Computation-Limited Signals: A Channel Capacity Regime Constrained by Computational Complexity

In this letter, we introduce the computational-limited (comp-limited) signals, a communication capacity regime in which the signal time computational complexity overhead is the key constraint -- rather than power or bandwidth -- to the overall communication capacity. To relate capacity and time complexity, we propose a novel mathematical framework that builds on concepts of information theory and computational complexity. In particular, the algorithmic capacity stands for the ratio between the upper-bound number of bits modulated in a symbol and the lower-bound time complexity required to turn these bits into a communication symbol. By setting this ratio as function of the channel resources, we classify a given signal design as comp-limited if its algorithmic capacity nullifies as the channel resources grow. As a use-case, we show that an uncoded OFDM transmitter is comp-limited unless the lower-bound computational complexity of the N-point DFT problem verifies as $\Omega(N)$, which remains an open challenge in theoretical computer science.