  We present a radio survey carried out with the Australia Telescope Compact
Array. A motivation for the survey was to make a complete inventory of the
diffuse emission components as a step towards a study of the cosmic evolution
in radio source structure and the contribution from radio-mode feedback on
galaxy evolution. The Australia Telescope low-brightness survey (ATLBS) at 1388
MHz covers 8.42 sq deg of the sky in an observing mode designed to yield images
with exceptional surface brightness sensitivity and low confusion. The ATLBS
radio images, made with 0.08 mJy/beam rms noise and 50" beam, detect a total of
1094 sources with peak flux exceeding 0.4 mJy/beam. The ATLBS source counts
were corrected for blending, noise bias, resolution, and primary beam
attenuation; the normalized differential source counts are consistent with no
upturn down to 0.6 mJy. The percentage integrated polarization Pi_0 was
computed after corrections for the polarization bias in integrated polarized
intensity; Pi_0 shows an increasing trend with decreasing flux density.
Simultaneous visibility measurements made with longer baselines yielded images,
with 5" beam, of compact components in sources detected in the survey. The
observations provide a measurement of the complexity and diffuse emission
associated with mJy and sub-mJy radio sources. 10% of the ATLBS sources have
more than half of their flux density in extended emission and the fractional
flux in diffuse components does not appear to vary with flux density, although
the percentage of sources that have complex structure increases with flux
density. The observations are consistent with a transition in the nature of
extended radio sources from FR-II radio source morphology, which dominates the
mJy population, to FR-I structure at sub-mJy flux density. (Abridged)
