The relation of particle transport of relativistic particles in plasmas with high-amplitude isotropic sub-Larmor-scale magnetic turbulence to the spectra of radiation simultaneously produced by these particles is investigated both analytically and numerically. We have found that in the asymptotic regime of very small particle deflections, the pitch-angle diffusion coefficient is directly related to the spectrum of the emitted radiation. Moreover, this spectrum provides much information about the statistical properties of the underlying magnetic turbulence. The transition from small- to large-scale jitter to synchrotron radiation regimes as a function of turbulence properties has also been explored. These results can readily be used to diagnose laboratory and astrophysical plasmas.