on Turbo-Decoding Message-Passing (TDMP) and Normalized Min-Sum (NMS) algorithm, an area efficient LDPC decoder that supports both structured and unstructured LDPC codes is proposed in this paper. We introduce a solution to solve the memory access conflict problem caused by TDMP algorithm. We also arrange the main timing schedule carefully to handle the operations of our solution while avoiding much additional hardware consumption. To reduce the memory bits needed, the extrinsic message storing strategy is also optimized. Besides the extrinsic message recover and the accumulate operation are merged together. To verify our architecture, a LDPC decoder that supports both China Multimedia Mobile Broadcasting (CMMB) and Digital Terrestrial/ Television Multimedia Broadcasting (DTMB) standards is developed using SMIC 0.13µm standard CMOS process. The core area is 4.75mm2 and the maximum operating clock frequency is 200MHz. The estimated power consumption is 48.4mW at 25MHz for CMMB and 130.9mW at 50MHz for DTMB with 5 iterations and 1.2V supply.

Accumulate-Repeat-Delay-Partial-Delay Codes

Inspired by Accumulate-Repeat-Accumulate (ARA) codes, in this letter we propose a new channel coding scheme called Accumulate-Repeat-Delay-Partial-Delay (ARDPD) codes. Contrary to ARA codes, ARDPD codes simultaneously achieve good threshold and linear minimum distance. Based on EXIT for LDPC codes, we show that for maximum variable node degree 5, the threshold of ARDPD codes outperforms the best known unstructured irregular LDPC codes. Iterative decoding simulation results show that the proposed codes perform as predicted.

A Self-Adaptive Strategy for the Time Integration of Navier-Stokes Equations

An efficient self-adaptive strategy for the explicit time integration of Navier-Stokes equations is presented. Unlike the conventional explicit integration schemes, it is not based on a standard CFL condition. Instead, the eigenvalues of the dynamical system are analytically bounded and the linear stability domain of the time-integration scheme is adapted in order to maximize the time step. The method works independently of the underlying spatial mesh; therefore, it can be easily integrated into structured or unstructured codes. The additional computational cost is minimal, and a significant increase of the time step is achieved without losing accuracy. The effectiveness and robustness of the method are demonstrated on both a Cartesian staggered and an unstructured collocated formulation. In practice, CPU cost reductions up to more than 4 with respect to the conventional approach have been measured.

On Distributed Compression of Linear Functions

Distributed compression of a pair of Gaussian sources in which the goal is to reproduce a linear function of the sources at the decoder is considered. It has recently been noted that lattice codes can provide improved compression rates for this problem compared to conventional, unstructured codes. It is first shown that the state-of-the-art lattice scheme can be improved by including an additional linear binning stage. An outer bound on the rate-distortion region and a separate lower bound on the optimal sum rate are then established. The outer bound implies that for the special case of communicating the difference of two positively correlated Gaussian sources, the unimproved lattice scheme achieves within one bit of the rate region at any distortion level. The sum rate lower bound implies that unstructured codes achieve within one bit of the optimal sum rate whenever the weights of the two sources in the linear combination differ by more than a factor of two.

Performance of a pressure-based unstructured code and a multi-block structured code for heat transfer and fluid flow

This paper reports a multi-block unstructured method for incompressible flows and the performance comparison with a multi-block structured method. The unstructured collocated grid is composed of arbitrary cell shapes. Pressure and velocity are stored at cell centres; Rhie and Chow interpolation is used to prevent checker boarding. The SIMPLE algorithm is used for pressure-velocity coupling. The code is calibrated with benchmark cases using hexahedral and prism meshes, and is shown to perform very well for all cases considered. In addition, the performances of the structured and unstructured codes are compared.

Converting best manual practice into generic automatable strategies for unstructured mesh parallelisation

The manual effort required to convert sequential computational mechanics programs into a useful, scalable parallel form is considerable. Tools that can assist in the conversion process are clearly required. Computer aided parallelisation tools (CAPTools) have been developed to generate efficient parallel code for real world structured grid application codes such as Computational Fluid Dynamics. Automatable single-program multi-data (SPMD) overlapping domain decomposition (DD) techniques established for structured grid codes have been adapted by the authors to manually parallelise unstructured mesh applications. Inspector loops have been used to provide generic techniques for the run-time support necessary to extend the capabilities of CAPTools to automatic implementation of SPMD DD techniques in the parallelisation of unstructured mesh codes. Copyright © 1999 John Wiley & Sons, Ltd.

THE EFFICIENT CREATION OF SINGLE ASSIGNMENT FORMS FROM UNSTRUCTURED CODE*

Transformation to single assignment form is presented as a technique enabling the exploitation of fine-grain parallelism in programs. An efficient algorithm is presented for the creation of Single Assignment and Static Single Assignment code from unstructured FORTRAN codes, including programs with irreducible flow graphs. The algorithm transforms code directly without requiring conversion to flow graph form. The algorithm creates code of near optimal quality with respect to both the number of names and assignment statements added to the code. Experimental results show the degree of enlargement of storage and program length when creating single assignment code, and the containment of enlargement using name reclamation. Other results show the extent of improved parallelizalion using single assignment code.