We present the results of the radio halo survey of 16 REXCESS southern clusters up to a redshift of 0.2 with the Australia Telescope Compact Array (ATCA) at 1.4 and 2.1 GHz. This cluster sample called the ATCA REXCESS Diffuse Emission Survey (ARDES) includes clusters in a wide range of X-ray luminosities and is morphologically unbiased. We find two diffuse radio sources in the clusters RXCJ2234.5−3744 (Abell 3888) and RXCJ0225.1−2928. The diffuse radio emission in RXCJ2234.5−3744 is a giant radio halo and the diffuse emission in RXCJ0225.1−2928 is a peculiar radio relic candidate. The radio halo has a spectral index of α = −1.48 ± 0.14 and the K-corrected P 1.4 is 1.9 ± 0.2 × 1024 W Hz−1. The properties of the detected halo are consistent with both the current P 1.4–L X and P 1.4–Y SZ correlations. The putative radio relic is located approximately 1 Mpc from the cluster in a filament and has a physical extent of 346 ± 20 kpc and a power of P 1.4 = 3.3 ± 0.8 × 1023 W Hz−1, which places it in the lower power region of currently known relics.