A framework for coded computation

Rachlin, Eric; Savage, John E.

doi:10.1109/isit.2008.4595409

Cited by 10 publications

(6 citation statements)

References 15 publications

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“…classical results [34], [35], [37], [55] on applying error control coding to noisy computing, instead of computing after encoding, the proposed scheme combines encoding and computing into a joint module (see Fig. 2).…”

Section: A Encoded: a Multi-stage Error-resilient Computation Schemementioning

confidence: 99%

Computing Linear Transformations With Unreliable Components

Yang

Grover

Kar

2017

IEEE Trans. Inform. Theory

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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 use of a "voltagescaling" 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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Section: A Encoded: a Multi-stage Error-resilient Computation Schemementioning

confidence: 99%

Computing Linear Transformations With Unreliable Components

Yang

Grover

Kar

2017

IEEE Trans. Inform. Theory

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“…Similarly, recent research has investigated techniques for executing computation on encoded representations in order to obtain exact or approximate results in the presence of noise. These methods have been referred to in the research literature as coded computation [67,140]. One plausible direction for future research is to identify computing abstractions that unify the above techniques via new computational operators that execute on encoded representations.…”

Section: From Information and Coding Theory To Coded Computationmentioning

confidence: 99%

Exploiting Errors for Efficiency

et al. 2020

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When a computational task tolerates a relaxation of its specification or when an algorithm tolerates the effects of noise in its execution, hardware, system software, and programming language compilers or their runtime systems can trade deviations from correct behavior for lower resource usage. We present, for the first time, a synthesis of research results on computing systems that only make as many errors as their end-to-end applications can tolerate. The results span the disciplines of computer-aided design of circuits, digital system design, computer architecture, programming languages, operating systems, and information theory. Rather than over-provisioning the resources controlled by each of these layers of abstraction to avoid errors, it can be more efficient to exploit the masking of errors occurring at one layer and thereby prevent those errors from propagating to a higher layer. We demonstrate the potential benefits of end-to-end approaches using two illustrative examples. We introduce a formalization of terminology that allows us to present a coherent view across the techniques traditionally used by different research communities in their individual layer of focus. Using this formalization, we survey tradeoffs for individual layers of computing systems at the circuit, architecture, operating system, and programming language levels as well as fundamental information-theoretic limits to tradeoffs between resource usage and correctness.

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“…Recent references continue to extend the stream opened by Von Neumann's seminal paper [16], for example [24], [7], [12], [21] and [19]. These works identify theoretical limits or bounds (e.g., depth and size of circuits) but also propose frameworks to design reliable computations mainly thanks to gate redundancy.…”

Section: Introductionmentioning

confidence: 99%

On the capacity of noisy computations

Simon

2011

2011 IEEE Information Theory Workshop

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Abstract-This paper presents an analysis of the concept of capacity for noisy computations, i.e. algorithms implemented by unreliable computing devices (e.g. noisy Turing Machines). The capacity of a noisy computation is defined and justified by companion coding theorems. Under some constraints on the encoding process, capacity is the upper bound of input rates allowing reliable computation, i.e. decodability of noisy outputs into expected outputs. A model of noisy computation of a perfect function f thanks to an unreliable device F is given together with a model of reliable computation based on input encoding and output decoding. A coding lemma (extending the Feinstein's theorem to noisy computations), a joint source-computation coding theorem and its converse are proved. They apply if the input source, the function f , the noisy device F and the cascade f −1 F induce AMS and ergodic one-sided random processes.

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A framework for coded computation

Cited by 10 publications

References 15 publications

Computing Linear Transformations With Unreliable Components

Computing Linear Transformations With Unreliable Components

Exploiting Errors for Efficiency

On the capacity of noisy computations

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