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

In this letter, we introduce the computation-limited (comp-limited) signals, a communication capacity regime where the computational complexity of signal processing is the primary constraint for communication performance, overriding factors such as power or bandwidth. We present the Spectro-Computational (SC) analysis, a novel mathematical framework designed to enhance classic concepts of information theory –such as data rate, spectral efficiency, and capacity – to accommodate the computational complexity overhead of signal processing. We explore a specific Shannon regime where capacity is expected to increase indefinitely with channel resources. However, we identify conditions under which the time complexity overhead can cause capacity to decrease rather than increase, leading to the definition of the comp-limited signal regime. Furthermore, we provide examples of SC analysis and demonstrate that the Orthogonal Frequency Division Multiplexing (OFDM) waveform falls under the comp-limited regime unless the lower-bound computational complexity of the N-point Discrete Fourier Transform (DFT) problem verifies as
$\Omega (N)$
, which remains an open challenge in the theory of computation.