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

TL;DR

This paper introduces the concept of computational-limited signals where computational complexity, not power or bandwidth, constrains communication capacity, and develops a new analysis framework to understand this regime.

Contribution

It proposes the Spectro-Computational analysis framework that extends classical information theory to include computational complexity constraints in communication systems.

Findings

Capacity can decrease with increasing channel resources under certain complexity conditions.

OFDM waveform is potentially comp-limited unless DFT complexity is proven to be (N).

Identifies conditions where computational overhead impacts capacity growth.

Abstract

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. We present the Spectro-Computational (SC) analysis, a novel mathematical framework that enhances classic concepts of information theory -- such as throughput, spectral efficiency and capacity -- to account for the signal processing computational complexity overhead. We consider a specific Shannon regime under which capacity is expected to get arbitrarily large as channel resources grow. Under that regime, we identify the conditions under which the time complexity overhead causes capacity to decrease rather than increasing, thereby creating the case for the comp-limited regime. We also provide examples of the SC analysis and show the OFDM waveform is comp-limited unless the lower-bound computational complexity of the $N$-point DFT problem verifies as $\Omega(N)$, which remains an open challenge.