Energy, Latency, and Reliability Tradeoffs in Coding Circuits

Abstract

Using the Thompson circuit complexity model, it is shown that fully parallel encoding and decoding schemes with asymptotic block error probability that scales as $O(f(n))$ have energy that scales as $\Omega (n{-\ln f(n)}^{1/2})$ . In addition, it is shown that the number of clock cycles [ $T(n)$ ] required for any encoding or decoding scheme that reaches this bound must scale as $T(n)\ge {-\ln f(n)}^{1/2}$ . Similar scaling results are extended to serialized computation. A similar approach is extended to three dimensions by generalizing the Grover information-friction energy model. Within this model, it is shown that encoding and decoding schemes with probability of block error $P_{\mathrm {e}}(n)$ consume at least $\Omega (n(-\ln P_{\mathrm {e}}(n))^{({1}/{3})})$ energy.