Energy, Latency, and Reliability Tradeoffs in Coding Circuits

TL;DR

This paper investigates the fundamental tradeoffs between energy, latency, and reliability in coding circuits, establishing lower bounds on energy consumption and computation time for encoding and decoding schemes under various error and performance constraints.

Contribution

It derives new theoretical lower bounds on energy and latency for coding circuits, extending models to three dimensions and considering different error probabilities.

Findings

Energy scales as at least  extbackslash ext{Omega}(\u221a{ ext{ln}f(n)} n)

Number of clock cycles T(n) scales as at least  extbackslash ext{Omega}( extbackslash ext{sqrt}( ext{ln}f(n)))

Optimal energy for schemes with block error probability P_e scales as  extbackslash ext{Omega}(n ( ext{ln} P_e(n))^{1/3})

Abstract

It is shown that fully-parallel encoding and decoding schemes with asymptotic block error probability that scales as $O\left(f\left(n\right)\right)$ have Thompson energy that scales as $\Omega\left(\sqrt{\ln f\left(n\right)}n\right)$. As well, it is shown that the number of clock cycles (denoted $T\left(n\right)$) required for any encoding or decoding scheme that reaches this bound must scale as $T\left(n\right)\ge\sqrt{\ln f\left(n\right)}$. 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 $P_\mathrm{e}$ is shown to be at least $\Omega\left(n\left(\ln P_{\mathrm{e}}\left(n\right)\right)^{\frac{1}{3}}\right)$.