Compact steep-spectrum sources (CSSs) likely represent a population of young radio-loud active galactic nuclei (AGNs) and have been identified as gamma-ray emitting sources. We present a comprehensive analysis of their gamma-ray emission observed with Fermi/LAT and establish their broadband spectral energy distributions (SEDs). We derive their jet properties by the SED fits with a two-zone leptonic model for radiations from the compact core and large-scale extended region, and explore the possible signature of a unification picture of jet radiation among subclasses of AGNs. We show that the observed gamma-rays of CSSs with significant variability are contributed by the radiation of their compact cores via the inverse Compton process of the torus photons. The derived power-law distribution index of the radiating electrons is p_1~1.5-1.8, magnetic field strength is B~0.15-0.6 G, and Doppler boosting factor is delta~2.8-8.9. Assuming that the jet is composed of electron-positron pairs, the compact cores of CSSs are magnetized and have a high radiation efficiency, similar to that of flat spectrum radio quasars. The six CSSs on average have higher Eddington ratio and black hole mass than those non-GeV-detected CSSs, and they follow the correlation between the jet power in units of Eddington luminosity (P_jet/L_Edd) and Eddington ratio (R_Edd) with other sub-classes of AGNs, P_jet/L_Edd~R_Edd^0.52, indicating that R_Edd would be a key physical driver for the unification scheme of AGN jet radiation.
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