Codes over Matrix Rings for Space-Time Coded Modulations

It is known that, for transmission over quasi-static MIMO fading channels with n transmit antennas, diversity can be obtained by using an inner fully diverse space-time block code while coding gain, derived from the determinant criterion, comes from an appropriate outer code. When the inner code has a cyclic algebra structure over a number field, as for perfect space-time codes, an outer code can be designed via coset coding. More precisely, we take the quotient of the algebra by a two-sided ideal which leads to a finite alphabet for the outer code, with a cyclic algebra structure over a finite field or a finite ring. We show that the determinant criterion induces various metrics on the outer code, such as the Hamming and Bachoc distances. When n=2, partitioning the 2x2 Golden code by using an ideal above the prime 2 leads to consider codes over either M2(F_2) or M2(F_2[i]), both being non-commutative alphabets. Matrix rings of higher dimension, suitable for 3x3 and 4x4 perfect codes, give rise to more complex examples

Ideal codes over separable ring extensions

This paper investigates the application of the theoretical algebraic notion of a separable ring extension, in the realm of cyclic convolutional codes or, more generally, ideal codes. We work under very mild conditions, that cover all previously known as well as new non trivial examples. It is proved that ideal codes are direct summands as left ideals of the underlying non-commutative algebra, in analogy with cyclic block codes. This implies, in particular, that they are generated by an idempotent element. Hence, by using a suitable separability element, we design an efficient algorithm for computing one of such idempotents

MMSE Optimal Algebraic Space-Time Codes

Design of Space-Time Block Codes (STBCs) for Maximum Likelihood (ML) reception has been predominantly the main focus of researchers. However, the ML decoding complexity of STBCs becomes prohibitive large as the number of transmit and receive antennas increase. Hence it is natural to resort to a suboptimal reception technique like linear Minimum Mean Squared Error (MMSE) receiver. Barbarossa et al and Liu et al have independently derived necessary and sufficient conditions for a full rate linear STBC to be MMSE optimal, i.e achieve least Symbol Error Rate (SER). Motivated by this problem, certain existing high rate STBC constructions from crossed product algebras are identified to be MMSE optimal. Also, it is shown that a certain class of codes from cyclic division algebras which are special cases of crossed product algebras are MMSE optimal. Hence, these STBCs achieve least SER when MMSE reception is employed and are fully diverse when ML reception is employed.Comment: 5 pages, 1 figure, journal version to appear in IEEE Transactions on Wireless Communications. Conference version appeared in NCC 2007, IIT Kanpur, Indi

Computational Fluid Dynamics Methods Used in the Development of the Space Launch System Liftoff and Transition Lineloads Databases

The objective of this paper is to document the reasoning and trade studies that supported the selection of appropriate tools for constructing aerodynamic lineload databases for the Liftoff and Transition phases of flight for launch vehicles. These decisions were made amid the maturation of an evolving workflow for generating databases on variants of the Space Launch System launch vehicle, with most being based on results from brief developmental studies performed in response to specific, unforeseen challenges that were encountered in analyzing a given configuration. This report is intended to provide a summary of the results and the decision-making processes chronologically over the design cycles of various configurations, starting with isolated free-air bodies for the Block 1 Crew, then the Block 1B Crew and Cargo configurations, and most recently the Block 1B Crew configuration in proximity to the launch tower. The results from these analyses led to the selection of the CREATE-AV Kestrel flowsolver for simulating these problems. The need to accurately capture the expected leeward-wake flow field characteristics required the use of Delayed Detached Eddy Simulation (DDES) method, for which the vorticity magnitude was employed as the solution Adaptive Mesh Refinement (AMR) function over the off-body Cartesian grid region. In addition, the Spalart-Allmaras (SA) model is used to account for the flow turbulence effects

Code improvement and model validation for Asco-II Nuclear Power Plant model using a coupled 3D neutron kinetics/thermal-hydraulic code

This paper provides a Best Estimate validation calculation with a coupled thermal–hydraulic and 3D neutron kinetic model for Ascó-II Nuclear Power Plant. Common NRC codes have been used for its purpose. TRACE is the code used for the thermal–hydraulic system calculations; PARCS is the code used for the 3D neutron kinetics calculations. Cross section calculations were performed with the HELIOS lattice physics code, finally GenPMAXS was used to convert the cross section into the PARCS format. A simplified three dimensional 3D neutronics model of the Ascó II NPP is used as a core kinetics model. A 3D cylindrical thermal–hydraulic vessel plus 1D representation of the remainder of the full plant model is used as the thermal–hydraulic model. The transient selected to ensure the model validation is an actual 50% Loss of Load. This transient is characterized by space–time effects and was used to validate different thermal–hydraulic system models for the GET university group in the past. The scenario is also good to ensure the validation of a coupled 3D neutron kinetics code since it provides a transient situation between two stable regions at 100% and 50%. From the current code versions used, some source code modifications have been carried out in order to ensure the correct feedback between thermal–hydraulic and neutron kinetics code. In that sense, a dynamic control rod movement between TRACE and PARCS has been implemented. This is a complete control rod position feedback during transient scenarios. After all the work was performed, the important TH and NK time trend parameters were compared to the plant data and the comparison was reasonable with some discrepancy, thus the developed system models and the code modifications are robust enough to be used for future safety analysis. New coupled code capability has been tested and found as a required capability, when validating 3D NK–TH coupled calculations.Peer ReviewedPostprint (published version