Modeling Energy-Time Trade-Offs in VLSI Computation

Bingham, Brad; Greenstreet, Mark R.

doi:10.1109/tc.2011.40

Cited by 4 publications

(3 citation statements)

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“…In [20], Bingham et al classify the tradeoffs between the "energy" complexity of parallel algorithms and "time" complexity for the problem of sorting, addition, and multiplication using a model similar to, but not the same as the model we use. In the grid model used by these authors, a circuit is composed of processing elements laid out on a grid, in which each element can perform an operation.…”

Section: Other Energy Models Of Computationmentioning

confidence: 99%

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Energy, Latency, and Reliability Tradeoffs in Coding Circuits

Blake

Kschischang

2019

IEEE Trans. Inform. Theory

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It is shown that fully-parallel encoding and decoding schemes with asymptotic block error probability that scales as O (f (n)) have Thompson energy that scales as Ω ln f (n)n . As well, it is shown that the number of clock cycles (denoted T (n)) required for any encoding or decoding scheme that reaches this bound must scale as T (n) ≥ ln f (n). Similar scaling results are extended to serialized computation. The Grover information-friction energy model is generalized to three dimensions and the optimal energy of encoding or decoding schemes with probability of block error Pe is shown to be at least Ω n (ln Pe (n)) 1 3 .. This approach is generalized to serial implementations. Recent work on the energy complexity of good decoding has focused largely on planar circuits. However, circuits implemented in three-dimensions exist [6], and so we generalize the recent information friction (or bit-meters) model introduced by Grover in [3] to circuits implemented in three-dimensions and extend the technique of Grover to show that, in terms of block length n, a bit-meters coding scheme in which block error probability is given by P e (n) has encoding/decoding energy that scales as Ω n (ln P e (n)) 1 3. We show how this approach can be generalized to an arbitrary number of dimensions. In Section II we discuss prior work, and in particular we discuss existing results on complexity lower bounds for different models of computation for different notions of "good" encoders and decoders. The main technical results of this work are in Section III, where we study the Thompson energy model, and in Section IV, where we study a multi-dimensional generalization of the Grover bit-meters model. In these sections we present lower bounds for decoders, as the derivation for encoding lower bounds is almost exactly the same. We provide an outline of the technique for encoder lower bounds in Section V. In Section VI we discuss limitations and weaknesses in the model used. In Section VII, we discuss other energy models of computation.

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Section: Other Energy Models Of Computationmentioning

confidence: 99%

“…Real circuits run at higher voltages can result in lower delay for each processing element but higher energy [21]. The model used by the authors in [20] captures some of this fundamental tradeoff. Note that our model assumes constant voltage.…”

Section: Other Energy Models Of Computationmentioning

confidence: 99%

Energy, Latency, and Reliability Tradeoffs in Coding Circuits

Blake

Kschischang

2019

IEEE Trans. Inform. Theory

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show abstract

“…Another class of work specifically deals with energy-time tradeoffs that arise form VLSI circuits (e.g., [22,3]). These explore the impact of tuning voltage and sizing (ET 2 ), which we did not address in this paper.…”

Section: Related Workmentioning

confidence: 99%