Computing Linear Transformations With Unreliable Components

We consider the problem of computing a binary linear transformation when all circuit components are unreliable. Two models of unreliable components are considered: probabilistic errors and permanent errors. We introduce the "ENCODED" technique that ensures that the error probability of the...

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Vydáno v:IEEE transactions on information theory Ročník 63; číslo 6; s. 3729 - 3756
Hlavní autoři: Yaoqing Yang, Grover, Pulkit, Kar, Soummya
Médium: Journal Article
Jazyk:angličtina
Vydáno: New York IEEE 01.06.2017
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Témata:
Binary system
Codes
Coding
Computation
Computational modeling
Decoders
Decoding
Electric potential
Encoding
encoding and decoding errors
Energy consumption
energy of coding and decoding
Error probability
Error-correcting codes
Errors
Gates (circuits)
Linear transformations
Logic circuits
Logic gates
Lower bounds
Noise measurement
Reliability
Scaling
Studies
unreliable components
ISSN:0018-9448, 1557-9654
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Shrnutí:We consider the problem of computing a binary linear transformation when all circuit components are unreliable. Two models of unreliable components are considered: probabilistic errors and permanent errors. We introduce the "ENCODED" technique that ensures that the error probability of the computation of the linear transformation is kept bounded below a small constant independent of the size of the linear transformation even when all logic gates in the computation are noisy. By deriving a lower bound, we show that in some cases, the computational complexity of the ENCODED technique achieves the optimal scaling in error probability. Further, we examine the gain in energy-efficiency from the use of a "voltage-scaling" scheme, where gate-energy is reduced by lowering the supply voltage. We use a gate energy-reliability model to show that tuning gate-energy appropriately at different stages of the computation ("dynamic" voltage scaling), in conjunction with ENCODED, can lead to orders of magnitude energy-savings over the classical "uncoded" approach. Finally, we also examine the problem of computing a linear transformation when noiseless decoders can be used, providing upper and lower bounds to the problem.
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ISSN:0018-9448
1557-9654
DOI:10.1109/TIT.2017.2692244