Hardware Design of a 7-DFT Computing Circuit Operating on a Galois Field

Reed-Solomon (RS) codes are efficiently used to correct transmission errors in any communication system. Sensors used by Wireless Sensor Networks (WSN) and different portable devices need to communicate with low power consumptions, small delays and usually with little processing resources. According to the concept Software in Silicon, it is advantageous to use a hardware circuit instead of running a software algorithm in a processor in order to encode and decode data. The processing time can be significantly reduced applying this concept. In this letter, a battery-powered circuit that calculates the Discrete Fourier Transform (DFT) of a 7-symbol vector over the Galois Field GF (8) is designed. This transform is used for error-checking by the RS (7, 5) decoder. The 7-DFT circuit is implemented with GF (8) adders and multipliers that are also used for RS (7, 5) data encoder. The minimum bit period value allowed for data input and the minimum voltage required to operate correctly are investigated. 7-DFT circuit simulation and analysis are made using OrCAD/PSpice program. The simulation results are presented and compared.