17–20 Jun 2018
Leuven, Belgium
Europe/Brussels timezone
On-site registration will be possible on Monday, June 18, 08:30 to 10:00

Radiation Tolerant Stochastic Fourier-Transformation Implementation

19 Jun 2018, 14:00
2h
IMEC (Leuven, Belgium)

IMEC

Leuven, Belgium

Kapeldreef 75 3001 Heverlee Belgium
Poster Custom cell-, circuit-, and system design of ICs for space applications Poster

Speaker

Mr Kris Niederkleine (Institute of Electrodynamics and Microelectronics - Universität Bremen)

Description

The Fourier-Transformation is used in numerous applications. The Fast Fourier-Transform (FFT) algorithm allows an efficient hardware implementation. For space applications, radiation (R) is one of the most significant factors to be taken into account, when the reliability of electronic equipment is in the focus. Long-term usage and large temperature variations are present for electronic devices in satellites as well. On circuit level for terrestrial applications the keyword summing up these effects is PVTA, which is the short form for process variations (P), supply voltage variations (V), temperature (T) and aging (A). All these effects (PVTAR) cause bit errors in digital circuits leading to wrong calculations. Since charged particles have the major influence on the accuracy, we will limit ourselves to Single Event Effects (SEE) in the following. Within a fixed-point (FI) representation, such errors have of course the highest impact on the MSB. On the contrary, stochastic computation (SxC) uses bit streams and stores the information in the frequency of a logical 1 or the ratio of logical 1's to 0's. This way all bits have the identical significance and the outlined impacts are expected to have less severe effects on the reliable calculation. This will be demonstrated for the Fourier-Transform. Considering two bit flips, the first one from a 0 to a 1 and the second one vice versa, the actual impact on the FI representation depends on the positions in the digital word, while for the SxC case the errors impacts cancel each other out. A simulation environment is set up to compare both approaches: on the one hand a double precision, scaled fixed-point FFT and on the other hand a stochastic DFT using the two line bipolar representation. Evaluations on the performance are based on the accuracy of the calculated spectrums for a given complex input signal with 64 samples. The FI representation uses 64 bits on the real and 64 bits on the imaginary part for each sample. The SxC system encodes the input signal with four streams (real / imaginary + positive / negative) with 1024 bits each. Both systems are analyzed for different scenarios. Each sample in each case is calculated 100 times and its respective mean is used to compare the systems with each other. In the first place, when no PVTAR effects are present, the FI system can show its higher accuracy and precision compared to the SxC approach; both setups are related to the built in FFT function. The absolute error of the mean of the FI setup is in the order of $10^{-16}$. This value needs to be compared to the order of $10^{-3}$, which was achieved for the SXC approach. Both results prove the afore mentioned expectations and offer good spectral analysis, high accuracy and good precision. Assuming additional scenarios with increased linear energy transfer (LET), process variations, temperature of e.g. 120°C and a supply voltage of 0.8V both setups will need to show its performance. The normalized mean squared error (NMSE) and the signal to noise ratio (SNR) show the PVTAR tolerant characteristic of the SxC approach. Secondly, the aspect of computational complexity is discussed. The stochastic approach has an overall factor of 32 more bits to be stored and processed for calculations. One has to take into account, the more bits are used, the more errors will be present. It is known, that a common N point FFT requires operations of order $O(N log_2 N)$. In more detail the stochastic approach can be reduced to 16N parallel multiplications (logical AND gates) and one large adder (multiplexer with 16 inputs).

Summary

The SXC system shows great potential for accurate calculations in extreme environments like space. The current approach works with 32 times more bits than the FI setup and requires a stochastic computational processing logic. The total amount of bit errors is increased by the same factor. Nevertheless simultaneous bit flips from 0 to 1 and 1 to 0 cancel each other out. However, only by requiring simple logical gates, very high parallelism possibilities and a higher system clock can be realized.

Primary authors

Mr Kris Niederkleine (Institute of Electrodynamics and Microelectronics - Universität Bremen) Mr Nils Hülsmeier (Universität Bremen) Mr Theodor Hillebrand (Institute of Elecrodynamics and Microelectronics - Universität Bremen)

Co-authors

Dr Jochen Rust (Institute of Elecrodynamics and Microelectronics - Universität Bremen) Prof. Steffen Paul (Institute of Elecrodynamics and Microelectronics - Universität Bremen)

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