Computing a Group of Polynomials over a Galois Field in FPGA Architecture

For the most extensive range of tasks, such as real-time data processing in intelligent transport systems, etc., advanced computer-based techniques are required. They include field-programmable gate arrays (FPGAs). This paper proposes a method of pre-calculating the hardware complexity of computing a group of polynomial functions depending on the number of input variables of the said functions, based on the microchips of FPGAs. These assessments are reduced for a group of polynomial functions due to computing the common values of elementary polynomials. Implementation is performed using similar software IP-cores adapted to the architecture of user-programmable logic arrays. The architecture of FPGAs includes lookup tables and D flip-flops. This circumstance ensures that the pipelined data processing provides the highest operating speed of a device, which implements the group of polynomial functions defined over a Galois field, independently of the number of variables of the said functions. A group of polynomial functions is computed based on common variables. Therefore, the input/output blocks of FPGAs are not a significant limiting factor for the hardware complexity estimates. Estimates obtained in using the method proposed allow evaluating the amount of the reconfigurable resources of FPGAs, required for implementing a group of polynomial functions defined over a Galois field. This refers to both the existing FPGAs and promising ones that have not yet been implemented.

PROJECT DESIGN FOR COMPUTER ARCHITECTURE PRACTICAL SESSIONS BASED ON FIELD-PROGRAMMABLE GATE ARRAY

Field-programmable logic arrays are often used in courses on computer architecture. The student must describe the processor with the external components necessary for its operation in the specified HDL (hardware description language) language according to the provided specification during a certain number of projects. The weakness of this approach is that the basis of such projects is a processor of one specific architecture, so the lecturer faces the issue of individualization of projects. This article proposes a solution based on dedicated processors instead of one programmable processor of a specific architecture. It’s shown here that the issue of project individualization is easier solvable in the proposed way, and it does not deviate from the theory of computer architecture, because the programmable processor is a generalization of a dedicated processor. The article describes project design ideas based on dedicated processors and gives some examples. Represented different instance than was applied during practical sessions of Computer Architecture that are held at the Department of Electronic Systems within VILNIUS TECH, i.e. certain modifications, and additions were applied.

RESEARCH OF PECULIARITIES OF ERROR DETECTION ON THE OUTPUTS OF PROGRAMMABLE LOGIC INTEGRATED CIRCUITS WITH FUNCTIONAL CONTROL BASED ON MODULAR CODES WITH SUMMATION

The article provides examples of the use of programmable logic integrated circuits in various industries. Possible faults in FPGA blocks and their difference from faults in programmable logic arrays are described. Particular attention is paid to the failures of the LUT element. Features of the organization of technical diagnostics systems operating in the operating mode of the objects of diagnostics for combinational logic devices, implemented on the basis of programmable logic integrated circuits are described. Using the example of modular summation codes, it is shown that the known approaches to organizing such systems for devices implemented on a valve basis can be directly applied to devices of the type under consideration. Since malfunctions in the form of errors are recorded, and not the malfunctions themselves, the approaches to the organization of diagnostic systems are universal. It also provides a comparative characteristic of modular sum codes depending on the code module. A code has been proposed that will detect all faults in the example under study.

Application of Generalized Reed–Muller Expression for Development of Non-Binary Circuits

Semiconductor devices and binary information technology reach their limits set by the atomic size of miniaturization, calculation speed, and the fundamental principle of energy dissipation per bit processing. Therefore, new technologies in logic design and mathematical approaches must be investigated. Application of multiple-valued logic (MVL) in logic design allows developing gates and circuits with more than two stable states. This enables packing an unprecedented high-density of information. Based on this idea, a new technique of the programmable logic arrays (PLA) construction based on MVL units is considered. The unique aspect of this technique is the application of recurrent generalized Reed–Muller expression (GRME) for MVL function representation. The recurrent procedure for this expression’s construction is considered and applied in the PLA development. The proposed structure of PLA consists of two blocks that are memory and logic block. In this paper, we also consider the possibility to use the ferroelectrics for the implementation of cells of the memory block of PLA. The development of gates with multi-stable states is possible by the ferroelectrics ability to pin the polarization as a sequence of stable states.

Thermal-aware Output Polarity Selection Based on And-Inverter Graph Manipulation

Background: Output polarity of the sub-function is generally considered to reduce the area and power of a circuit at the two-level realization. Along with area and power, the power-density is also one of the significant parameter which needs to be consider, because power-density directly converges to circuit temperature. More than 50% of the modern day integrated circuits are damaged due to excessive overheating. Methods: This work demonstrates the impact of efficient power density based logic synthesis (in the form of suitable polarity selection of sub-function of Programmable Logic Arrays (PLAs) for its multilevel realization) for the reduction of temperature. Two-level PLA optimization using output polarity selection is considered first and compared with other existing techniques and then And-Invert Graphs (AIG) based multi-level realization has been considered to overcome the redundant solution generated in two-level synthesis. AIG nodes and associated power dissipation can be reduced by rewriting, refactoring and balancing technique. Reduction of nodes leads to the reduction of the area but on the contrary increases power and power density of the circuit. A meta-heuristic search approach i.e., Nondominated Sorting Genetic Algorithm-II (NSGA-II) is proposed to select the suitable output polarity of PLA sub-functions for its optimal realization. Results: Best power density based solution saves up to 8.29% power density compared to ‘espresso – dopo’ based solutions. Around 9.57% saving in area and 9.67% saving in power (switching activity) are obtained with respect to ‘espresso’ based solution using NSGA-II. Conclusion: Suitable output polarity realized circuit is converted into multi-level AIG structure and synthesized to overcome the redundant solution at the two-level circuit. It is observed that with the increase in power density, the temperature of a particular circuit is also increases.