We compute the escape of ionizing radiation from galaxies in the redshift interval z=4-10, i.e., during and after the epoch of reionization, using a high-resolution set of galaxies, formed in fully cosmological simulations. The simulations invoke early, energetic feedback, and the galaxies evolve into a realistic population at z=0. Our galaxies cover nearly four orders of magnitude in masses (10^{7.8}-10^{11.5}msun) and more than five orders in star formation rates (10^{-3.5}-10^{1.7}msunyr^{-1}), and we include an approximate treatment of dust absorption. We show that the source-averaged Lyman-limit escape fraction at z=10.4 is close to 80% declining monotonically with time as more massive objects build up at lower redshifts. Although the amount of dust absorption is uncertain to 1-1.5 dex, it is tightly correlated with metallicity; we find that dust is unlikely to significantly impact the observed UV output. These results support reionization by stellar radiation from low-luminosity dwarf galaxies and are also compatible with Lyman continuum observations and theoretical predictions at zsim3-4.
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