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Context. Ideally, one would like to know which type of core-collapse supernovae (SNe) is produced by different progenitors and what channels of stellar evolution lead to these progenitors. These links have to be very well known to use the observed frequency of different types of SN events for probing the star formation rate and massive star evolution in different types of galaxies. Aims. We investigate the link between luminous blue variables (LBVs) as SN progenitors and the appearance of episodic light curve modulations in the radio light curves of the SN event. Methods. We use the 20 M☉ and 25 M☉ models with rotation at solar metallicity, which are part of an extended grid of stellar models computed by the Geneva team. At their pre-SN stage, these two models have recently been shown to have spectra similar to those of LBV stars, and they possibly explode as Type IIb SNe. Based on the wind properties before the explosion, we derive the density structure of their circumstellar medium. This structure is used as input for computing the SN radio light curve. Results. We find that the 20 M☉ model shows radio light curves with episodic luminosity modulations similar to those observed in some Type IIb SNe. This occurs because the evolution of the 20 M☉ model terminates in a region of the HR diagram where radiative stellar winds present strong density variations, caused by the bistability limit. Ending its evolution in a zone of the HR diagram where no change of the mass-loss rates is expected, the 25 M☉ model presents no such modulations in its radio SN light curve. Conclusions. Our results reinforce the link between SN progenitors and LBV stars. We also confirm the existence of a physical mechanism for a single star to have episodic radio light curve modulations. In the case of the 25 M☉ progenitors, we do not obtain modulations in the radio light curve, but our models may miss some outbursting behavior in the late stages of massive stars. [ABSTRACT FROM AUTHOR]